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How to convert Mathematica notebook to jupyter notebooks and vice versa?
https://community.wolfram.com/groups//m/t/2562963
Hi,
Is there a way to convert Mathematica notebooks to jupyter notebooks and vice versa?
If you are writing lecture notes using jupyter notebooks is a better option. However, in doing calculations Mathematica notebook is superior. If there is a simple conversion between two of them it would be very useful.
virtual mind
20220703T13:03:40Z

Unusually large coeff in Conditional Logit
https://community.wolfram.com/groups//m/t/2627027
I run a conditional logit model with only one categorical variable with 6 levels. This a 1:5 matched sample. One of the coefficeints from this model is very large. What could be the reason behind this?
Pam G
20220929T21:53:41Z

Books on machine learning based on Wolfram Language?
https://community.wolfram.com/groups//m/t/1277274
Hi, I noticed that there are a lot of books and courses on machine learning with Python,R,Matlab.
Are there any good books based on Wolfram Language?
Thx.
l van Veen
20180201T20:28:18Z

Is the atlas 2 addon no longer supported by anyone?
https://community.wolfram.com/groups//m/t/1303742
Is `atlas 2` addon to *Mathematica* supported by anybody now? Links to it at wolfram.com have gone dead, and the website of the publisher, digiarea.com, also has vanished.
Murray Eisenberg
20180317T20:12:04Z

How to calculate the entropy of a discrete probability distribution?
https://community.wolfram.com/groups//m/t/2625975
For example, the Poisson distribution has (credit to [Wikipedia][1]) PMF
![enter image description here][2]
and entropy
![Poisson distribution entropy][3]
Is there a simple (textbook) way to derive that entropy from the distribution?
In general, I need to derive the entropy for many discrete probability distributions given a PMF that is determined by combinatorial analysis. (It seems Mathematica calls it the PDF for discrete distributions?)
I suspect that it's actually not trivial, based on [this][4] paper, but I'm very far from being an expert, which is why I'm asking.
Thanks, cheers.
Jeremy
[1]: https://en.wikipedia.org/wiki/Poisson_distribution
[2]: https://community.wolfram.com//c/portal/getImageAttachment?filename=PoissonPMF.svg&userId=2625938
[3]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Poissonentropy.svg&userId=2625938
[4]: https://ieeexplore.ieee.org/abstract/document/8648470
Jeremy Murphy
20220929T07:13:12Z

Inference of signaling mechanism from cellular responses to multiple cues
https://community.wolfram.com/groups//m/t/2626642
&[Wolfram Notebook][1]
[1]: https://www.wolframcloud.com/obj/bec913cf57084856812896d8812f9152
Soutick Saha
20220929T19:59:33Z

Precision of numerical series value in WolframAlpha
https://community.wolfram.com/groups//m/t/2625887
[Error](https://www.wolframalpha.com/input?i=sum%28%281%29%5Ek%2F%28k%5E2%2B2*k%2B2%29%2Ck%2C0%2Cinf%29%3B)
It is gives
$$\sum_{k=0}^{\infty}\frac{(1)^k}{k^2+2k+2}\approx 0.363998$$
but exact value:
$$\sum_{k=0}^{\infty}\frac{(1)^k}{k^2+2k+2}=\frac{1}{2}\frac{\pi}{e^{\pi}e^{\pi}}\approx 0.3639854725089334$$
Yuri Artamonov
20220929T07:29:08Z

Markdown to Mathematica converter
https://community.wolfram.com/groups//m/t/2625639
&[Wolfram Notebook][1]
[1]: https://www.wolframcloud.com/obj/f71bffb184f242c6abcd4f3388ebf9c2
Anton Antonov
20220928T13:58:35Z

[CBTW2022] Comunicação  Conferência Brasileira de Tecnologia Wolfram 2022
https://community.wolfram.com/groups//m/t/2559136
**Save the date: Saturday, November 5, 2022**
Communication  Brazilian Technology Conference Wolfram 2022 (CBTW2022)
To answer questions, share and learn more about the "Brazilian Conference on Technology Wolfram 2022" and hackathon send your message here ...
Conference date: November 5, 2022 (Saturday) from 9:00 pm to 5:00 pm (GMT 3  São Paulo, SP, Brazil) at Universidade Presbiteriana Mackenzie
Online HACKATON starting: Monday, October 31 to Monday, November, 7th, 2022, online
Website and more details coming soon...

FOR PORTUGUESE READERS:

**Comunicação  Conferência Brasileira de Tecnologia Wolfram 2022 (CBTW2022)**
Para tirar dúvidas, compartilhar e saber mais sobre a "Conferência Brasileira de Tecnologia Wolfram 2022" e **hackathon** mande sua mensagem aqui...
Data da conferência: Dia 5 de novembro de 2022 (Sábado) das 09:00 as 17:00 em São Paulo, SP, Brasil, na Universidade Presbiteriana Mackenzie
Hackathon online: Dia 31 de oubutro até a 7 de novembro de 2022
Website e mais detalhes em breve...
Dicas para inspiração:
 Para se inspirar use o [Wolfram Language Hackathon Project Generator][3]
 Ou veja os aplicativos disponíveis no [Product Hunt][4] projetos podem ser prototipados e extendidos com a tecnologia Wolfram de forma muito produtiva
 Expore um problema usando [ciências dos dados][5].
 Veja os projetos vencedores do ano passado [2021][6] e [2020][7]:
[1]: https://www.wolfram.com/events/virtualconferencebr/2021/
[2]: https://www.wolfram.com/events/virtualconferencebr/2021/hackathon/
[3]: http://hackathon.guru/
[4]: https://www.producthunt.com/
[5]: https://www.wolfram.com/wolframu/multiparadigmdatascience/
[6]: https://www.wolfram.com/events/virtualconferencebr/2021/hackathon/
[7]: https://www.wolfram.com/events/virtualconferencebr/2020/hackathon/
Daniel Carvalho
20220627T18:50:03Z

Penrose pattern and rhombic enneacontahedron
https://community.wolfram.com/groups//m/t/2626142
![enter image description here][1]
&[Wolfram Notebook][2]
[1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Penrosepatternandrhombicenneacontahedron.png&userId=20103
[2]: https://www.wolframcloud.com/obj/10b455dd581341f990df9b7c9a6d1337
Sandor Kabai
20220929T09:37:28Z

Make a working USB camera discoverable by Mathematica on macbook?
https://community.wolfram.com/groups//m/t/1362109
I'm trying to use Mathematica to automate capture and analysis of USB camera images attached to a microscope. I believe the camera to be correctly installed because 1) The camera successfully captures images using the microscope's own software on my macbook pro through the USB directly to the camera and 2) the System Information >> Hardware >> USB >> USB2.0 Camera shows the camera recognized by the macbook pro's system setup.
However, calls to FindDevices[] discover no camera but the iSight builtin camera. (I'm familiar with Mathematica's help files on this and related functions at http://reference.wolfram.com/language/ref/device/Camera.html).
Any advice to make it discoverable?
System Info:
 Mathematica 11
 Computer: Macbook Pro
 OS 10.10.5
 AmScope MU1400 USB Camera (connected to USB2.0 port on the macbook pro)
Thanks, All.
Stephen
Stephen Guimond
20180624T02:01:34Z

Manipulate sliders don't seem to be working?
https://community.wolfram.com/groups//m/t/2626355
I am trying to plot a function that has the form T=f(r,t,s(t)) in the domain (0,0.05). If I input the numerical values of t and s(t), and then plot T as a function of r, Mathematica gives me the graph of T as a function of r.
Plot[T, {r, 0, 0.05}]
But when I try to use the Manipulate function to see how the plot of T as a function of r varies for different numerical values of t and s(t),
Manipulate[Plot[T, {r, 0, R}],
{{t, 15(*h*)*60*60}, 0, 24(*h*)*60*60},
{{s, 0.0225}, 0, 0.05}]
I get an output with sliders for t and s(t), but moving the sliders do not change the output. What am I missing here?
Here is the notebook:
&[Wolfram Notebook][1]
[1]: https://www.wolframcloud.com/obj/384d40b8f3c94ef680cb0d91dbc0c8a0
Safi Ahmed
20220929T13:31:58Z

Error in integrating Bessel function combined with exponential term
https://community.wolfram.com/groups//m/t/2625348
I've been trying to solve a similar integral equation to the following :
$$\int_{\infty }^{+\infty} \int_{0}^{r*}\frac{1}{t}\int_{0}^{t}\left ( \sum_{n=0}^{\infty} J_{0}(\frac{\beta_{n}}{d}r)e^{\frac{\beta_{n}^{2}Dt}{d^{2}}} \right )dtdr\left ( \frac{1}{\sqrt{4\pi Dt}}e^{\frac{u^{2}}{4Dt}} \right )du$$
Here, $J_{0}$ is a Bessel function of order 1 and $\beta_{n}$ is $n^{th}$ root of Bessel function of order 1; D, and d are constants.
I tried solving the first integral manually, got the following solution to the first integral as:
$$\int_{\infty }^{+\infty} \int_{0}^{r*}\frac{1}{t}\sum_{n=0}^{\infty} J_{0}(\frac{\beta_{n}}{d}r)\frac{(1e^{\frac{\beta_{n}^{2}Dt}{d}})}{\frac{\beta_{n}^{2}D}{d}}dr\left ( \frac{1}{\sqrt{4\pi Dt}}e^{\frac{u^{2}}{4Dt}} \right )du$$
For second integral since only the Bessel function is changing with respect to $dr$, we could consider the rest as constant for second integration.
Now, for second integral I used two methods using Wolfram and by hand using table of integral.
##1st Method:
I directly tried to solve in Wolfram, using the Integrate function. But, I faced some error in solving the third integral. By applying Integrate[L, {u, Infinity, Infinity},
Assumptions > v > 0 && x >= 0 && d > 0 && k >= 0 && t >= 0], where L represent the function of interest.
Please refer the attached notebook for the same.
##2nd Method:
I tried solving the second integral using the table of integral. Where, definite integration of Bessel function is directly expressed as:
$$\int_{0}^{a}J_{v} (x)dx = 2\sum_{k=0}^{\infty}J_{v+2k+1}(a)\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:[Re\: v > 1] $$
Which would be valid in my case since, v = 0. Using the above expression for solving the second integral.
Now, for third integral, I again used Wolfram, and faced same issue for solving third integral. Please refer to the attached notebook for the same.
Please let me know the reason for the problem and how I could rectify it to get the desired solution. I would really appreciate your help. Thank you.
Kathan Joshi
20220928T10:36:30Z

Extracting a single Voronoi cell from a Mesh
https://community.wolfram.com/groups//m/t/2626187
I saw that in the new version of Mathematica they finally introduced the possibility to compute a Voronoi mesh for a 3D set of points. What I need, however, is just one cell from the Voronoi mesh as a polyhedron object. Is there a function that would explode a 3D mesh into a set of polyhedra or, alternatively, return a polyhedron in the mesh that contains a specific point? I am looking for a simple way to plot a Brillouin zone for an arbitrary lattice, and I was surprised to find no examples and almost no information in the help.
Dmytro Inosov
20220929T09:54:03Z

Cannot export gzip directly to network path in Windows
https://community.wolfram.com/groups//m/t/2625994
Exporting a file as *.gz works for local folders and mapped network drives but not for a full network address, without the "GZIP" everything works.
I first thought is was the way i defined my own Export MIME type, but for normal jpeg export it also fails.
al files are created as they should expect the *.gz with fill network paths.
![enter image description here][1]
Does anyone have an idea how to solve this.
In[3]:= << QMRITools`
In[4]:= im = ExampleData[{"TestImage", "Mandrill"}];
dat = RandomReal[{0, 1}, {100, 100, 100}];
vox = {1, 1, 1};
fol1 = "Z:\\F_DataAnalysis\\Development";(*mapped network drive*)
fol2 = "D:\\Werk";(*local drive*)
fol3 = "\\\\xxx\\F_DataAnalysis\\Development";(*full network path*)
In[10]:= DirectoryQ /@ {fol1, fol2, fol3}
Out[10]= {True, True, True}
In[11]:= Export[FileNameJoin[{fol1, "Mandrill1.jpg"}], im, {"JPEG"}]
Export[FileNameJoin[{fol2, "Mandrill2.jpg"}], im, {"JPEG"}]
Export[FileNameJoin[{fol3, "Mandrill3.jpg"}], im, {"JPEG"}]
Export[FileNameJoin[{fol1, "Mandrill1.jpg.gz"}], im, {"GZIP",
"JPEG"}]
Export[FileNameJoin[{fol2, "Mandrill2.jpg.gz"}], im, {"GZIP",
"JPEG"}]
Export[FileNameJoin[{fol3, "Mandrill3.jpg.gz"}], im, {"GZIP", "JPEG"}]
Out[11]= "Z:\\F_DataAnalysis\\Development\\Mandrill1.jpg"
Out[12]= "D:\\Werk\\Mandrill2.jpg"
Out[13]= \
"\\\xxx\\F_DataAnalysis\\Development\\Mandrill3.jpg"
Out[14]= "Z:\\F_DataAnalysis\\Development\\Mandrill1.jpg.gz"
Out[15]= "D:\\Werk\\Mandrill2.jpg.gz"
During evaluation of In[11]:= Export::fmterr: Invalid GZIP format.
Out[16]= \
"\\\\xxx\\F_DataAnalysis\\Development\\Mandrill3.jpg.gz"
In[17]:= Export[
FileNameJoin[{fol1, "test1.nii"}], {dat,
vox}, {"Nii", {"Data", "VoxelSize"}}]
Export[FileNameJoin[{fol2, "test2.nii"}], {dat,
vox}, {"Nii", {"Data", "VoxelSize"}}]
Export[FileNameJoin[{fol3, "test3.nii"}], {dat,
vox}, {"Nii", {"Data", "VoxelSize"}}]
Export[FileNameJoin[{fol1, "test1.nii.gz"}], {dat, vox}, {"GZIP",
"Nii", {"Data", "VoxelSize"}}]
Export[FileNameJoin[{fol2, "test2.nii.gz"}], {dat, vox}, {"GZIP",
"Nii", {"Data", "VoxelSize"}}]
Export[FileNameJoin[{fol3, "test3.nii.gz"}], {dat, vox}, {"GZIP",
"Nii", {"Data", "VoxelSize"}}]
Out[17]= "Z:\\F_DataAnalysis\\Development\\test1.nii"
Out[18]= "D:\\Werk\\test2.nii"
Out[19]= \
"\\\\xxx\\F_DataAnalysis\\Development\\test3.nii"
Out[20]= "Z:\\F_DataAnalysis\\Development\\test1.nii.gz"
Out[21]= "D:\\Werk\\test2.nii.gz"
During evaluation of In[17]:= Export::fmterr: Invalid GZIP format.
Out[22]= \
"\\\\xxx\\F_DataAnalysis\\Development\\test3.nii.gz"
[1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=export.png&userId=1332602
Martijn Froeling
20220929T11:46:54Z

Errors in Plot after setting global CompilationOptions
https://community.wolfram.com/groups//m/t/2626257
I stumbled upon a strange error while working with Mathematica 12.3.1
I tried to set global settings for the "CompilationOptions" of "Compile" using the function SetOptions.
SetOptions[Compile,CompilationOptions>{
"InlineCompiledFunctions" > True,
"InlineExternalDefinitions" > True
}];
The options influence the compilation of "Compile" as expected, however a different error message started to appear as i went on.
Suddenly when i tried using the regular "Plot"function in a simple example of:
Plot[x,{x,0,1}]
the following error messages appeared:
 Plot::colvl: The value {InlineCompiledFunctions>True,InlineExternalDefinitions>True} of the option CompileOptimizations is not 0, 1, 2, All, or None.
 None::colvl: The value {InlineCompiledFunctions>True,InlineExternalDefinitions>True} of the option CompileOptimizations is not 0, 1, 2, All, or None.
How does this influence each other and can i fix the error message without having to manually set the options in every Compile function?
Michael Haring
20220929T06:39:21Z

Take real or complex entries of eigensystem or separate them as a whole
https://community.wolfram.com/groups//m/t/2625202
I want to do the conditional assignment of variables as shown below:
{val, vec}={{((1 + I)/Sqrt[2]), (1 + I)/Sqrt[2], ((1  I)/Sqrt[2]), (1  I)/
Sqrt[2]}, {{(1  I)/Sqrt[2], I, (1 + I)/Sqrt[2],
1}, {((1  I)/Sqrt[2]), I, ((1 + I)/Sqrt[2]), 1}, {(1 + I)/Sqrt[
2], I, (1  I)/Sqrt[2],
1}, {((1 + I)/Sqrt[2]), I, ((1  I)/Sqrt[2]), 1}}};
If [(Select[{val, vec}//Transpose, Element[#,Reals]&]//Length)>0,
{rval,rvec}=Select[{val, vec}//Transpose, Element[#,Reals]&]
]
But I didn't come up with a more concise method to achieve this goal. Any hints will be appreciated.
Regards,
Zhao
Hongyi Zhao
20220928T00:40:04Z

How can I display a dataset that has only 1 row horizontally?
https://community.wolfram.com/groups//m/t/2625030
I have noticed that if one has a Dataset with multiple rows, the dataset is displayes with the keys horizontally at the top and the rows are displayed one under the other vertically.
However, if the dataset only has 1 row, the keys are displayed vertically to the left, in column fashion with the values to the right of the keys.
Is there any way to have a single row Dataset to be shown horizontally?
Henrick Jeanty
20220928T05:32:41Z

WolframAlpha on the Microsoft Store not working anymore
https://community.wolfram.com/groups//m/t/2625061
Hi, It seems the Windows App of the WolframAlpha is not working anymore. ink to the app: https://apps.microsoft.com/store/detail/wolframalpha/9WZDNCRDMZKP?hl=enus&gl=us
I only get "Error: Something went wrong while trying to load that information. Please try again."
I am on doing simple things like 3+1 on the attached file. I'm not even asking it anything complicated. So I assume there are some connection issues, or WA is not supporting this anymore. This is a paid app, and yet there is no contact or any support on the Microsoft Store. I have tried uninstalling and reinstalling. I am using the latest update, which is version 1.0.5.682. Not sure what else I can do here. It has been working for a while, but now it seems dead. Is this a deprecated app?
James H
20220928T07:45:18Z

⭐ [R&DL] Wolfram R&D Developers on LIVE Stream
https://community.wolfram.com/groups//m/t/2593151
**Join us for the unique Wolfram R&D livestreams on [Twitch][1] and [YouTube][2] led by our developers! Share this with your friends and colleagues:** https://wolfr.am/RDlive
You will see **LIVE** stream indicators on these channels on the dates listed below. The live streams provide tutorials and behind the scenes look at Mathematica and the Wolfram Language directly from developers.
Join our livestreams every Wednesday at 11 AM CST and interact with developers who work on data science, machine learning, image processing, visualization, geometry, and other areas.

⭕ **UPCOMING** EVENTS
 Oct. 5th  A Computational Exploration of Alcoholic Beverages by [Isabel Skidmore][3]
 Oct 12th  Tree Representation for XML, JSON and symbolic expressions by [Ian Ford][4]
 Oct 19th  Behind the scenes at the Wolfram Technology Conference 2022

✅ **PAST** EVENTS
 Sept. 28th  [Q&A with Visualization & Graphics Developers][16]
 Sept. 14th  [Paclet Development][5]
 Sept. 7th  [Overview of Chemistry][6]
 Aug. 24th  [Dive into Visualization][7]
 Aug. 17th  [Latest in Graphics & Shaders][8]
 Aug. 10th  [What's new in Calculus & Algebra][9]
> **What are your interests? Leave a comment here on this post to share your favorite topic suggestions for our livestreams.**
Follow us on out live broadcasting channels [Twitch][10] and [YouTube][11] and for the uptodate announcements on our social media: [Facebook][12] and [Twitter][13].
[![enter image description here][14]][15]
[1]: https://www.twitch.tv/wolfram
[2]: https://www.youtube.com/channel/UCJekgf6k62CQHdENWf2NgAQ
[3]: https://community.wolfram.com/web/isabels
[4]: https://community.wolfram.com/web/ianf
[5]: https://community.wolfram.com/groups//m/t/2616863
[6]: https://community.wolfram.com/groups//m/t/2613617
[7]: https://community.wolfram.com/groups//m/t/2605432
[8]: https://community.wolfram.com/groups//m/t/2600997
[9]: https://community.wolfram.com/groups//m/t/2596451
[10]: https://www.twitch.tv/wolfram
[11]: https://www.youtube.com/channel/UCJekgf6k62CQHdENWf2NgAQ
[12]: https://www.facebook.com/wolframresearch
[13]: https://twitter.com/WolframResearch
[14]: https://community.wolfram.com//c/portal/getImageAttachment?filename=RDAnno_image.png&userId=20103
[15]: https://www.wolfram.com/mathematica/coreareas/
[16]: https://community.wolfram.com/groups//m/t/2618033
Charles Pooh
20220805T21:37:19Z

The eigenvalue problem for the elastic cable loaded with a mass point
https://community.wolfram.com/groups//m/t/2625796
&[Wolfram Notebook][1]
[1]: https://www.wolframcloud.com/obj/20235e4c367243d3afbafad368d637f5
Markus Wenin
20220928T18:03:10Z

Building an isomatrix
https://community.wolfram.com/groups//m/t/2626011
I have a very basic problem that I cannot figure out. I have a (fairly simple) expression (attached) that I want to evaluate on two variables (within predetermined ranges), k and sigma.
I'm trying to ascertain the domain of k/sigma indifference, i.e., the combinations of k and sigma lead to the same value for BSPut.
Thank you.&[Wolfram Notebook][1]
[1]: https://www.wolframcloud.com/obj/17da950fe5ec4721be7cbd01b7941b95
Carlos Abadi
20220928T18:18:21Z

[R&DL] Q&A with Visualization and Graphics Developers
https://community.wolfram.com/groups//m/t/2618033
We will be hosting the first ever [Wolfram R&D Live][1] **Q&A session** on Twitch and YouTube featuring developers from Visualization and Graphics! Join us Wednesday SEP 28 at 11 AM CST.
[Brett Champion][2] (Visualization), [Yuzhu Lu][3] (Graphics  Desktop) and [Matthew Adams][4] (Cloud) will be the developers answering questions. You can help us narrow down topics interesting to you by discussing them on this thread.
> **What are some topics that you would like to see them discuss? Please comment below.**
Here are some examples of topics:
 Animated plots
 Exporting Graphics3D objects to 3DS, OBJ, DAE, STL
 Highlighting in GeoGraphPlot
 RGBColor, GrayColor and Hue
 Legends in different types of graphs
Add your topic suggestions and questions below!
Find out more about Wolfram Visualization [here][5].
[![enter image description here][6]][5]
[1]: https://wolfr.am/RDlive
[2]: https://community.wolfram.com/web/brettc
[3]: https://community.wolfram.com/web/yuzhu
[4]: https://community.wolfram.com/web/matthewa
[5]: https://www.wolfram.com/language/coreareas/visualization/
[6]: https://community.wolfram.com//c/portal/getImageAttachment?filename=sadf34vaewdf.jpg&userId=11733
Keren Garcia
20220916T16:08:23Z

Issues with accessing Wolfram certified course
https://community.wolfram.com/groups//m/t/2624056
Hello
Since this morning, I cannot access the course "[An Elementary Introduction to the Wolfram Language][1]" and the Wolfram Certification page. I have tried other beginner level course and they all shows "Oops!
The page you're looking for can't be found." I am wondering if it is a technical issue with the website.
Thank you for your help.
[1]: https://www.wolfram.com/wolframu/courses/wolframlanguage/anelementaryintroductiontothewolframlanguage/
Kaiyang Zeng
20220926T21:37:56Z

What is the difference between Local kernel and Linksnooper kernel?
https://community.wolfram.com/groups//m/t/2624674
What is the difference between Local kernel and Linksnooper kernel
as there are those two kernels, I was wondering what if one has some differences?
ISLAM farag
20220927T19:31:41Z

Display how units are converted
https://community.wolfram.com/groups//m/t/2624984
Hi
I use quantities and UnitConvert in Mathematica. To better understand what happens in the conversions, I would love if Mathematica can somehow display the proces.
A simple example to clarify what I mean could be
UnitConvert[Quantity[1000, "Revolutions"/"Minutes"],
"Revolutions"/"Seconds"]
Does Mathematica have some kind of builtin function/command that displays the conversion in detail? As a student, I would expect this kind of feature could help me understand unit conversions deeper.
Thanks in advance.
Jak SD
20220928T08:33:37Z

Rhombic enneacontahedron explained
https://community.wolfram.com/groups//m/t/2625496
![enter image description here][1]
&[Wolfram Notebook][2]
[1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=RS_book_Oldal_068.jpg&userId=20103
[2]: https://www.wolframcloud.com/obj/37df28aa6a754a69b6b57ddf0c215dc2
Sandor Kabai
20220928T12:58:43Z

Universal Equilibrium in Quantum Light Theory
https://community.wolfram.com/groups//m/t/2625512
![Newtonian Equilibrium in Light][2]
**Quantum Light Theory** has been completely based on **Newton's Third Law of Equilibrium**:
**In Quantum Light Theory:**
The **Electric** Force densities only interact with the **Electric** Force Densities
The **Magnetic** Force densities only interact with the **Magnetic** Force Densities
The **Gravitational** Force Densities only interact with a group of Force Densities:
**Inertia** Force Densities
Energy **Gradient** Force Densities (Radiation Pressure)
**Gravitational** Force Densities
&[Wolfram Notebook][1]
[1]: https://www.wolframcloud.com/obj/8b0ff0c633674eb7a35271d39b3c3bcb
[2]: https://community.wolfram.com//c/portal/getImageAttachment?filename=BlackHole4.jpg&userId=2576650
Wim Vegt
20220928T13:32:55Z

Solving a triple integral with assumptions
https://community.wolfram.com/groups//m/t/2625098
In a physics problem, I came across the following triple integral:
exp = (r Sin[\[Alpha]] (Cos[\[Theta]] Cos[\[Phi]] Sin[\[Alpha]] 
Cos[\[Alpha]] Sin[\[Theta]]))/(
4 (2 + Sqrt[2]) \[Pi]^2 (p^2 + r^2 
2 p r Cos[\[Alpha]] Cos[\[Theta]] 
2 p r Cos[\[Phi]] Sin[\[Alpha]] Sin[\[Theta]])^(3/2));
Assuming[0 < r < 1 && 0 < \[Alpha] < \[Pi]/4 && \[Alpha] != \[Theta] &&
0 < \[Theta] < \[Pi]/4 && 0 < \[Phi] < 2 \[Pi], \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(0\), \(2 \[Pi]\)]\(
\*SubsuperscriptBox[\(\[Integral]\), \(0\), \(\[Pi]/4\)]\(
\*SubsuperscriptBox[\(\[Integral]\), \(0\), \(1\)]exp\
\*SuperscriptBox[\(p\), \(2\)] Sin[\[Alpha]]\ \[DifferentialD]p \
\[DifferentialD]\[Alpha] \[DifferentialD]\[Phi]\)\)\)]
I tried to perform each integration separately, but got no result. Is there any transformation or procedure, that I am not aware of, to accomplish this task?
There is also an attached file.
Grateful,
Sinval
sinval santos
20220928T12:12:07Z

Clear all the values associated with a subscripted variable
https://community.wolfram.com/groups//m/t/2623355
See my following code snippet:
In[764]:= xTM
N[x] =.
xTM
Out[764]= {{Subscript[x, 1, 1], Subscript[x, 1, 2], Subscript[x, 1,
3]}, {Subscript[x, 2, 1], Subscript[x, 2, 2], Subscript[x, 2,
3]}, {Subscript[x, 3, 1], Subscript[x, 3, 2], Subscript[x, 3, 3]}}
During evaluation of In[764]:= Unset::norep: Assignment on x for N[x,{MachinePrecision,MachinePrecision}] not found.
Out[765]= $Failed
Out[766]= {{Subscript[x, 1, 1], Subscript[x, 1, 2], Subscript[x, 1,
3]}, {Subscript[x, 2, 1], Subscript[x, 2, 2], Subscript[x, 2,
3]}, {Subscript[x, 3, 1], Subscript[x, 3, 2], Subscript[x, 3, 3]}}
I want to clear all the values associated with the subscripted variable, in this case, x. But as you can see, my method failed to do the trick. Any tips for achieving this goal?
Regards,
Zhao
Hongyi Zhao
20220926T08:22:31Z

Does anyone else have a problem with 13.1 on a Mac running Big Sur?
https://community.wolfram.com/groups//m/t/2625073
I am running 13.1 on a MacBook under Big Sur 11.7. On two occasions, the software crashes on launch with error code 814. This error persisted for several days, and it seemed to be resolved by an update for Safari, but this may have been a coincidence.
Wolfram Tech support suggests that there is no fix for 13.1, which implies that the product is potentially unusable for an extended period of time.
David Mackay
20220928T07:46:51Z

Try to beat these MRB constant records!
https://community.wolfram.com/groups//m/t/366628
CMRB is the MRB constant.
POSTED BY: Marvin Ray Burns,
![enter image description here][1]![enter image description here][2]
'
WITH COAUTHORS: Giuseppe Peano in the
![enter image description here][3]
(FORMULATION of CMRB MATHEMATICS)

'
Issac Newton in the
![enter image description here][4]
(PRINCIPLES OF CMRB MATHEMATICS)

'
Gottfried Wilhelm Leibniz in the
![enter image description here][5] fandom.com/
(REPORTS OF CMRB SCHOLARS)

'
and most significantly,
Euclid in the
![enter image description here][6] important7.com/
ELEMENTS OF CMRB GEOMETRY
=========================
(assuming a different form of the parallel postulate)
.
When asked for an image of that matches everything contained in this discussion, Google's AI gave the following cartoon credited to V.J Motto.
![enter image description here][7]
**An Easter egg for you to find below:**
> (In another reality, I invented CMRB and then discovered many of its
> qualities.)


![enter image description here][8]

Proof of Leibniz criterion, summoned is proven here:
We will prove that both the partial sums $S_{2m+1}=\sum_{n=1}^{2m+1} (1)^{n1} a_n$ with odd number of terms, and $S_{2m}=\sum_{n=1}^{2m} (1)^{n1} a_n$ with even number of terms, converge to the same number ''L''. Thus the usual partial sum $S_k=\sum_{n=1}^k (1)^{n1} a_n$ also converges to ''L''.
The odd partial sums decrease monotonically:
$$ S_{2(m+1)+1}=S_{2m+1}a_{2m+2}+a_{2m+3} \leq S_{2m+1} $$
while the even partial sums increase monotonically:
$$ S_{2(m+1)}=S_{2m}+a_{2m+1}a_{2m+2} \geq S_{2m} $$
both because a<sub>n</sub> decreases monotonically with n.
Moreover, since a<sub>n</sub> are positive, $ S_{2m+1}S_{2m}=a_{2m+1} \geq 0 $. Thus we can collect these facts to form the following suggestive inequality:
$ a_1  a_2 = S_2 \leq S_{2m} \leq S_{2m+1} \leq S_1 = a_1. $
Now, note that a<sub>1</sub> &minus; a<sub>2</sub> is a lower bound of the monotonically decreasing sequence S<sub>2m+1</sub>, the [monotone convergence theorem][9] then implies that this sequence converges as ''m'' approaches infinity. Similarly, the sequence of even partial sum converges too.
Finally, they must converge to the same number because
$$ \lim_{m\to\infty}(S_{2m+1}S_{2m})=\lim_{m\to\infty}a_{2m+1}=0. $$
Call the limit ''L'', then the [monotone convergence theorem][10] also tells us extra information that
$$ S_{2m} \leq L \leq S_{2m+1} $$
for any ''m''. This means the partial sums of an alternating series also "alternates" above and below the final limit. More precisely, when there is an odd (even) number of terms, i.e. the last term is a plus (minus) term, then the partial sum is above (below) the final limit.


![enter image description here][11]
![enter image description here][12]
The first of the above plots has a point at about n=40 where the alternating series fails to alternate. The second has that quality at the limit of n as n goes to infinity (showing the series converges for x0=1. The third has no point with that quality. Together they show that x0=1 is the only value for which the series converges. See this Wolfram Demonstration:
&[Wolfram Notebook][13]
I had the following conversation with a math professor.
![enter image description here][14]
![enter image description here][15]



Content of the first post, as of September 2, 2022
==========================
1. Q and A,
2. My claim to the MRB constant (CMRB), or a case of calculus déjà vu?
3. What exactly is it?
4. Where is it found?
5. How it all began,
6. The why and what of the **C**<sub>*MRB*</sub> Records,
7. **C**<sub>*MRB*</sub> and its applications.
The following contents of the first post have been moved. Use CNRL+F to locate.
1. CNRTL+F "RealWorld, and beyond, Applications".
2. CNRL+F "MeijerG Representation for" **C**<sub>*MRB*</sub>,
3. CNRL+F "the Laplace transform analogy to" CMRB.
4. **C**<sub>*MRB*</sub> CNRL+F "formulas and identities",
5. CNRL+F "Primary Proof 1",
6. CNRL+F "Primary Proof 2",
7. CNRL+F "Primary Proof 3",
8. CNRL+F "The relationship between" **C**<sub>*MRB*</sub> and its integrated analog,
9. The MRB constant supercomputer 0
Second post:

The following might help anyone serious about breaking my record.
Third post

The following email Crandall sent me before he died might be helpful for anyone checking their results.
Fourth post

Perhaps some of these speed records will be easier to beat.
Many more interesting posts

...including the MRB constant supercomputers 1 and 2.
...including records of computing the MRB constant from Crandall's eta derivative formulas.
...including all the methods used to compute **C**<sub>*MRB*</sub> and their efficiency.
...including the dispersion of the 09th decimals in **C**<sub>*MRB*</sub> decimal expansions.
...including the convergence rate of 3 major different forms of **C**<sub>*MRB*</sub>.
...including complete documentation of all multimilliondigit records with many highlights.
...including arbitrarily close approximation formulas for **C**<sub>*MRB*</sub>.
...including efficient programs to compute the integrated analog (MKB) of **C**<sub>*MRB*</sub>.
...including a recent discovery that could help in verifying digital expansions of the integrated analog (MKB) of **C**<sub>*MRB*</sub>.
...including CNRL+F "the Laplace transform analogy to" **C**<sub>*MRB*</sub>.
...including CNRTL+F "RealWorld, and beyond, Applications".
... including an overview of all **C**<sub>*MRB*</sub> speed records, by platform.
...including a few attempts at a spectacular 7 million digits using Mathematica.
...including an inquiry for a closed form for CMRB.
...including question as to how normal is CMRB.


Q&A
===
Q:
What can you expect from reading about **C**<sub>*MRB*</sub> and its record computations?
A:
> As you see, the war treated me kindly enough, in spite of the heavy
> gunfire, to allow me to get away from it all and take this walk in the
> land of your ideas.
— Karl Schwarzschild (1915), “Letter to Einstein”, Dec 22
Q:
Can you calculate more digits of the MRB constant?
A:
> With the availability of highspeed electronic computers, it is now
> quite convenient to devise statistical experiments for the purpose of
> estimating certain mathematical constants and functions.
Copyright © 1966 ACM
(Association for Computing Machinery)
New York, NY, United States
Q:
How can you compute them?
A:
> The value of $\pi$ has engaged the attention of many mathematicians and
> calculators from the time of Archimedes to the present day, and has
> been computed from so many different formulae, that a complete account
> of its calculation would almost amount to a history of mathematics.
 James Glaisher (18481928)
Q:
Why should you do it?
A:
> While it is never safe to affirm that the future of Physical Science
> has no marvels in store even more astonishing than those of the past,
> it seems probable that most of the grand underlying principles have
> been firmly established and that further advances are to be sought
> chiefly in the rigorous application of these principles to all the
> phenomena which come under our notice. It is here that the science of
> measurement shows its importance — where quantitative work is more to
> be desired than qualitative work. An eminent physicist remarked that
> the future truths of physical science are to be looked for in the
> sixth place of decimals.
Albert A. Michelson (1894)
Q:
Why are those digits there?
A:
>There is nothing without a reason.
Read more at: https://minimalistquotes.com/gottfriedleibnizquote229585/



This discussion is not crass bragging; it is an attempt by this amateur to share his discoveries with the greatest audience possible.
Amateurs have been known to make a few significant discoveries as discussed in ![enter image description here][16] [here.][17]
This amateur has made his best attempts at proving his discoveries and has often asked for help in doing so. Great thanks to all of those who offered a hand! If I've failed to give you credit for any of your suggestions, let me know and I will correct that issue!
As I went more and more public with my discoveries, I made several attempts to see what portion of them was original. What I concluded from these investigations was that the only original thought I had was the obstinacy to think anything meaningful can be found in the infinite sum shown next. ![CMRB sum][18]
Nonetheless, it is possible that someone might have a claim to this thought to whom I have not given proper credit. If that is you I apologize. The last thing we need is another calculus war, this time for a constant. However, if your thought was published after mine, as Newton said concerning Leibniz's claim to calculus, “To take away the Right of the first inventor, and divide it between him and that other would be an Act of Injustice.” [Sir Isaac Newton, The Correspondence of Isaac Newton, 7 v., edited by H. W. Turnbull, J. F. Scott, A. Rupert Hall, and Laura Tilling, Cambridge University Press, 1959–1977: VI, p. 455]
Here is what Google says abut the MRB constant as of August 8, 2022 at
https://www.google.com/search?q=who+discovered+the+%22MRB+constant%22
![enter image description here][19]
![If you see this instead of an image, reload the page.][20]![enter image description here][21]
(the calculus war for CMRB)

CREDIT
https://soundcloud.com/cmrb/homersimpsonvspetergriffincmrb
'
From Wikipedia, the free encyclopedia
'
The calculus controversy (German: Prioritätsstreit, "priority dispute") was an argument between the mathematicians Isaac Newton and Gottfried Wilhelm Leibniz over who had first invented calculus.
![enter image description here][22]
(Newton's notation as published in PRINCIPIS MATHEMATICA [PRINCIPLES OF MATHEMATICS])
![enter image description here][23]
( Leibniz's notation as published in the scholarly journal, Acta Eruditorum [Reports of Scholars])
Whether or not we divide the credit between the two pioneers,
![Wikipedia][24] said one thing that distinguishes their finds from the work of their antecedents:
> Newton came to calculus as part of his investigations in physics and
> geometry. He viewed calculus as the scientific description of the
> generation of motion and magnitudes. In comparison, Leibniz focused on
> the tangent problem and came to believe that calculus was a
> metaphysical explanation of the change. Importantly, the core of their
> insight was the formalization of the inverse properties between the
> integral and the differential of a function. This insight had been
> anticipated by their predecessors, but they were the first to conceive
> calculus as a system in which new rhetoric and descriptive terms were
> created.[24] Their unique discoveries lay not only in their
> imagination but also in their ability to synthesize the insights
> around them into a universal algorithmic process, thereby forming a
> new mathematical system.
Like as Newton and Leibniz created a *new system* from the elaborate, confusing structure
designed and built by their predecessors, my forerunners studied series for centuries leading to a
labyrinth of sums, and then I created a "new scheme" for the CMRB "realities" to escape it!

![it][25] is defined in all of the following places, the majority of which attribute to my curiosity.
 [ค่าคงที่ลุ่มแม่น้ำโขง][26] (in Thai);
 [ar.wikipedia.org/wiki/][27] (In Arabic);
 [Constante MRB][28] (in French);
 [Constanta MRB  MRB constant][29] (in Romanian);
 http://constant.one/ ;
 Crandall, R. E. "The MRB Constant." §7.5 in [Algorithmic Reflections: Selected Works][30]. PSI Press, pp. 2829, 2012,ISBN10 : 193563819X ISBN13: 9781935638193;
 Crandall, R. E. "[Unified Algorithms for Polylogarithm, LSeries, and Zeta Variants][31]." 2012;
 [https://enacademic.com/][32], Wikipedia, Mathematical constant;
 Encyclopedia of Mathematics (Series #94);
 [Engineering Tools][33] of the Iran Civil Center, (translated from Persian), an international community dedicated to the construction industry, ISSN: 1735–2614;
 Etymologie CA Kanada Zahlen" (in German). [etymologie.info][34];
 Finch, S. R. [Mathematical Constants][35], Cambridge, England:
Cambridge University Press, p. 450, 2003, ISBN13: 9780521818056, ISBN10: 0521818052;
 Finch's original essay on [Iterated Exponential Constants][36];
 Finch, Steven & Wimp, Jet. (2004). Mathematical constants. The Mathematical Intelligencer. 26. 7074. 10.1007/BF02985660;
 Journal of Mathematics Research; [Vol. 11, No. 6; December 2019][37] ISSN 19169795 EISSN 19169809 Published by Canadian Center of Science and Education;
 Mauro Fiorentina’s [math notes][38] (in Italian);
 MATHAR, RICHARD J. "NUMERICAL EVALUATION OF THE OSCILLATORY INTEGRAL OVER exp(iπx) x^(1/x) BETWEEN 1 AND INFINITY" [(PDF)][39]. arxiv. Cornell University;
 [Mathematical Constants and Sequences][40] a selection compiled by
Stanislav Sýkora, Extra Byte, Castano Primo, Italy. Stan’s Library,
ISSN 24211230, Vol.II;
 ["Matematıksel Sabıtler"][41] (in Turkish). Türk Biyofizik Derneği;
 [MathWorld Encyclopedia][42];
 [MRB常数][43] (in Chinese);
 [mrb constantとは][44] 意味・読み方・使い方 ( in Japanese);
 [MRB константа][45] (in Bulgarian);
 [OEIS Encyclopedia (The MRB constant);][46]
 Patuloy ang MRB  [MRB constant][47] (in Filipino)
 [Plouffe's Inverter;][48]
 the LACM [Inverse Symbolic Calculator;][49]
 The OnLine Encyclopedia of Integer Sequences® (OEIS®) as
[A037077][50], Notices Am. Math. Soc. 50 (2003), no. 8, 912–915, MR 1992789 (2004f:11151);
 [Wikipedia Encyclopedia][51].
![enter image description here][52]


![CMRB][53]
## = B =##
![enter image description here][54]
and from Richard Crandall in 2012 courtesy of Apple Computer's advanced computational group we have the following computational scheme using equivalent sums of the zeta variant, Dirichlet eta:
> ![enter image description here][55]
> ![enter image description here][56]
Eta denotes the kth derivative of the Dirichlet eta function of m and 0 respectively,
The c<sub>j</sub>'s are found by the code,
N[ Table[Sum[(1)^j Binomial[k, j] j^(k  j), {j, 1, k}], {k, 1, 10}]]
(* {1., 1., 2., 9., 4., 95., 414., 49., 10088., 55521.}*)
> ...
> ![enter image description here][57]![enter image description here][58]
Crandall's first "B" is proven below by Gottfried Helms and it is proven more rigorously, considering the conditionally convergent sum,![CMRB sum][59] afterward. Then the formula (44) is a Taylor expansion of eta(s) around s = 0.
> ![n^(1/n)1][60]
At ![enter image description here][61] [here,][62] we have the following explanation.
> Even though one has cause to be a little bit wary around formal
> rearrangements of conditionally convergent sums (see the
[Riemann series theorem][63]), it's not very difficult to validate the formal
> manipulation of Helms. The idea is to cordon off a big chunk of the
> infinite double summation (all the terms from the second column on)
> that we know is *absolutely* convergent, which we are then free to
> rearrange with impunity. (Most relevantly for our purposes here, see
> pages 8085 of this [document.][64]
> culminating with the Fubini theorem which is essentially the
> manipulation Helms is using.)
>
> So, by definition the MRB constant $B$ is the conditionally convergent
> sum $\sum_{n \geq 1} (1)^n (n^{1/n}  1)$. Put $a_n = (1)^n (n^{1/n}=  1)$,
> so $B = \sum_{n \geq 1} a_n.$
>
> Looking at the first column, put $b_n = (1)^n \frac{\log(n)}{n}.$
>
> so $\eta^{(1)}(1) = \sum_{n \geq 1}> b_n$
>
> as a conditionally convergent series.
>
> We have
>
> $$B  \eta^{(1)} = \sum_{n \geq 1} a_n  b_n = \sum_{n \geq 1} \sum_{m
> \geq 2} (1)^n \frac{(\log n)^m}{n^m m!}$$
>
> (The first equation is an elementary limit statement that says if
> $\sum_{n \geq 1} a_n$ converges and $\sum_{n \geq 1} b_n$ converges,
> then also $\sum_{n \geq 1} a_n  b_n$ converges and $\sum_{n \geq 1}
> a_n  \sum_{n \geq 1} b_n = \sum_{n \geq 1} a_n  b_n$. It doesn't at
> all matter whether the convergence of either series is conditional or
> absolute.)
>
> So now we check the *absolute* convergence of the righthand side,
> i.e., that $\sum_{n \geq 1} \sum_{m \geq 2} \frac{(\log n)^m}{n^m m!}$
> converges. (Remember what this means in the case of infinite sums of
> *positive* terms: it means that there is a number $K$ such that every finite partial sum $S$ is bounded above by $K$; the least such upper
> bound will be the number that the infinite sum converges to.) So take
> any such finite partial sum $S$, and rearrange its terms so that the
> terms in the $m = 2$ column come first, then the terms in the $m = 3$
> column, and so on. An upper bound for the terms of $S$ in the $m = 2$
> column is $\frac{\zeta^{(2)}(2)}{2!}$. Put that one aside.
>
> For the $m = 3$ column, an upper bound is $\sum_{n \geq 2} \frac{(\log
> n)^3}{n^3 3!}$ (we drop the $n=1$ term which is $0$). By calculus we
> have $\log n \leq n^{1/2}$ for all $n \geq 2$, so this has upper bound
> $\frac1{3!} \sum_{n \geq 2} \frac1{n^{3/2}} \leq \frac1{3!}
> \int_1^\infty \frac{dx}{x^{3/2}}$ by an integral test, which yields
> $\frac{2}{3!}$ as an upper bound. Applying the same reasoning for the
> $m$ column from $m = 4$ on, an upper bound for that column would be
> $\frac1{m!} \int_1^\infty \frac{dx}{x^{m/2}} = \frac{2}{m!(m2)}$.
> Adding all those upper bounds together, an upper bound for the entire
> doubly infinite sum would be
>
> $$\frac{\zeta^{(2)}(2)}{2!} + \sum_{m \geq 3} \frac{2}{m!(m2)}$$
>
> which certainly converges. So we have absolute convergence of the
> doubly infinite sum.
>
> Thus we are in a position to apply the Fubini theorem, which justifies
> the rearrangement expressed in the first of the following equations
>
> $$\sum_{n \geq 1} \sum_{m \geq 2} (1)^n \frac{(\log n)^m}{n^m m!} =
> \sum_{m \geq 2} \sum_{n \geq 1} (1)^n \frac{(\log n)^m}{n^m m!} =
> \sum_{m \geq 2} (1)^{m+1} \frac{\eta^{(m)}(m)}{m!}$$
>
> giving us what we wanted.

![enter image description here][65]
**The integral forms for CMRB differ by only a trigonometric multiplicand to that of its analog.**
![enter image description here][66]
In[147]:= CMRB =
Re[NIntegrate[(I*E^(r*t))/Sin[Pi*t] /. r > Log[t^(1/t)  1]/t,
{t, 1, I*Infinity}, WorkingPrecision > 30]]
Out[147]= 0.187859642462067120248517934054
In[148]:= Quiet[MKB = NIntegrate[E^(r*t)*(Cos[Pi*t] + I*Sin[Pi*t]) /.
r > Log[t^(1/t)  1]/t, {t, 1, I*Infinity},
WorkingPrecision > 30,
Method > "Trapezoidal"]]
Out[148]= 0.0707760393115292541357595979381 
0.0473806170703505012595927346527 I
![enter image description here][67]
In[182]:= CMRB =
Re[NIntegrate[(I*E^(r*t))/Sin[Pi*t] /. r > Log[t^(1/t)  1]/t, {t,
1, I*Infinity}, WorkingPrecision > 30]]
Out[182]= 0.187859642462067120248517934054
In[203]:= CMRB 
N[NSum[(E^( r*t))/Cos[Pi*t] /. r > Log[t^(1/t)  1]/t, {t, 1,
Infinity}, Method > "AlternatingSigns", WorkingPrecision > 37],
30]
Out[203]= 5.*10^30
In[223]:= CMRB 
Quiet[N[NSum[
E^(r*t)*(Cos[Pi*t] + I*Sin[Pi*t]) /. r > Log[t^(1/t)  1]/t, {t,
1, Infinity}, Method > "AlternatingSigns",
WorkingPrecision > 37], 30]]
Out[223]= 5.*10^30
In[204]:= Quiet[
MKB = NIntegrate[
E^(r*t)*(Cos[Pi*t] + I*Sin[Pi*t]) /. r > Log[t^(1/t)  1]/t, {t,
1, I*Infinity}, WorkingPrecision > 30, Method > "Trapezoidal"]]
Out[204]= 0.0707760393115292541357595979381 
0.0473806170703505012595927346527 I

We derive the preceding and following integral forms of CMRB from the AbelPlana Formula, considering the following result.

ExpToTrig[Re[Exp[2 Pi z  1]]]
![r][68]
![APformula][69]
![APproof][70]
\&[MRB equations][71]






How it all began
==================
**From these meager beginnings:**
My life has proven that one's grades in school are not necessarily a prognostication of achievement in mathematics. For evidence of my poor grades see [my report cards][72].
The eldest child, raised by my sixthgradeeducated mother, I was a D and F student through 6th grade the second time, but in Jr high, in 1976, we were given a selfpaced program. Then I noticed there was more to math than rote multiplication and division of 3 and 4digit numbers! Instead of repetition, I was able to explore what was out there. The more I researched, the better my grades got! It was amazing!! So, having become proficient in mathematics during my high school years, on my birthday in 1994, I decided to put down the TV remote control and pick up a pencil. I began by writing out the powers of 2, like 2*2, 2*2*2, etc. I started making up algebra problems to work at solving, and even started buying books on introductory calculus.
Then came my first opportunity to attend university. I took care of my mother, who suffered from Alzheimer's, so instead of working my usual 60+ hours a week. I started taking a class or two a semester. After my mom passed away, I went back to working my long number of hours but always kept up on my math hobby!
Occasionally, I make a point of going to school and taking a class or two to enrich myself and my math hobby. This has become such a successful routine that some strangers listed me on Wikipedia as an amateur mathematician alphabetically following Jost Bürgi who constructed a table of progressions that is now understood as antilogarithms independently of John Napier at the behest of Johannes Kepler.
I've even studied a few graduatelevel topics in Mathematics.
Why I started so slow and am now a pioneer is a mystery! Could it say something about the educational system? Can the reason be found deep in psychology? (After all, I never made any progress in math or discoveries without first assuming I could, even when others were telling me, I couldn't!) Or could it be that the truth is a little of both and more?


**From these meager beginnings:**
On January 11 and 23,1999 I wrote,
I have started a search for a new mathematical constant! Does anyone want to help me? Consider, 1^(1/1)2^(1/2)+3^(1/3)...I will take it apart and examine it "bit by bit." I hope to find connections to all kinds of arithmetical manipulations. I realize I am in "no man's land," but I work best there! If anyone else is foolhardy enough to come along and offer advice, I welcome you.
The point is that I *found* the MRB constant (**C**<sub>*MRB*</sub>), meaning after all the giants were through roaming the forest of numbers and founding all they found, one virgin mustard seedling caught my eye. So I carefully "brought it up" to a level of maturity, and my own understanding of math along with it! (In another reality, I invented **C**<sub>*MRB*</sub> and then discovered many of its qualities.)
In doing so, I came to find out that this constant (**C**<sub>*MRB*</sub>)
> ![MRB math world snippit][73]
(from https://mathworld.wolfram.com/MRBConstant.html)
was more closely related to other constants than I could have imagined.
As the apprentice of all, building upon the foundation of Chebyshev (1854–1859) on the best uniform approximation of functions, as vowed on January 23, 1999. "I took **C**<sub>*MRB*</sub> apart and examined it 'bit by bit,' finding connections to all kinds of arithmetical manipulations." Not satisfied with conveniently construed constructions (halfhazardously put together formulas) that a naïve use of numeric search engines like Wolfram Alpha or the OEIS, might give, I set out to determine the most interesting (by being the most improbable but true) approximations for each constant in relation to it.
For example, consider its relationship to Viswanath's constant (VC)
> ![Viswanath' math world snippit][74]
(from https://mathworld.wolfram.com/RandomFibonacciSequence.html)
**With both being functions of x<sup>1/x</sup> alone,** we have these nearzeors of VC using **C**<sub>*MRB*</sub>, which have a ratio of [Gelfond's constant][75] $=e^\pi.$
![=e^\pi][76]
Notice, by "nearzeros," I mean we have the following.
![nearzeros][77]
VC/(6*(11/7  ProductLog[1]))  CMRB
CMRB  (5*VC^6)/56
3.4164*10^8
1.47*10^9
Out[54]= 3.4164*^8
Out[55]= 1.47*^9
See [cloud notebook][78].
The near zero, CMRB  (5*VC^6)/56, is so small that Wolfram Alpha yields a rational power of VC for the nth root of 56/6 CMRB.
![enter image description here][79]


Then there is the Rogers  Ramanujan Continued Fraction, R(q),
of **C**<sub>*MRB*</sub> that is welllinearlyapproximated by terms of itself alone:
&[Wolfram Notebook][80]


**From these meager beginnings:**
On Feb 22, 2009, I wrote,
> It appears that the absolute value, minus 1/2, of the limit(integral of (1)^x*x^(1/x) from 1 to 2N as N>infinity) would equal the partial sum of (1)^x*x^(1/x) from 1 to where the upper summation is even and growing without bound. Is anyone interested in improving or disproving this conjecture?
>
> ![enter image description here][81]
I came to find out my discovery, a very slow to converge [oscillatory integral,][82] would later be further defined by [Google Scholar.][83]
Here is proof of a faster converging integral for its integrated analog (The MKB constant) by Ariel Gershon.
g(x)=x^(1/x), M1=![hypothesis][84]
Which is the same as
![enter image description here][85]
because changing the upper limit to 2N + 1 increases MI by $2i/\pi.$
MKB constant calculations have been moved to their discussion at [http://community.wolfram.com/groups//m/t/1323951?p_p_auth=W3TxvEwH][86] .
![Iimofg>1][87]
![Cauchy's Integral Theorem][88]
![Lim surface h gamma r=0][89]
![Lim surface h beta r=0][90]
![limit to 2n1][91]
![limit to 2n][92]
Plugging in equations [5] and [6] into equation [2] gives us:
![left][93]![right][94]
Now take the limit as N?? and apply equations [3] and [4] :
![QED][95]
He went on to note that
![enter image description here][96]
After I mentioned it to him, Richard Mathar published his meaningful work on it [here in arxiv][97], where M is the MRB constant and M1 is MKB:
> ![enter image description here][98]
M1 has a convergent series,
![enter image description here][99]
which has lines of symmetry across wholeandhalf number points on the xaxis, and **halfperiods of exactly 1**, for both real and imaginary parts as in the following plots.
And where
f[x_] = Exp[I Pi x] (x^(1/x)  1); Assuming[
x \[Element] Integers && x > 1,
FullSimplify[Re[f[x + 1/2]]  Im[f[x]]]]
gives
0
ReImPlot[(1)^x (x^(1/x)  1), {x, 1, Infinity}, PlotStyle > Blue,
Filling > Axis, FillingStyle > {Green, Red}]
![big plot][100]
![small plot][101]

Every 75 *i* of the upper value of the partial integration yields 100 additional digits of M2=![enter image description here][102] and of CMRB=![enter image description here][103]=![enter image description here][104]
&[Wolfram Notebook][105]
Here is a heuristic explanation for the observed behavior.
Write the integral as an infinite series, $m= \sum_{k = 1}^\infty a_k$ with
$a_k = \int_{i kM}^{i (k+1)M} \frac{t^{1/t}1}{\sin (\pi t)} \, dt$ for $k \ge 2$ and the obvious modification for $k = 1$. we are computing the partial sums of these series with $M = 75$ and the question is why the series remainders decrease by a factor of $10^{100}$ for each additional term.
The integrand is a quotient with numerator $t^{1/t}  1 \approx \log t\, / t$ and denominator $1/\sin \pi t \approx e^{i \pi t}$ for large imaginary $t$. The absolute values of these terms therefore are $a_k \approx \log kM/kM \cdot e^{\pi kM}$. This implies
![o$][106]
as $k \to \infty$. Consequently the remainders $\sum_{k = N}^\infty$ behave like $e^{ \pi N M}$. They decrease by a factor of $e^{\pi M}$ for each additional term. And for $M = 75$, this is approximately $10^{100}$, predicting an increase in accuracy of 100 digits whenever the upper integration bound increased by $75i$.
I used the fact that ![enter image description here][107]
The following "partial proof of it" is from Quora.
While![enter image description here][108]
![enter image description here][109]
![enter image description here][110]

**I developed a lot more theory behind it and ways of computing many more digits in [this linked][111] Wolfram post.**
Here is how my analysis (along with improvements to Mathematica) has improved the speed of calculating that constant's digits:
(digits and seconds)
![enter image description here][112]
Better 2022 results are expected soon!
2022 results documentation:
&[Wolfram Notebook][113]


**From these meager beginnings:**
In October 2016, I wrote the following [here in researchgate][114]:
First, we will follow the path the author took to find out that for
![ratio of a1 to a][115]
the limit of the ratio of a to a  1, as a goes to infinity is Gelfond's Constant, (e ^ pi). We will consider the hypothesis and provide hints for proof using L’ Hospital’s Rule (since we have indeterminate forms as a goes to infinity):
The following should help in a proof of the hypothesis:
Cos[Pi*I*x] == Cosh[Pi*x], Sin[Pi*I*x] == I Sinh[Pi*x], and Limit[x^(1/x),x>Infinity]==1.
Using L’Hospital’s Rule, we have the following:
![L’ Hospital’s a's][116]
(17) (PDF) Gelfond' s Constant using MKB constant like integrals. Available from: [https://www.researchgate.net/publication/309187705_Gelfond%27_s_Constant_using_MKB_constant_like_integrals][117] [accessed Aug 16 2022].
We find there is no limit a goes to infinity, of the ratio of the previous forms of integrals when the "I" is left out, and give a small proof for their divergence.
That was responsible for the integralequationdiscovery mentioned in one of the following posts, where it is written, "Using those ratios, it looks like" (There ![m][118] is the MRB constant.)
> ![enter image description here][119]

**From these meager beginnings:**
In November 2013, I wrote:
$C$MRB is approximately 0.1878596424620671202485179340542732. See [this](http://www.wolframalpha.com/input/?i=0.1878596424620671202485179340542732300559030949001387&lk=1&a=ClashPrefs_*Math)
and [this.](http://www.wolframalpha.com/input/?i=mrb+constant&t=elga01)
$\sum_{n=1}^\infty (1)^n\times(n^{1/n}a)$ is formally convergent only when $a =1$. However, if you extend the meaning of $\sum$ through "summation methods", whereby series that diverge in one sense converge in another sense (e.g. Cesaro, etc.) you get results for other $a$.
A few years ago it came to me to ask what value of $a$ gives $$\sum_{n=1}^\infty (1)^n\times(n^{1/n}a)=0\text{ ?}$$(For what value of a is the Levin's utransform's and Cesàro's sum result 0 considering weak convergence?)
The solution I got surprised me: it was $a=12\times C\mathrm{MRB}=0.6242807150758657595029641318914535398881938101997224\ldots$.
Where $C\mathrm{MRB}$ is $\sum_{n=1}^\infty (1)^n\times(n^{1/n}1)$.
I asked, "If that's correct can you explain why?" and got the following comment.
![enter image description here][120]
To see this for yourself in Mathematica enter
`FindRoot[NSum[(1)^n*(n^(1/n)  x), {n, 1, Infinity}], {x, 1}]` where regularization is used so that the sum that formally diverges returns a result that can be interpreted as evaluation of the analytic extension of the series.
Finally let a = M2 = $12\times C$MRB = 0.6242807150758... and the two limitpoints of the series $\sum_{n=1}^\infty (1)^n\times(n^{1/n}M2)$ are +/ $C$MRB with its Levin's utransform's result being 0. See [here.](http://oeis.org/A173273)
Also,
![enter image description here][121]



Scholarly works about **C**<sub>*MRB*</sub>.

**From these meager beginnings:**
In 2015 I wrote:
> Mathematica makes some attempts to project hyperdimensions onto
> 2space with the Hypercube command. Likewise, some attempts at tying
> them to our universe are mentioned at
> [https://bctp.berkeley.edu/extraD.html][122] . The MRB constant from
> infinitedimensional space is described at
> http://marvinrayburns.com/ThegeometryV12.pdf. It is my theory that
> like the MRB constant the universe, under inflation, started in an
> infinite number of space dimensions. And they almost all
> instantly collapsed, as far as our sensory realm is concerned, leaving
> all but the few we enjoy today.
I'm not the first person to think the universe consists of an infinitude of dimensions. Some string theories and theorists propose it too.
Michele Nardelli added the following.
> In string theory, perturbation methods involve such a high degree of
> approximation that the theory is unable to identify which of the
> Calabi  Yau spaces are candidates for describing the universe. The
> consequence is that it does not describe a single universe, but
> something like 10^500 universes. In reality, admitting 10^500
> different quantum voids would allow the only mechanism known at the
> moment to explain the present value of the cosmological constant
> following an idea by Steven Weinberg. Furthermore, a very large value
> of different voids is typical of any type of matter coupled to gravity
> and is also obtained when coupling the standard model. I believe that
> the multiverse is a "space of infinite dimensions" with infinite
> degrees of freedom and infinite possible potential wave functions that
> when they collapse, formalize a particle or a universe in a quantum
> state. The strings vibrating, like the strings of a musical
> instrument, emit frequencies that are not always precise numbers,
> indeed, very often they are decimal, irrational, and/or transcendent
> numbers. The MRB constant serves as a "regularizer" to obtain
> solutions as precise as possible and this in various sectors of string
> theory, black holes, and cosmology
In [this physics.StackExchange question][123] his concept of the dimensions in string theory and a possible link with number theory is inquired about.
Many MRB constant papers by Michele Nardelli are found [here in Google Scholar][124], which include previous versions of these.
> Hello. Here are the links of my more comprehensive articles describing
> the various applications of the CMRB in various fields of theoretical
> physics and cosmology. Thanks always for your availability, see you
> soon.
> 
>
> [Analyzing several equations concerning Geometric Measure Theory, various Ramanujan parameters and the developments of the MRB Constant. New possible mathematical connections with some sectors of String Theory. XII][125]
> 
>
> [On several equations concerning Geometric Measure Theory, various Ramanujan parameters and the developments of the MRB Constant. New possible mathematical connections with some sectors of Cosmology (Bubble universes) and String Theory][126]
> 
>
> [Analyzing several equations concerning Geometric Measure Theory, various Ramanujan parameters and the developments of the MRB Constant. New possible mathematical connections with some sectors of Cosmology (Bubble universes) and String Theory. III][127]
> 
>
> [Analyzing several equations concerning Geometric Measure Theory, various Ramanujan parameters and the developments of the MRB Constant. New possible mathematical connections with some equations concerning various aspects of Quantum Mechanics and String Theory. VI][128]
> 
>
> [Analyzing several equations concerning various aspects of String Theory and oneloop graviton correction to the conformal scalar mode function. New possible mathematical connections with various Ramanujan parameters and some developments of the MRB Constant.][129]
> 
>
> [Analyzing several equations concerning Geometric Measure Theory, various Ramanujan parameters and the developments of the MRB Constant. New possible mathematical connections with some equations concerning Multiverse models and the Lorentzian path integral for the vacuum decay process][130]
> 
>
> [On the study of various equations concerning Primordial Gravitational Waves in Standard Cosmology and some sectors of String Theory. New possible mathematical connections with various Ramanujan formulas and various developments of the MRB Constant][131]
> 
>
>[On the study of some equations concerning the mathematics of String Theory. New possible connections with some sectors of Number Theory and MRB Constant][132]
> 
>
>[On the study of some equations concerning the mathematics of String Theory. New possible connections with some sectors of Number Theory and MRB Constant. II][133]
> 
>
>[Analyzing some equations of Manuscript Book 2 of Srinivasa Ramanujan. New possible mathematical connections with several equations concerning the Geometric Measure Theory, the MRB Constant and various sectors of String Theory][134]
> 
>
>[Analyzing the MRB Constant in Geometric Measure Theory and in a Ramanujan equation. New possible mathematical connections with ζ(2), ϕ , the Quantum Cosmological Constant and some sectors of String Theory][135]
> 
>
> [Analyzing some equations of Manuscript Book 2 of Srinivasa Ramanujan. New possible mathematical connections with several equations concerning the Geometric Measure Theory, the MRB Constant, various sectors of Black Hole Physics and String Theory][136]
> 
>
> [Analyzing further equations of Manuscript Book 2 of Srinivasa Ramanujan. New possible mathematical connections with the MRB Constant, the RamanujanNardelli Mock General Formula and several equations concerning some sectors of String Theory III][137]
His latest papers on the MRB constant, follow.
> Hi Marvin, for me the best links you could post are those related to
> the works concerning the Ramanujan continued fractions and
> mathematical connections with MRB Constant and various sectors of
> String Theory.
>
> Here are the links (in all there are 40):
>
>
>
> https://www.academia.edu/80247977/ https://www.academia.edu/80298701/
> https://www.academia.edu/80376615/ https://www.academia.edu/80431963/
> https://www.academia.edu/80508286/ https://www.academia.edu/80590932/
> https://www.academia.edu/80660709/ https://www.academia.edu/80724379/
> https://www.academia.edu/80799006/ https://www.academia.edu/80894850/
> https://www.academia.edu/81033980/ https://www.academia.edu/81150262/
> https://www.academia.edu/81231887/ https://www.academia.edu/81313294/
> https://www.academia.edu/81536589/ https://www.academia.edu/81625054/
> https://www.academia.edu/81705896/ https://www.academia.edu/81769347/
> https://www.academia.edu/81812404/ https://www.academia.edu/81874954/
> https://www.academia.edu/81959191/ https://www.academia.edu/82036273/
> https://www.academia.edu/82080277/ https://www.academia.edu/82129372/
> https://www.academia.edu/82155422/ https://www.academia.edu/82204999/
> https://www.academia.edu/82231273/ https://www.academia.edu/82243774/
> https://www.academia.edu/82347058/ https://www.academia.edu/82399680/
> https://www.academia.edu/82441768/ https://www.academia.edu/82475969/
> https://www.academia.edu/82516896/ https://www.academia.edu/82521506/
> https://www.academia.edu/82532215/ https://www.academia.edu/82622577/
> https://www.academia.edu/82679726/ https://www.academia.edu/82733681/
> https://www.academia.edu/82777895/ https://www.academia.edu/82828901/
He recently added the following.
> Hi Marvin,
>
> The MRB Constant, also in the case of the Ramanujan's expressions that
> we are slowly analyzing, serves to "normalize", therefore to rectify
> the approximations we obtain. For example, for the value of zeta (2),
> which is always approximate (1.64382 ....)" [from the string theory equations, example below], "adding an expression
> containing the MRB Constant gives a result much closer to the real
> value which is 1.644934 ... This procedure is carried out on all those
> we call "recurring numbers" (Pi, zeta (2), 4096, 1729 and the golden
> ratio), which, developing the expressions, are always approximations,
> from which, by inserting the CMRB in various ways, we obtain results
> much closer to the real values of the aforementioned recurring
> numbers. Finally, remember that Ramanujan's expressions and the
> recurring numbers that are obtained are connected to the frequencies
> of the strings, therefore to the vibrations of the same.
One example of his procedure from
[https://www.academia.edu/81812404/On_further_Ramanujans_continued_fractions_mathematical_connections_with_MRB_Constant_various_equations_concerning_some_sectors_of_String_Theory_XIX?][138]
was to analyze some expressions from Ramanujan's notebooks.
Finding other expressions from series of their antiderivative and derivatives, in this case, dividing two previous expressions, after some calculations, he obtained this expression from it."
> ![enter image description here][139]
Then finally "by inserting the CMRB, obtaining results much closer to the real values of the aforementioned recurring numbers:"
(referring to Ramanujan's equation, and the after more work..)
>, ![enter image description here][140]
**You need to look at the paper entirely to see how he puts it all together.** He uses Wolfram Alpha for a lot of it.
7/7/2022 I just found a [video][141] he made concerning his work on string theory with its connection to Ramanujan and **C**<sub>*MRB*</sub>. English subtitles are available on youtube.

There are around 200 papers concerning the MRB contact [here][142] at acadeia.edu.
![enter image description here][143]
More Google Scholar results on **C**<sub>*MRB*</sub>t are [here,][144] which include the following.
**[Dr. Richard Crandall][145] called the MRB constant a [key fundamental constant][146]**
> ![enter image description here][147]
**in [this linked][148] wellsourced and equally greatly cited Google Scholar promoted paper. Also [here][149].**
**[Dr. Richard J. Mathar][150] wrote on the MRB constant [here.][151]**
**Xun Zhou, School of Water Resources and Environment, China University of Geosciences (Beijing), [wrote][152] the following in "on Some Series and Mathematic Constants Arising in Radioactive Decay" for the Journal of Mathematics Research, 2019.**
> A divergent infinite series may also lead to mathematical constants if
> its partial sum is bounded. The Marvin Ray Burns’ (MRB) constant is
> the upper bounded value of the partial sum of the divergent and
> alternating infinite series:
> 1<sup>1/1</sup>+2<sup>1/2</sup>3<sup>1/3</sup>+4<sup>1/4</sup>5<sup>1/5</sup>+6<sup>1/6</sup>···=0.187859···(M. Chen, & S. Chen, 2016). Thus, construction of new infinite series has the possibility
> of leading to new mathematical constants.




MRB Constant Records,
====================
My inspiration to compute a lot of digits of **C**<sub>*MRB*</sub> came from [the following website by Simon Plouffe][153].
There, computer mathematicians calculate millions, then billions of digits of constants like pi, when with only 65 decimal places of pi, we could determine the size of the observable universe to within a Planck length (where the uncertainty of our measure of the universe would be greater than the universe itself)!
In contrast 65 digits of the MRB constant "measures" the value of 1+ssqrt(2)3^(1/3) up to n^(1/n) where n is 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000, which can be called 1 unvigintillion or just 10^66.
And why compute 65 digits of the MRB constant? Because having that much precision is the only way to solve such a problem as
> 1465528573348167959709563453947173222018952610559967812891154^ mm,
> where m is the MRB constant, which gives the near integer "to beat
> all,"
> 200799291330.9999999999999999999999999999999999999999999999999999999999999900450...
And why compute millions of digits of it? uhhhhhhhhhh.... "Because it's there!" (...Yeah, thanks George Mallory!)
And why?? (c'est ma raison d'être!!!)
> ![enter image description here][154]
> ![enter image description here][155]
> ![enter image description here][156]
>![enter image description here][157]
So, below you find reproducible results with methods. The utmost care has been taken to assure the accuracy of the record number of digits calculations. These records represent the advancement of consumerlevel computers, 21st century Iterative methods, and clever programming over the past 23 years.
Here are some record computations of **C**<sub>*MRB*</sub>. If you know of any others let me know, and I will probably add them!
1 digit of the (additive inverse of ) **C**<sub>*MRB*</sub> with my TI92s, by adding 1sqrt(2)+3^(1/3)4^(1/4)+... as far as I could, was computed. That first digit, by the way, was just 0. Then by using the sum key, to compute $\sum _{n=1}^{1000 } (1)^n \left(n^{1/n}\right),$ the first correct decimal of $\text{CMRB}=\sum _{n=1}^{\infty } (1)^n \left(n^{1/n}1\right)$ i.e. (.1). It gave (.1_91323989714) which is close to what Mathematica gives for summing to only an upper limit of 1000.

4 decimals(.1878) of CMRB were computed on Jan 11, 1999 with the Inverse Symbolic Calculator, applying the command evalf( 0.1879019633921476926565342538468+sum((1)^n* (n^(1/n)1),n=140001..150000)); where 0.1879019633921476926565342538468 was the running total of t=sum((1)^n* (n^(1/n)1),n=1..10000), then t= t+the sum from (10001.. 20000), then t=t+the sum from (20001..30000) ... up to t=t+the sum from (130001..140000).

5 correct decimals (rounded to .18786), in Jan of 1999 were drawn from CMRB using Mathcad 3.1 on a 50 MHz 80486 IBM 486 personal computer operating on Windows 95.

9 digits of CMRB shortly afterward using Mathcad 7 professional on the Pentium II mentioned below, by summing (1)^x x^(1/x) for x=1 to 10,000,000, 20,000,000, and a many more, then linearly approximating the sum to a what a few billion terms would have given.

500 digits of CMRB with an online tool called Sigma on Jan 23, 1999. See [http://marvinrayburns.com/Original_MRB_Post.html][158] if you can read the printed and scanned copy there.

5,000 digits of CMRB in September of 1999 in 2 hours on a 350 MHz PentiumII,133 MHz 64 MB of RAM using the simple PARI commands \p 5000;sumalt(n=1,((1)^n*(n^(1/n)1))), after allocating enough memory.
To beat that, I did it on July 4, 2022, in 1 second on the 5.5 GHz CMRBSC 3 with 4800MHz 64 GB of RAM by Newton's method using Convergence acceleration of alternating series. Henri Cohen, Fernando Rodriguez Villegas, Don Zagier acceleration "Algorithm 1" to at least 5000 decimals. (* Newer loop with Newton interior. *)
![PII][159]
documentation [here][160]

6,995 accurate digits of CMRB were computed on June 1011, 2003 over a period, of 10 hours, on a 450 MHz P3 with an available 512 MB RAM,.
To beat that, I did it in <2.5 seconds on the MRBCSC 3 on July 7, 2022 (more than 14,400 times as fast!)
![PIII][161]
documentation [here][162]

8000 digits of CMRB completed, using a Sony Vaio P4 2.66 GHz laptop computer with 960 MB of available RAM, at 2:04 PM 3/25/2004,

11,000 digits of CMRB> on March 01, 2006, with a 3 GHz PD with 2 GB RAM available calculated.

40, 000 digits of CMRB in 33 hours and 26 min via my program written in Mathematica 5.2 on Nov 24, 2006. The computation was run on a 32bit Windows 3 GHz PD desktop computer using 3.25 GB of Ram.
The program was
Block[{a, b = 1, c = 1  d, d = (3 + Sqrt[8])^n,
n = 131 Ceiling[40000/100], s = 0}, a[0] = 1;
d = (d + 1/d)/2; For[m = 1, m < n, a[m] = (1 + m)^(1/(1 + m)); m++];
For[k = 0, k < n, c = b  c;
b = b (k + n) (k  n)/((k + 1/2) (k + 1)); s = s + c*a[k]; k++];
N[1/2  s/d, 40000]]

60,000 digits of CMRB on July 29, 2007, at 11:57 PM EST in 50.51 hours on a 2.6 GHz AMD Athlon with 64bit Windows XP. Max memory used was 4.0 GB of RAM.

65,000 digits of CMRB in only 50.50 hours on a 2.66 GHz Core 2 Duo using 64bit Windows XP on Aug 3, 2007, at 12:40 AM EST, Max memory used was 5.0 GB of RAM.

100,000 digits of CMRB on Aug 12, 2007, at 8:00 PM EST, were computed in 170 hours on a 2.66 GHz Core 2 Duo using 64bit Windows XP. Max memory used was 11.3 GB of RAM. The typical daily record of memory used was 8.5 GB of RAM.
To beat that, on the 4th of July, 2022, I computed the same digits in 1/4 of an hour. CNTRL+F "4th of July, 2022" for documentation.
To beat that, on the 7th of July, 2022, I computed the same digits in 1/5 of an hour. CNTRL+F "7th of July, 2022" for documentation (850 times as fast as the first 100,000 run!)

150,000 digits of CMRB on Sep 23, 2007, at 11:00 AM EST. Computed in 330 hours on a 2.66 GHz Core 2 Duo using 64bit Windows XP. Max memory used was 22 GB of RAM. The typical daily record of memory used was 17 GB of RAM.

200,000 digits of CMRB using Mathematica 5.2 on March 16, 2008, at 3:00 PM EST,. Found in 845 hours, on a 2.66 GHz Core 2 Duo using 64bit Windows XP. Max memory used was 47 GB of RAM. The typical daily record of memory used was 28 GB of RAM.

300,000 digits of CMRB were destroyed (washed away by Hurricane Ike ) on September 13, 2008 sometime between 2:00 PM  8:00 PM EST. Computed for a long 4015. Hours (23.899 weeks or 1.4454*10^7 seconds) on a 2.66 GHz Core 2 Duo using 64bit Windows XP. Max memory used was 91 GB of RAM. The Mathematica 6.0 code is used follows:
Block[{$MaxExtraPrecision = 300000 + 8, a, b = 1, c = 1  d,
d = (3 + Sqrt[8])^n, n = 131 Ceiling[300000/100], s = 0}, a[0] = 1;
d = (d + 1/d)/2; For[m = 1, m < n, a[m] = (1 + m)^(1/(1 + m)); m++];
For[k = 0, k < n, c = b  c;
b = b (k + n) (k  n)/((k + 1/2) (k + 1)); s = s + c*a[k]; k++];
N[1/2  s/d, 300000]]

225,000 digits of CMRB were started with a 2.66 GHz Core 2 Duo using 64bit Windows XP on September 18, 2008. It was completed in 1072 hours.

250,000 digits were attempted but failed to be completed to a serious internal error that restarted the machine. The error occurred sometime on December 24, 2008, between 9:00 AM and 9:00 PM. The computation began on November 16, 2008, at 10:03 PM EST. The Max memory used was 60.5 GB.

250,000 digits of CMRB on Jan 29, 2009, 1:26:19 pm (UTC0500) EST, with a multiplestep Mathematica command running on a dedicated 64bit XP using 4 GB DDR2 RAM onboard and 36 GB virtual. The computation took only 333.102 hours. The digits are at http://marvinrayburns.com/250KMRB.txt. The computation is completely documented.

300000 digit search of CMRB was initiated using an i7 with 8.0 GB of DDR3 RAM onboard on Sun 28 Mar 2010 at 21:44:50 (UTC0500) EST, but it failed due to hardware problems.

299,998 Digits of CMRB: The computation began Fri 13 Aug 2010 10:16:20 pm EDT and ended 2.23199*10^6 seconds later  Wednesday, September 8, 2010. I used Mathematica 6.0 for Microsoft Windows (64bit) (June 19, 2007) Which is an average of 7.44 seconds per digit. I used my Dell Studio XPS 8100 i7 860 @ 2.80 GHz with 8GB physical DDR3 RAM. Windows 7 reserved an additional 48.929 GB virtual Ram.

300,000 digits to the right of the decimal point of CMRB from Sat 8 Oct 2011 23:50:40 to Sat 5 Nov 2011 19:53:42 (2.405*10^6 seconds later). This run was 0.5766 seconds per digit slower than the 299,998 digit computation even though it used 16 GB physical DDR3 RAM on the same machine. The working precision and accuracy goal combination were maximized for exactly 300,000 digits, and the result was automatically saved as a file instead of just being displayed on the front end. Windows reserved a total of 63 GB of working memory of which 52 GB were recorded being used. The 300,000 digits came from the Mathematica 7.0 command`
Quit; DateString[]
digits = 300000; str = OpenWrite[]; SetOptions[str,
PageWidth > 1000]; time = SessionTime[]; Write[str,
NSum[(1)^n*(n^(1/n)  1), {n, \[Infinity]},
WorkingPrecision > digits + 3, AccuracyGoal > digits,
Method > "AlternatingSigns"]]; timeused =
SessionTime[]  time; here = Close[str]
DateString[]

314159 digits of the constant took 3 tries due to hardware failure. Finishing on September 18, 2012, I computed 314159 digits, taking 59 GB of RAM. The digits came from the Mathematica 8.0.4 code`
DateString[]
NSum[(1)^n*(n^(1/n)  1), {n, \[Infinity]},
WorkingPrecision > 314169, Method > "AlternatingSigns"] // Timing
DateString[]

1,000,000 digits of CMRB for the first time in history in 18 days 9 hours 11 minutes 34.253417 seconds by Sam Noble of the Apple Advanced Computation Group.

1,048,576 digits of CMRB in a lightningfast 76.4 hours, finishing on Dec 11, 2012 were scored by Dr Richard Crandall, an Apple scientist and head of its advanced computational group. That's on a 2.93 GHz 8core Nehalem.
To beat that, on Aug of 2018, I computed 1,004,993 digits in 53.5 hours 34 hours computation time (from the timing command) with 10 DDR4 RAM (of up to 3000 MHz) supported processor cores overclocked up to 4.7 GHz! Search this post for "53.5" for documentation.
To beat that, on Sept 21, 2018: I computed 1,004,993 digits in 50.37 hours of absolute time and 35.4 hours of computation time (from the timing command) with 18 (DDR3 and DDR4) processor cores! Search this post for "50.37 hours" for documentation.**
To beat that, on May 11, 2019, I computed over 1,004,993 digits, in 45.5 hours of absolute time and only 32.5 hours of computation time, using 28 kernels on 18 DDR4 RAM (of up to 3200 MHz) supported cores overclocked up to 5.1 GHz Search 'Documented in the attached ":3 fastest computers together 3.nb." ' for the post that has the attached documenting notebook.
To beat that, I accumulated over 1,004,993 correct digits in 44 hours of absolute time and 35.4206 hours of computation time on 10/19/20, using 3/4 of the MRB constant supercomputer 2  see https://www.wolframcloud.com/obj/bmmmburns/Published/44%20hour%20million.nb for documentation.
To beat that I did a 1,004,993 correct digits computation in 36.7 hours of absolute time and only 26.4 hours of computation time, on Sun 15 May 2022 at 06:10:50, using 3/4 of the MRB constant supercomputer 3. Ram Speed was 4800MHz and all of the 30 cores were clocked at up to 5.2 GHz.
To beat that I did a 1,004,993 correct digits computation in 35.6 hours of absolute time and only 25.3 hours of computation time, on Wed 3 Aug 2022 08:05:38, using the MRB constant supercomputer 3. Ram Speed was 4000MHz and all of the 40 cores were clocked at up to 5.5 GHz.
[44 hours million notebook][163]
[36.7 hours million notebook][164]
[35.6 hours million notebook][165]

A little over 1,200,000 digits, previously, of CMRB in 11 days, 21 hours, 17 minutes, and 41 seconds (I finished on March 31, 2013, using a sixcore Intel(R) Core(TM) i73930K CPU @ 3.20 GHz. see https://www.wolframcloud.com/obj/bmmmburns/Published/36%20hour%20million.nb
for details.

2,000,000 or more digit computation of CMRB on May 17, 2013, using only around 10GB of RAM. It took 37 days 5 hours 6 minutes 47.1870579 seconds. I used my sixcore Intel(R) Core(TM) i73930K CPU @ 3.20 GHz 3.20 GHz.

3,014,991 digits of CMRB, world record computation of **C**<sub>*MRB*</sub> was finished on Sun 21 Sep 2014 at 18:35:06. It took 1 month 27 days 2 hours 45 minutes 15 seconds. The processor time from the 3,000,000+ digit computation was 22 days. I computed the 3,014,991 digits of **C**<sub>*MRB*</sub> with Mathematica 10.0. I Used my new version of Richard Crandall's code in the attached 3M.nb, optimized for my platform and large computations. I also used a sixcore Intel(R) Core(TM) i73930K CPU @ 3.20 GHz with 64 GB of RAM of which only 16 GB was used. Can you beat it (in more number of digits, less memory used, or less time taken)? This confirms that my previous "2,000,000 or more digit computation" was accurate to 2,009,993 digits. they were used to check the first several digits of this computation. See attached 3M.nb for the full code and digits.

Over 4 million digits of CMRB was finished on Wed 16 Jan 2019 19:55:20.
It took 4 years of continuous tries. This successful run took 65.13 days absolute time, with a processor time of 25.17 days, on a 3.7 GHz overclocked up to 4.7 GHz on all cores Intel 6 core computer with 3000 MHz RAM. According to this computation, the previous record, 3,000,000+ digit computation, was accurate to 3,014,871 decimals, as this computation used my algorithm for computing n^(1/n) as found in chapter 3 in the paper at
https://www.sciencedirect.com/science/article/pii/0898122189900242 and the 3 million+ computation used Crandall's algorithm. Both algorithms outperform Newton's method per calculation and iteration.
Example use of M R Burns' algorithm to compute 123456789^(1/123456789) 10,000,000 digits:
ClearSystemCache[]; n = 123456789;
(*n is the n in n^(1/n)*)
x = N[n^(1/n),100];
(*x starts out as a relatively small precision approximation to n^(1/n)*)
pc = Precision[x]; pr = 10000000;
(*pr is the desired precision of your n^(1/n)*)
Print[t0 = Timing[While[pc < pr, pc = Min[4 pc, pr];
x = SetPrecision[x, pc];
y = x^n; z = (n  y)/y;
t = 2 n  1; t2 = t^2;
x = x*(1 + SetPrecision[4.5, pc] (n  1)/t2 + (n + 1) z/(2 n t)
 SetPrecision[13.5, pc] n (n  1)/(3 n t2 + t^3 z))];
(*You get a much faster version of N[n^(1/n),pr]*)
N[n  x^n, 10]](*The error*)];
ClearSystemCache[]; n = 123456789; Print[t1 = Timing[N[n  N[n^(1/n), pr]^n, 10]]]
Gives
{25.5469,0.*10^9999984}
{101.359,0.*10^9999984}
More information is available upon request.

More than 5 million digits of CMRB were found on Fri 19 Jul 2019 18:49:02, Methods described in the reply below which begins with "Attempts at a 5,000,000 digit calculation ." For this 5 million digit calculation of **C**<sub>*MRB*</sub> using the 3 node MRB supercomputer: processor time was 40 days. and the actual time was 64 days. That is in less absolute time than the 4milliondigit computation which used just one node.

6,000,000 digits of CMRB after 8 tries in 19 months. (Search "8/24/2019 It's time for more digits!" below.) finishing on Tue 30 Mar 2021 at 22:02:49 in 160 days.
The MRB constant supercomputer 2 said the following:
Finished on Tue 30 Mar 2021 22:02:49. computation and absolute time were
5.28815859375*10^6 and 1.38935720536301*10^7 s. respectively
Enter MRB1 to print 6029991 digits. The error from a 5,000,000 or moredigit calculation that used a different method is
0.*10^5024993.
That means that the 5,000,000digit computation Was actually accurate to 5024993 decimals!!!

5,609,880, verified by 2 distinct algorithms for x^(1/x), digits of CMRB on Thu 4 Mar 2021 at 08:03:45. The 5,500,000+ digit computation using a totally different method showed that many decimals are in common with the 6,000,000+ digit computation in 160.805 days.

6,500,000 digits of CMRB on my second try,
The MRB constant supercomputer said,
Finished on Wed 16 Mar 2022 02: 02: 10. computation and absolute time
were 6.26628*10^6 and 1.60264035419592*10^7s respectively Enter MRB1
to print 6532491 digits. The error from a 6, 000, 000 or more digit
calculation that used a different method is
0.*10^6029992.
"Computation time" 72.526 days
"Absolute time" 185.491 days







**C**<sub>*MRB*</sub> and its applications
=====================================
**Definition 1**
**C**<sub>*MRB*</sub> is defined at [https://en.wikipedia.org/wiki/MRB_constant][166] .
From [Wikipedia:][167]
> ![If you see this instead of an image, reload the page][168]
> ![If you see this instead of an image, reload the page][169]
References
Plouffe, Simon. "mrburns". Retrieved 12 January 2015.
Burns, Marvin R. (23 January 1999). "RC". math2.org. Retrieved 5 May 2009.
Plouffe, Simon (20 November 1999). "Tables of Constants" (PDF). Laboratoire de combinatoire et d'informatique mathématique. Retrieved 5 May 2009.
Weisstein, Eric W. "MRB Constant". MathWorld.
Mathar, Richard J. (2009). "Numerical Evaluation of the Oscillatory Integral Over exp(iπx) x^*1/x) Between 1 and Infinity". arXiv:0912.3844 [math.CA].
Crandall, Richard. "Unified algorithms for polylogarithm, Lseries, and zeta variants" (PDF). PSI Press. Archived from the original (PDF) on April 30, 2013. Retrieved 16 January 2015.
(sequence A037077 in the OEIS)
(sequence A160755 in the OEIS)
(sequence A173273 in the OEIS)
Fiorentini, Mauro. "MRB (costante)". bitman.name (in Italian). Retrieved 14 January 2015.
Finch, Steven R. (2003). Mathematical Constants. Cambridge, England: Cambridge University Press. p. 450. ISBN 0521818052.
`
The following equation that was shown in the Wikipedia definition shows how closely the MRB constant is related to root two.
![enter image description here][170]
In[1]:= N[Sum[Sqrt[2]^(1/n)* Sqrt[n]^(1/n)  ((Sqrt[2]^y*Sqrt[2]^x)^(1/Sqrt[2]^x))^Sqrt[2]^(y)/.
x > 2*Log2[a^2 + b^2] /.
y > 2*Log2[ai^2  bi^2] /.
a > 1  (2*n)^(1/4) /.
b > 2^(5/8)*Sqrt[n^(1/4)] /.
ai > 1  I*(2*n)^(1/4) /.
bi > 2^(5/8)*Sqrt[I*n^(1/4)], {n, 1, Infinity}], 7]
Out[1]= 0.1878596 + 0.*10^8 I
The complex roots and powers above are found to be welldefined because
we get all either "integer" and "rational" the first of the following lists only, also by working from the bottom to the top of the above list of equations.
![enter image description here][171]
Code:
In[349]:= Table[
Head[FullSimplify[
Expand[(Sqrt[2])^y/(Sqrt[2])^x] //.
x > 2 (Log[1 + Sqrt[2] Sqrt[n]]/Log[2]) /.
y > 2 (Log[1 + Sqrt[2] Sqrt[n]]/Log[2])]], {n, 1, 10}]
Out[349]= {Integer, Rational, Rational, Rational, Rational, Rational, \
Rational, Rational, Rational, Rational}
In[369]:= Table[
Head[FullSimplify[
Expand[(Sqrt[2])^y/(Sqrt[2])^x] //.
x > 2 (Log[1 + Sqrt[2] Sqrt[n]]/Log[3]) /.
y > 2 (Log[1 + Sqrt[2] Sqrt[n]]/Log[2])]], {n, 1, 10}]
Out[369]= {Times, Rational, Times, Times, Times, Times, Times, Times, \
Times, Times}

**Definition 2**
**C**<sub>*MRB*</sub> is defined at [http://mathworld.wolfram.com/MRBConstant.html][172].
From MathWorld:
> ![MathWorld MRB][173] ![MathWorld MRB 2][174]
>
> SEE ALSO:
> GlaisherKinkelin Constant, Power Tower, Steiner's Problem
> REFERENCES:
> Burns, M. R. "An Alternating Series Involving n^(th) Roots." Unpublished note, 1999.
>
> Burns, M. R. "Try to Beat These MRB Constant Records!" http://community.wolfram.com/groups//m/t/366628.
>
> Crandall, R. E. "Unified Algorithms for Polylogarithm, LSeries, and Zeta Variants." 2012a.
> http://www.marvinrayburns.com/UniversalTOC25.pdf.
>
> Crandall, R. E. "The MRB Constant." §7.5 in Algorithmic Reflections: Selected Works. PSI Press, pp. 2829, 2012b.
>
> Finch, S. R. Mathematical Constants. Cambridge, England: Cambridge University Press, p. 450, 2003.
>
> Plouffe, S. "MRB Constant." http://pi.lacim.uqam.ca/piDATA/mrburns.txt.
>
> Sloane, N. J. A. Sequences A037077 in "The OnLine Encyclopedia of Integer Sequences."
>
> Referenced on WolframAlpha: MRB Constant
> CITE THIS AS:
> Weisstein, Eric W. "MRB Constant." From MathWorldA Wolfram Web Resource. https://mathworld.wolfram.com/MRBConstant.html
**How would we show that the any of the series in the above MathWorld definition are convergent, or even absolutely convergent?**

For "a"<sub>k</sub>=k<sup>1/k</sup>, given that the sequence is monotonically decreasing according to [Steiner's Problem][175], next, we would like to show (5) is the alternating sum of a sequence that converges to 0 monotonically and use the Alternating series test to see that it is conditionally convergent
Here is proof that 1 is the limit of "a" as k goes to infinity:
> ![enter image description here][176]
[Here][177] are many other proofs that 1 is the limit of "a" as k goes to infinity.
Thus, (k<sup>1/k</sup>1) is a monotonically decreasing and bounded below by 0 **sequence.**
If we want an absolutely convergent **series**, we can use (4).
S<sub>k</sub>![enter image description here][178] which, since the sum of the absolute values of the summands is finite, the sum converges absolutely!
There is no closedform for **C**<sub>*MRB*</sub> in the MathWorld definition; this could be due to the following: in [Mathematical Constants][179],(
Finch, S. R. Mathematical Constants, Cambridge, England: Cambridge University Press, p. 450), Steven Finch wrote that it is difficult to find an "exact formula" ([closedform solution][180]) for it.
> ![enter image description here][181]
![enter image description here][182]




RealWorld, and beyond, Applications
====================================
This section and the rest of the content of this first post were moved below to improve loading times. CNRL+F "RealWorld, and beyond, Applications" to finish reading it.
[1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=330pxMRB_messy.gif&userId=366611
[2]: https://community.wolfram.com//c/portal/getImageAttachment?filename=293pxMRBGif.gif&userId=366611
[3]: https://community.wolfram.com//c/portal/getImageAttachment?filename=tumblr_inline_pe4ta8y3zq1sejrrf_1280.png&userId=366611
[4]: https://community.wolfram.com//c/portal/getImageAttachment?filename=newton.JPG&userId=366611
[5]: https://community.wolfram.com//c/portal/getImageAttachment?filename=f5bb7221eef911827cbc628f5af64a053.jpeg&userId=366611
[6]: https://community.wolfram.com//c/portal/getImageAttachment?filename=euclid.JPG&userId=366611
[7]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Picture1.jpg&userId=366611
[8]: https://community.wolfram.com//c/portal/getImageAttachment?filename=58721.jpg&userId=366611
[9]: https://en.wikipedia.org/wiki/Monotone_convergence_theorem
[10]: https://en.wikipedia.org/wiki/Monotone_convergence_theorem
[11]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot20220927230939.png&userId=366611
[12]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot20220927231006.png&userId=366611
[13]: https://www.wolframcloud.com/obj/3b0e4c1b94464b919ef089f32d11774e
[14]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot20220927231037.png&userId=366611
[15]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot20220927231113.png&userId=366611
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[17]: https://mathoverflow.net/questions/44244/whatrecentdiscoverieshaveamateurmathematiciansmade
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[20]: https://community.wolfram.com//c/portal/getImageAttachment?filename=1ac.JPG&userId=366611
[21]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot20220813035505.jpg&userId=366611
[22]: https://community.wolfram.com//c/portal/getImageAttachment?filename=N.jpg&userId=366611
[23]: https://community.wolfram.com//c/portal/getImageAttachment?filename=L.jpg&userId=366611
[24]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot20220816112453.jpg&userId=366611
[25]: https://community.wolfram.com//c/portal/getImageAttachment?filename=o.jpg&userId=366611
[26]: https://hmong.in.th/wiki/MRB_constant
[27]: https://ar.wikipedia.org/wiki/%D9%82%D8%A7%D8%A6%D9%85%D8%A9_%D8%A7%D9%84%D8%AB%D9%88%D8%A7%D8%A8%D8%AA_%D8%A7%D9%84%D8%B1%D9%8A%D8%A7%D8%B6%D9%8A%D8%A9
[28]: https://fr.wikipedia.org/wiki/Constante_MRB
[29]: https://wikicro.icu/wiki/MRB_constant
[30]: https://www.amazon.com/exec/obidos/ASIN/193563819X/ref=nosim/ericstreasuretro
[31]: http://www.marvinrayburns.com/UniversalTOC25.pdf
[32]: https://enacademic.com/dic.nsf/enwiki/11755
[33]: http://web.archive.org/web/20081121134611/http://www.irancivilcenter.com/en/tools/units/math_const.php
[34]: http://etymologie.info/
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[36]: https://web.archive.org/web/20010616211903/http://pauillac.inria.fr/algo/bsolve/constant/itrexp/itrexp.html
[37]: https://pdfs.semanticscholar.org/f3dc/9f828442123015c5d52535fdefc0ab450bf5.pdf
[38]: https://web.archive.org/web/20210812083640/http://www.bitman.name/math/article/962
[39]: https://arxiv.org/pdf/0912.3844v3.pdf
[40]: http://ebyte.it/library/educards/constants/MathConstants.pdf
[41]: https://web.archive.org/web/20090702134146/http://www.turkbiyofizik.com/sabitler.html
[42]: https://mathworld.wolfram.com/MRBConstant.html
[43]: https://upwikizh.top/wiki/MRB_constant
[44]: https://ejje.weblio.jp/content/mrb+constant
[45]: https://ewikibg.top/wiki/MRB_constant
[46]: http://oeis.org/wiki/MRB_constant
[47]: https://ewikitl.top/wiki/mrb_constant
[48]: https://web.archive.org/web/20030415202103/http://pi.lacim.uqam.ca/eng/table_en.html
[49]: https://web.archive.org/web/20001210231700/http://www.lacim.uqam.ca/piDATA/mrburns.txt
[50]: https://oeis.org/A037077
[51]: https://en.wikipedia.org/wiki/MRB_constant
[52]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Capture9.PNG&userId=366611
[53]: https://community.wolfram.com//c/portal/getImageAttachment?filename=CaptureA.JPG&userId=366611
[54]: https://community.wolfram.com//c/portal/getImageAttachment?filename=3959Capture7.JPG&userId=366611
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[56]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Capturef.JPG&userId=366611
[57]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Capturef1a.JPG&userId=366611
[58]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Capturef1b.JPG&userId=366611
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[60]: https://community.wolfram.com//c/portal/getImageAttachment?filename=10297Capture.JPG&userId=366611
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[62]: https://math.stackexchange.com/questions/1673886/isthereamorerigorouswaytoshowthesetwosumsareexactlyequal
[63]: https://en.wikipedia.org/wiki/Riemann_series_theorem
[64]: https://www.math.ucdavis.edu/~hunter/intro_analysis_pdf/ch4.pdf
[65]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot20220829021145.jpg&userId=366611
[66]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot20220827002149.jpg&userId=366611
[67]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot20220918014843.jpg&userId=366611
[68]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot20220829032717.jpg&userId=366611
[69]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot20220829030101.jpg&userId=366611
[70]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot20220829030138.jpg&userId=366611
[71]: https://www.wolframcloud.com/obj/986a70e91d554e31bd7c87c24eec5d81
[72]: https://www.wolframcloud.com/obj/bmmmburns/Published/MRB_report_cards_16.nb
[73]: https://community.wolfram.com//c/portal/getImageAttachment?filename=106291.jpg&userId=366611
[74]: https://community.wolfram.com//c/portal/getImageAttachment?filename=62082.jpg&userId=366611
[75]: https://mathworld.wolfram.com/GelfondsConstant.html
[76]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot20220524013821.jpg&userId=366611
[77]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot20220628181753.jpg&userId=366611
[78]: https://www.wolframcloud.com/obj/bmmmburns/Published/5_11_2022.nb
[79]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot20220515005626.jpg&userId=366611
[80]: https://www.wolframcloud.com/obj/f51f1b470d8c46b6a13e1ca522a44ceb
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[82]: https://en.wikipedia.org/wiki/Oscillatory_integral
[83]: https://scholar.google.com/scholar?hl=en&as_sdt=0,15&q=%22MKB%20constant%22&btnG=
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[85]: https://community.wolfram.com//c/portal/getImageAttachment?filename=580910.JPG&userId=366611
[86]: http://community.wolfram.com/groups//m/t/1323951?p_p_auth=W3TxvEwH
[87]: https://community.wolfram.com//c/portal/getImageAttachment?filename=28491.JPG&userId=366611
[88]: https://community.wolfram.com//c/portal/getImageAttachment?filename=76812.JPG&userId=366611
[89]: https://community.wolfram.com//c/portal/getImageAttachment?filename=100173.JPG&userId=366611
[90]: https://community.wolfram.com//c/portal/getImageAttachment?filename=57664.JPG&userId=366611
[91]: https://community.wolfram.com//c/portal/getImageAttachment?filename=74665.JPG&userId=366611
[92]: https://community.wolfram.com//c/portal/getImageAttachment?filename=49236.JPG&userId=366611
[93]: https://community.wolfram.com//c/portal/getImageAttachment?filename=15127.JPG&userId=366611
[94]: https://community.wolfram.com//c/portal/getImageAttachment?filename=92858.JPG&userId=366611
[95]: https://community.wolfram.com//c/portal/getImageAttachment?filename=49309.JPG&userId=366611
[96]: https://community.wolfram.com//c/portal/getImageAttachment?filename=3.PNG&userId=366611
[97]: https://arxiv.org/abs/0912.3844
[98]: http://community.wolfram.com//c/portal/getImageAttachment?filename=Capturemkb2.JPG&userId=366611
[99]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot20220705020911.jpg&userId=366611
[100]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot20220705021130.jpg&userId=366611
[101]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot20220705022313.jpg&userId=366611
[102]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot20220731235917.jpg&userId=366611
[103]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot20220801001529.jpg&userId=366611
[104]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot20220801001459.jpg&userId=366611
[105]: https://www.wolframcloud.com/obj/88e5ed593d0e4a63abdfc48a053428cd
[106]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot20220814085504.jpg&userId=366611
[107]: https://community.wolfram.com//c/portal/getImageAttachment?filename=22421.JPG&userId=366611
[108]: https://community.wolfram.com//c/portal/getImageAttachment?filename=97362.JPG&userId=366611
[109]: https://community.wolfram.com//c/portal/getImageAttachment?filename=31093.JPG&userId=366611
[110]: https://community.wolfram.com//c/portal/getImageAttachment?filename=63064.JPG&userId=366611
[111]: https://community.wolfram.com/groups//m/t/1323951?p_p_auth=zHVSqCM8
[112]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot20220727141516.jpg&userId=366611
[113]: https://www.wolframcloud.com/obj/f876faa0c7284c16b68b65b02efcef93
[114]: https://www.researchgate.net/publication/309187705_Gelfond%27_s_Constant_using_MKB_constant_like_integrals
[115]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot20220503083042.jpg&userId=366611
[116]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot20220816204240.jpg&userId=366611
[117]: https://www.researchgate.net/publication/309187705sConstantusingMKBconstantlikeintegrals
[118]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot20220608111905.jpg&userId=366611
[119]: https://community.wolfram.com//c/portal/getImageAttachment?filename=73892.JPG&userId=366611
[120]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot20220816210900.jpg&userId=366611
[121]: https://community.wolfram.com//c/portal/getImageAttachment?filename=b2.JPG&userId=366611
[122]: https://bctp.berkeley.edu/extraD.html
[123]: https://physics.stackexchange.com/questions/5207/numberofdimensionsinstringtheoryandpossiblelinkwithnumbertheory
[124]: https://scholar.google.com/citations?hl=it&user=iDJ9f5gAAAAJ&view_op=list_works&sortby=pubdate
[125]: https://www.academia.edu/75884771
[126]: https://www.academia.edu/76084911
[127]: https://www.academia.edu/76405749
[128]: https://www.academia.edu/76784160
[129]: https://www.academia.edu/77164290
[130]: https://www.academia.edu/77752950
[131]: https://www.academia.edu/77752950
[132]: https://www.academia.edu/77978967
[133]: https://www.academia.edu/78104771
[134]: https://www.academia.edu/72576179
[135]: https://www.academia.edu/72674127
[136]: https://www.academia.edu/73043410
[137]: https://www.academia.edu/73201689
[138]: https://www.academia.edu/81812404/On_further_Ramanujans_continued_fractions_mathematical_connections_with_MRB_Constant_various_equations_concerning_some_sectors_of_String_Theory_XIX?
[139]: https://community.wolfram.com//c/portal/getImageAttachment?filename=ra.jpg&userId=366611
[140]: https://community.wolfram.com//c/portal/getImageAttachment?filename=r1.jpg&userId=366611
[141]: https://www.youtube.com/watch?v=y_F_TwgvNMA
[142]: https://www.academia.edu/search?q=%22MRB%20constant%22
[143]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot20220904201330.jpg&userId=366611
[144]: https://scholar.google.com/scholar?hl=en&as_sdt=0,15&q=%22MRB%20constant%22&btnG=
[145]: https://en.wikipedia.org/wiki/Richard_Crandall
[146]: https://scholar.google.com/scholar?hl=en&as_sdt=0,15&q=key%20fundamental%20constant%20zeta&btnG=
[147]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot20220502113359.jpg&userId=366611
[148]: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.695.5959&rep=rep1&type=pdf
[149]: https://www.marvinrayburns.com/UniversalTOC25.pdf
[150]: https://www2.mpiahd.mpg.de/~mathar/
[151]: https://arxiv.org/abs/0912.3844
[152]: https://pdfs.semanticscholar.org/f3dc/9f828442123015c5d52535fdefc0ab450bf5.pdf
[153]: https://web.archive.org/web/20120310223600/http://pi.lacim.uqam.ca/eng/records_en.html
[154]: https://community.wolfram.com//c/portal/getImageAttachment?filename=P1.JPG&userId=366611
[155]: https://community.wolfram.com//c/portal/getImageAttachment?filename=P2.JPG&userId=366611
[156]: https://community.wolfram.com//c/portal/getImageAttachment?filename=P3.JPG&userId=366611
[157]: https://community.wolfram.com//c/portal/getImageAttachment?filename=P5.JPG&userId=366611
[158]: http://marvinrayburns.com/Original_MRB_Post.html
[159]: https://community.wolfram.com//c/portal/getImageAttachment?filename=thumbnail%281%29.jpg&userId=366611
[160]: https://www.wolframcloud.com/obj/18c08d6babe94fbdb33a7e1167c9d243
[161]: https://community.wolfram.com//c/portal/getImageAttachment?filename=thumbnail%282%29.jpg&userId=366611
[162]: https://www.wolframcloud.com/obj/0b304705ed144c6bbd27fda9ff29536d
[163]: https://www.wolframcloud.com/obj/bmmmburns/Published/44%20hour%20million.nb
[164]: https://www.wolframcloud.com/obj/bmmmburns/Published/36%20hour%20million.nb
[165]: https://www.wolframcloud.com/obj/bmmmburns/Published/35%20hour%20million.nb
[166]: https://en.wikipedia.org/wiki/MRB_constant
[167]: https://en.wikipedia.org/wiki/MRB_constant
[168]: https://community.wolfram.com//c/portal/getImageAttachment?filename=w1.jpg&userId=366611
[169]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot20220424021607.jpg&userId=366611
[170]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot20220428212004.jpg&userId=366611
[171]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot20220427102212.jpg&userId=366611
[172]: http://mathworld.wolfram.com/MRBConstant.html
[173]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Capture30.JPG&userId=366611
[174]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot20211114113747.png&userId=366611
[175]: https://mathworld.wolfram.com/SteinersProblem.html
[176]: https://community.wolfram.com//c/portal/getImageAttachment?filename=limit_nto1on_eq1.jpg&userId=366611
[177]: https://math.stackexchange.com/questions/115822/howtoshowthatlimntoinftynfrac1n1
[178]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot20220404014455.jpg&userId=366611
[179]: https://www.amazon.com/exec/obidos/ASIN/0521818052/ref=nosim/ericstreasuretro
[180]: https://mathworld.wolfram.com/ClosedFormSolution.html#:~:text=An%20equation%20is%20said%20to,not%20be%20considered%20closedform.
[181]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot20220408065337.jpg&userId=366611
[182]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot20220506204151.jpg&userId=366611
Marvin Ray Burns
20141009T18:08:49Z

I'm having trouble interacting with Wolfram in Python
https://community.wolfram.com/groups//m/t/2625169
I have some tough problems:
As shown in Figure_1. How to use the Global.x in wlexpr( )?
![enter image description here][1]
Further more. As shown in Figure_2.
How to use python's interface "wl" to represent the "f" in this expression?
![enter image description here][2]
[1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Figure_1.png&userId=2625135
[2]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Figure_2.png&userId=2625135
Xiaochuan Wang
20220928T02:22:32Z

[GiF] Animating hurricane Ian satellite images and forecast cone
https://community.wolfram.com/groups//m/t/2624485
![enter image description here][1]
&[Wolfram Notebook][2]
[1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Ian_lead.gif&userId=20103
[2]: https://www.wolframcloud.com/obj/d48a4fd0ea704698b1bd3e44d352e9f2
Arnoud Buzing
20220927T19:09:12Z

[WSG22] Daily Study Group: Introduction to Elementary Algebra
https://community.wolfram.com/groups//m/t/2612270
A Wolfram U daily study group introducing and exploring the basic concepts in algebra begins on September 26, 2022. In order to better accommodate students, this study group will meet at **3:00PM** Central US time rather than the usual start time.
Join a cohort of fellow students in an enriching online community to learn algebra and prepare for further mathematics and statistics courses. This course starts with an explanation of the fundamental math operations and progresses to lessons on the order of operations, word problems, systems of equations and inequalities, polynomials and more. The study group also explores how the Wolfram Language can be used to help understand and reinforce algebraic problemsolving skills.
The Introduction to Elementary Algebra interactive course will soon be added to the Wolfram U catalog, and this Study Group offers early access to course lessons and resources, including the instructor (*i.e.* me)! This Study Group is aimed primarily at students, and the aforementioned meeting time reflects that. Moreover, **no prior mathematics or Wolfram Language experience is required.**
You can [**register here**][1]. I hope to see you there!
![Wolfram U Banner][2]
[1]: https://www.bigmarker.com/series/dailystudygroupintrotoelementaryalgebra/series_details?utm_bmcr_source=Community
[2]: https://community.wolfram.com//c/portal/getImageAttachment?filename=WolframUBanner%281%29.jpeg&userId=1711324
Arben Kalziqi
20220907T05:04:19Z

Golden polyhedra: five basic rhombic polyhedra
https://community.wolfram.com/groups//m/t/2624764
![enter image description here][1]![enter image description here][2]
&[Wolfram Notebook][3]
[1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=gif1_small.gif&userId=20103
[2]: https://community.wolfram.com//c/portal/getImageAttachment?filename=gif2_small.gif&userId=20103
[3]: https://www.wolframcloud.com/obj/be30e825869145ad92340b5b9a973310
Sandor Kabai
20220927T15:57:24Z

Sparse matrices with named rows and columns (Python)
https://community.wolfram.com/groups//m/t/2624461
&[Wolfram Notebook][1]
[1]: https://www.wolframcloud.com/obj/1a2055dc5e7d44df9a22da7a69f524bb
Anton Antonov
20220927T13:37:31Z

Voting communities in the UN general assembly
https://community.wolfram.com/groups//m/t/2622627
![enter image description here][1]
&[Wolfram Notebook][2]
*Also available [here][3].*
[1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=lead_geo.gif&userId=20103
[2]: https://www.wolframcloud.com/obj/5e19bb40c15f45f786077e874552aa65
[3]: https://christopherwolfram.com/projects/unvotingmodularity/
Christopher Wolfram
20220924T07:22:46Z

Why would I want to use paclets?
https://community.wolfram.com/groups//m/t/2624417
I didn't find any information about the why of paclets. How would they help me as a problem solving user? Would it help organize my library of functions?
Ernst Huijer
20220927T09:17:45Z

[WSS22] Analogs to elementary cellular automata on alternative tilings
https://community.wolfram.com/groups//m/t/2576045
&[Wolfram Notebook][1]
[1]: https://www.wolframcloud.com/obj/70ab74bc780e44ad9d49a0359b4eb74d
Chase Marangu
20220720T00:19:06Z

How to create a symmetry function
https://community.wolfram.com/groups//m/t/2623563
Hi,
I am new learner for Mathematica mainly following video and notebooks from Prof. Nikolay Gromov.
So I am trying to reproduce the Matrix calculation using orthogonal polynomial methods here http://msstp.org/sites/default/files/ProblemSet2_RandomMatricesOrthogonalPolynomials_Solutions_0.pdf . However, I am unable to reproduce the same result below. I try some changes but ultimately not the result wanted. Appreciate if anyone could give some hints? Thanks a lot.
![enter image description here][1]
[1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=test.png&userId=2623549
Clement Wong
20220926T18:04:51Z

Tables on Community and markdown ?
https://community.wolfram.com/groups//m/t/763005
I didn't find a way to create a table to list the options in the posting. Is there a way to do so?
Diego Zviovich
20151222T22:05:10Z

Parsing markdown files
https://community.wolfram.com/groups//m/t/2142852
![Symbolic Markdown Expression Graph][1]
&[Wolfram Notebook][2]
[Original]: https://www.wolframcloud.com/obj/wolframcommunity/Published/ParsingMarkdownFiles_5.nb
[1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=ScreenShot20201220at12.13.28AM.png&userId=1593884
[2]: https://www.wolframcloud.com/obj/672a6b0b095b41f49413feb2bfaeae10
Faizon Zaman
20201220T04:31:28Z

Intersection polyhedron of rotated Platonic solids: curious observation
https://community.wolfram.com/groups//m/t/2624111
![enter image description here][1]
&[Wolfram Notebook][2]
[1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Lead_GiF.gif&userId=20103
[2]: https://www.wolframcloud.com/obj/b032a934a04a4904bb80342f4d9668f2
Michael Trott
20220926T21:33:39Z

Issue with GeoGraphics using a variable
https://community.wolfram.com/groups//m/t/2623715
I'm working on a `GeoGraphics` plot of hurricane wind field data, which I have set up as the following (first two values are the lat and lng, the rest are values for the chart).
forecast = {
{19.1, 82.7, 20, 0, 0, 0, 40, 40, 0, 30, 100, 80, 40, 90},
{20.7, 83.5, 20, 20, 15, 20, 50, 50, 30, 40, 110, 100, 60, 100},
{22.7, 84.0, 25, 25, 20, 20, 60, 50, 40, 50, 130, 120, 80, 110},
{24.5, 84.0, 30, 30, 25, 25, 70, 60, 50, 60, 140, 130, 100, 130},
{26.1, 83.8, 40, 40, 30, 35, 80, 70, 60, 70, 160, 140, 110, 150},
{27.2, 83.5, 0, 0, 0, 0, 80, 70, 60, 70, 180, 130, 120, 150},
{28.0, 83.2, 0, 0, 0, 0, 90, 50, 60, 80, 180, 130, 120, 150}
}
If I use the following, I get a chart just fine:
GeoGraphics[
{
Red,
GeoDisk[{forecast[[1]][[1]], forecast[[1]][[2]]},
Quantity[forecast[[1]][[3]], "nmi"], {0, 90}],
GeoDisk[{forecast[[1]][[1]], forecast[[1]][[2]]},
Quantity[forecast[[1]][[4]], "nmi"], {90, 180}],
GeoDisk[{forecast[[1]][[1]], forecast[[1]][[2]]},
Quantity[forecast[[1]][[5]], "nmi"], {180, 270}],
GeoDisk[{forecast[[1]][[1]], forecast[[1]][[2]]},
Quantity[forecast[[1]][[6]], "nmi"], {270, 360}],
Yellow,
GeoDisk[{forecast[[1]][[1]], forecast[[1]][[2]]},
Quantity[forecast[[1]][[7]], "nmi"], {0, 90}],
GeoDisk[{forecast[[1]][[1]], forecast[[1]][[2]]},
Quantity[forecast[[1]][[8]], "nmi"], {90, 180}],
GeoDisk[{forecast[[1]][[1]], forecast[[1]][[2]]},
Quantity[forecast[[1]][[9]], "nmi"], {180, 270}],
GeoDisk[{forecast[[1]][[1]], forecast[[1]][[2]]},
Quantity[forecast[[1]][[10]], "nmi"], {270, 360}],
Blue,
GeoDisk[{forecast[[1]][[1]], forecast[[1]][[2]]},
Quantity[forecast[[1]][[11]], "nmi"], {0, 90}],
GeoDisk[{forecast[[1]][[1]], forecast[[1]][[2]]},
Quantity[forecast[[1]][[12]], "nmi"], {90, 180}],
GeoDisk[{forecast[[1]][[1]], forecast[[1]][[2]]},
Quantity[forecast[[1]][[13]], "nmi"], {180, 270}],
GeoDisk[{forecast[[1]][[1]], forecast[[1]][[2]]},
Quantity[forecast[[1]][[14]], "nmi"], {270, 360}]
}, GeoRange > Quantity[500, "NauticalMiles"]
]
However, if I replace the first value with a variable, say `a`, and plot, it fails.
a>1;
GeoGraphics[
{
Red,
GeoDisk[{forecast[[a]][[1]], forecast[[a]][[2]]},
Quantity[forecast[[a]][[3]], "nmi"], {0, 90}],
GeoDisk[{forecast[[a]][[1]], forecast[[a]][[2]]},
Quantity[forecast[[a]][[4]], "nmi"], {90, 180}],
GeoDisk[{forecast[[a]][[1]], forecast[[a]][[2]]},
Quantity[forecast[[a]][[5]], "nmi"], {180, 270}],
GeoDisk[{forecast[[a]][[1]], forecast[[a]][[2]]},
Quantity[forecast[[a]][[6]], "nmi"], {270, 360}],
Yellow,
GeoDisk[{forecast[[a]][[1]], forecast[[a]][[2]]},
Quantity[forecast[[a]][[7]], "nmi"], {0, 90}],
GeoDisk[{forecast[[a]][[1]], forecast[[a]][[2]]},
Quantity[forecast[[a]][[8]], "nmi"], {90, 180}],
GeoDisk[{forecast[[a]][[1]], forecast[[a]][[2]]},
Quantity[forecast[[a]][[9]], "nmi"], {180, 270}],
GeoDisk[{forecast[[a]][[1]], forecast[[a]][[2]]},
Quantity[forecast[[a]][[10]], "nmi"], {270, 360}],
Blue,
GeoDisk[{forecast[[a]][[1]], forecast[[a]][[2]]},
Quantity[forecast[[a]][[11]], "nmi"], {0, 90}],
GeoDisk[{forecast[[a]][[1]], forecast[[a]][[2]]},
Quantity[forecast[[a]][[12]], "nmi"], {90, 180}],
GeoDisk[{forecast[[a]][[1]], forecast[[a]][[2]]},
Quantity[forecast[[a]][[13]], "nmi"], {180, 270}],
GeoDisk[{forecast[[a]][[1]], forecast[[a]][[2]]},
Quantity[forecast[[a]][[14]], "nmi"], {270, 360}]
}, GeoRange > Quantity[500, "NauticalMiles"]
]
Part::pkspec1: The expression a cannot be used as a part specification.
Part::pkspec1: The expression a cannot be used as a part specification.
Part::pkspec1: The expression a cannot be used as a part specification.
General::stop: Further output of Part::pkspec1 will be suppressed during this calculation.
Part::partw: Part 3 of forecast[[a]] does not exist.
Part::partw: Part 4 of forecast[[a]] does not exist.
Part::partw: Part 5 of forecast[[a]] does not exist.
General::stop: Further output of Part::partw will be suppressed during this calculation.
GeoDisk::cntr: {forecast, a} is not a valid center location.
GeoDisk::cntr: {forecast, a} is not a valid center location.
GeoDisk::cntr: {forecast, a} is not a valid center location.
General::stop: Further output of GeoDisk::cntr will be suppressed during this calculation.
Out[2]= GeoGraphics[Graphics, GeoBackground > {GeoStyling[StreetMapNoLabels], GeoStyling[VectorLabels]},
> GeoCenter > GeoPosition[{28.02, 82.14}], GeoGridLines > None, GeoGridLinesStyle > GrayLevel[0.4, 0.3],
> GeoProjection > {LambertAzimuthal, Centering > GeoPosition[{28.02, 82.14}]},
> GeoRange > {{19.6594, 36.3705}, {91.5651, 72.7149}}, GeoRangePadding > Full, GeoResolution > Automatic,
> GeoServer > {Automatic}, GeoZoomLevel > 6,
> MetaInformation >
> <GeoMetaInformation >
> <Attribution >
> Hyperlink[Wolfram Knowledgebase, https://www.wolfram.com/],
> Hyperlink[⌐ MapTiler, https://www.maptiler.com/copyright/],
> Hyperlink[⌐ OpenStreetMap contributors, https://www.openstreetmap.org/copyright],
> AttributionType > Tooltip, GeoModel > ITRF00, LonLatBox > {{93.1605, 71.1195}, {19.3397, 36.6857}},
> PlotRange > {{0.155062, 0.155062}, {0.145791, 0.1511}},
> Projection > {LambertAzimuthal, Centering > GeoPosition[{28.02, 82.14}],
> LongitudeDetermination > 82.14}, Software > Created with the Wolfram Language: www.wolfram.com,
> TileSources > {Wolfram, OSM, MapTiler}>>]
Steven Buehler
20220926T17:39:49Z

Clear all variables defined in a given cell
https://community.wolfram.com/groups//m/t/2623005
Based on the suggested method [here](https://mathematica.stackexchange.com/questions/155643/isitpossibletoclearallvariablesdefinedinagivencell), I try to clear all variables defined in a given cell as follows:
In[281]:= SelectionMove[EvaluationNotebook[],All,EvaluationCell];Options[NotebookSelection[EvaluationNotebook[]],CellLabel]
{cell} = Cells@@%
ClearAll[#] & /@
Cases[NotebookRead[cell], HoldPattern[RowBox[{sym_, "=", _}]] :> sym,
Infinity];
gen2=SGGenSet229me[[2,1;;3,1;;3]];
ubasSG229me//FactorMatrix//Last//Inverse//HermiteDecomposition//Last
(*
tmInv is one of the bases of SG229me
*)
tmInv=TMSG229meToITA[[1;;3,1;;3]]//Inverse;
%//HermiteDecomposition//Last
G=Transpose[tmInv] . tmInv
%==Transpose[gen2] . G . gen2
(*
tm is the transformation matrix which convert the representation of this group to an orthogonal basis
*)
tm=tmInv//Inverse
conjgen2=noTranSGGenSet229meToITA[[2,1;;3,1;;3]]
Inverse[tm] . gen2 . tm==conjgen2
conj//OrthogonalMatrixQ
(*
The metric change under changeofbasis
*)
Transpose[tm] . G . tm == IdentityMatrix[3]
{valgen2,vecgen2}=Eigensystem[gen2]
{valconjgen2,vecconjgen2}=Eigensystem[conjgen2]
Out[281]= {CellLabel > "In[281]:="}
Out[282]= {
CellObject[
"09eef945c108482ca081f7198678f646",
"7e18a8bb14fb460e8275756c0388fd0c"]}
During evaluation of In[281]:= ClearAll::ssym: RowBox[{{,RowBox[{valgen2,,,vecgen2}],}}] is not a symbol or a string.
During evaluation of In[281]:= ClearAll::ssym: RowBox[{{,RowBox[{valconjgen2,,,vecconjgen2}],}}] is not a symbol or a string.
Out[285]= {{1/2, 1/2, 1/2}, {0, 2, 0}, {0, 0, 2}}
Out[287]= {{1/2, 1/2, 1/2}, {0, 2, 0}, {0, 0, 2}}
Out[288]= {{11/4, (5/4), (5/4)}, {(5/4), 11/
4, (5/4)}, {(5/4), (5/4), 11/4}}
Out[289]= True
Out[290]= {{1, 1/2, 1/2}, {1/2, 1, 1/2}, {1/2, 1/2, 1}}
Out[291]= {{0, 1, 0}, {1, 0, 0}, {0, 0, 1}}
Out[292]= True
Out[293]= True
Out[294]= True
Out[295]= {{1,
I, I}, {{1/2, 1/2, 1}, {3/2  I/2, 3/2 + I/2, 1}, {3/2 + I/2,
3/2  I/2, 1}}}
Out[296]= {{1, I, I}, {{0, 0, 1}, {I, 1, 0}, {I, 1, 0}}}
As you can see, this method will trigger the following warning messages:
During evaluation of In[281]:= ClearAll::ssym: RowBox[{{,RowBox[{valgen2,,,vecgen2}],}}] is not a symbol or a string.
During evaluation of In[281]:= ClearAll::ssym: RowBox[{{,RowBox[{valconjgen2,,,vecconjgen2}],}}] is not a symbol or a string.
Any tips for fixing this problem?
Regards,
Zhao
Hongyi Zhao
20220924T23:56:17Z

Why does RegionCentroid crash on 2DPolygons (WL V13.1)?
https://community.wolfram.com/groups//m/t/2615236
Use the following code which is copied from the reference documentation for [RegionCentroid][1]
reg = Polygon[{{0, 0}, {1, 0}, {1.5, 0.5}, {1, 1}, {0, 1}, {0.5, 0.5}}];
RegionCentroid[reg]
This crashes with a Beep and an unitialized kernel and nothing else. No error message.
[1]: https://reference.wolfram.com/language/ref/RegionCentroid.html?q=RegionCentroid
Werner Geiger
20220912T12:52:15Z

Break ParallelTable once a valid result is obtained.
https://community.wolfram.com/groups//m/t/2623367
See my code snippet below:
In[1539]:= Clear[sVecTM,TM];
ParallelTable[
lTM=tm;
sVecTM=Array[Subscript[x, #]&,{3}];
TM=AffineTransform[{lTM,sVecTM}]//TransformationMatrix;
(*gen2=SG229me[[5]]*)
gen2=i;
lgen2=gen2[[1;;3,1;;3]];
xx=Select[ SGITA229, #[[1;;3,1;;3]]==Inverse[lTM] . lgen2 . lTM && #[[1;;3,4]]!={0,0,0}&]//First;
If[Length[xx]>0,
sol=Solve[ gen2 . TM == TM . xx, Flatten[sVecTM], Rationals ];
If [ Length[sol] > 0 && Length[sol//First]==3,
TM=TM/.sol//First;
If[ SetEqualQ[AMTConjOnRight[SGGenSet229me,TM]//AMTSpaceGroupOnLeft//First, SGITA229]
,TM]
]
]
,{i,SG229me}]
(kernel 43) Solve::svars : Equations may not give solutions for all "solve" variables.
(kernel 7) Solve::svars : Equations may not give solutions for all "solve" variables.
(kernel 10) Solve::svars : Equations may not give solutions for all "solve" variables.
(kernel 11) Solve::svars : Equations may not give solutions for all "solve" variables.
(kernel 15) Solve::svars : Equations may not give solutions for all "solve" variables.
(kernel 16) Solve::svars : Equations may not give solutions for all "solve" variables.
(kernel 18) Solve::svars : Equations may not give solutions for all "solve" variables.
(kernel 25) Solve::svars : Equations may not give solutions for all "solve" variables.
(kernel 33) Solve::svars : Equations may not give solutions for all "solve" variables.
(kernel 36) Solve::svars : Equations may not give solutions for all "solve" variables.
(kernel 40) Solve::svars : Equations may not give solutions for all "solve" variables.
(kernel 41) Solve::svars : Equations may not give solutions for all "solve" variables.
(kernel 2) Solve::svars : Equations may not give solutions for all "solve" variables.
(kernel 18) Solve::svars : Equations may not give solutions for all "solve" variables.
(kernel 36) Solve::svars : Equations may not give solutions for all "solve" variables.
(kernel 29) Solve::svars : Equations may not give solutions for all "solve" variables.
(kernel 40) Solve::svars : Equations may not give solutions for all "solve" variables.
(kernel 1) Solve::svars : Equations may not give solutions for all "solve" variables.
(kernel 16) Solve::svars : Equations may not give solutions for all "solve" variables.
(kernel 31) Solve::svars : Equations may not give solutions for all "solve" variables.
(kernel 6) Solve::svars : Equations may not give solutions for all "solve" variables.
(kernel 21) Solve::svars : Equations may not give solutions for all "solve" variables.
(kernel 27) Solve::svars : Equations may not give solutions for all "solve" variables.
(kernel 3) Solve::svars : Equations may not give solutions for all "solve" variables.
(kernel 13) Solve::svars : Equations may not give solutions for all "solve" variables.
(kernel 37) Solve::svars : Equations may not give solutions for all "solve" variables.
Out[1540]= {Null, Null, Null, Null, {{1, 1/2, 1/2, (3/8)}, {1/2, 1,
1/2, (3/8)}, {1/2, 1/2, 1, (3/8)}, {0, 0, 0,
1}}, Null, Null, Null, Null, Null, {{1, 1/2, 1/2, (3/8)}, {1/2, 1,
1/2, (3/8)}, {1/2, 1/2, 1, (3/8)}, {0, 0, 0,
1}}, Null, Null, {{1, 1/2, 1/2, (3/8)}, {1/2, 1, 1/2, (3/8)}, {1/
2, 1/2, 1, (3/8)}, {0, 0, 0,
1}}, Null, Null, Null, Null, Null, {{1, 1/2, 1/2, (3/8)}, {1/2, 1,
1/2, (3/8)}, {1/2, 1/2, 1, (3/8)}, {0, 0, 0,
1}}, Null, Null, {{1, 1/2, 1/2, (3/8)}, {1/2, 1, 1/2, (3/8)}, {1/
2, 1/2, 1, (3/8)}, {0, 0, 0, 1}}, Null, {{1, 1/2, 1/
2, (3/8)}, {1/2, 1, 1/2, (3/8)}, {1/2, 1/2, 1, (3/8)}, {0, 0, 0,
1}}, Null, {{1, 1/2, 1/2, (3/8)}, {1/2, 1, 1/2, (3/8)}, {1/2, 1/
2, 1, (3/8)}, {0, 0, 0,
1}}, Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, \
Null, Null, {{1, 1/2, 1/2, (3/8)}, {1/2, 1, 1/2, (3/8)}, {1/2, 1/2,
1, (3/8)}, {0, 0, 0, 1}}, {{1, 1/2, 1/2, (3/8)}, {1/2, 1, 1/
2, (3/8)}, {1/2, 1/2, 1, (3/8)}, {0, 0, 0,
1}}, Null, Null, Null, Null, Null, Null, Null, Null, {{1, 1/2, 1/
2, (3/8)}, {1/2, 1, 1/2, (3/8)}, {1/2, 1/2, 1, (3/8)}, {0, 0, 0,
1}}, Null, Null, {{1, 1/2, 1/2, (3/8)}, {1/2, 1, 1/
2, (3/8)}, {1/2, 1/2, 1, (3/8)}, {0, 0, 0, 1}}, Null, Null, {{1,
1/2, 1/2, (3/8)}, {1/2, 1, 1/2, (3/8)}, {1/2, 1/2,
1, (3/8)}, {0, 0, 0,
1}}, Null, Null, Null, Null, Null, Null, Null, {{1, 1/2, 1/
2, (3/8)}, {1/2, 1, 1/2, (3/8)}, {1/2, 1/2, 1, (3/8)}, {0, 0, 0,
1}}, Null, {{1, 1/2, 1/2, (3/8)}, {1/2, 1, 1/2, (3/8)}, {1/2, 1/
2, 1, (3/8)}, {0, 0, 0,
1}}, Null, Null, Null, Null, Null, Null, {{1, 1/2, 1/
2, (3/8)}, {1/2, 1, 1/2, (3/8)}, {1/2, 1/2, 1, (3/8)}, {0, 0, 0,
1}}, Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, \
Null}
I want to eliminate the invalid results displayed as **Null** and **Break** the **ParallelTable** command once a valid result is obtained, which is, in the above example, the 5th entry in the result table. Any tips for achieving this goal?
Regards,
Zhao
Hongyi Zhao
20220926T09:59:45Z

Terminology of mathematics by computer
https://community.wolfram.com/groups//m/t/1343869
PM. This is a short essay, that has been included in the May 23 2018 update for this notebook and package:
http://community.wolfram.com/groups//m/t/1313302
Mathematics concerns patterns and can involve anything, so that we need flexibility in our tools when we do or use mathematics. In the dawn of mankind we used stories. When writing was invented we used pen and paper. It is a revolution for mankind, comparable to the invention of the wheel and the alphabet, that we now can do mathematics using a computer. Many people focus on the computer and would say that it is a computer revolution, but computers might also generate chaos, which shows that the true relevance comes from structured use.
I regard mathematics by computer as a twosided coin, that involves both human thought (supported by tools) and what technically happens within a computer. The computer language (software) is the interface between the human mind and the hardware with the flow of electrons, photons or whatever (I am no physicist). We might hold that thought is more fundamental, but this is of little consequence, since we still need consistency that 1+1 = 2 in math also is 1+1 = 2 in the computer, and properly interfaced by the language that would have 1+1 = 2 too. The clearest expression of mathematics by computer is in "computer algebra" languages, that understand what this revolution for mankind is about, and which were developed for the explicit support of doing mathematics by computer.
The makers of Mathematica (WRI) might be conceptually moving to regarding computation itself as a more fundamental notion than mathematics or the recognition and handling of patterns. Perhaps in their view there would be no such twosided coin. The brain might be just computation, the computer would obviously be computation, and the language is only a translator of such computations. The idea that we are mainly interested in the structured products of the brain could be less relevant.
Stephen Wolfram by origin is a physicist and the name "Mathematica" comes from Newton's book and not from "mathematics" itself, though Newton made that reference. Stephen Wolfram obviously has a long involvement with cellular automata, culminating in his New Kind of Science. Wolfram (2013) distinguishes Mathematica as a computer program from the language that the program uses and is partially written in. Eventually he settled for the term "Wolfram language" for the computer language that he and WRI use, like "English" is the language used by the people in England (codified by their committees on the use of the English language).
My inclination however was to regard "Mathematica" primarily as the name of the language that happened to be evaluated by the program of the same name. I compared Mathematica to Algol and Fortran. I found Wolfram's AddisonWesley book title in 1991 & 1998 "Mathematica. A system for doing mathematics by computers" as quite apt. Obviously the system consists of the language and the software that runs it, but the latter might be provided by other providers too, like Fortran has different compilers. Every programmer knows that the devil is in the details, and that a language documentation on paper might not give the full details of actually running the software. Thus when there are not more software providers then it is only accurate to state the the present definition of the language is given precisely by the one program that runs it. This is only practical and not fundamental. In this situation there is no conflict in thinking of "Mathematica as the language of Mathematica". Thus in my view there is no need to find a new name for the language. I thought that I was using a language but apparently in Wolfram's recent view the emphasis was on the computer program. I didn't read Wolfram's blog in 2013 and otherwise might have given this feedback.
Wolfram (2017) and (2018) uses the terms "computational essay" and "computational thinking" while the latter is used such that he apparently intends this to mean something like (my interpretation): programming in the Wolfram Language, using internet resources, e.g. the cloud and not necessarily the standalone version of Mathematica or now also Wolfram Desktop. My impression is that Wolfram indeed emphasizes computation, and that he perhaps also wants to get rid of a popular confusion of the name "Mathematica" with mathematics only. Apparently he doesn't want to get rid of that name altogether, likely given his involvement in its history and also its fine reputation.
A related website is https://www.computerbasedmath.org (CBM) by Conrad Wolfram. Most likely Conrad adopts Stephen's view on computation. It might also be that CBM finds the name "Mathematica" disinformative, as educators (i) may be unaware of what this language and program is, (ii) may associate mathematics with pen and paper, and (iii) would pay attention however at the word "computer". Perhaps CBM also thinks: You better adopt the language of your audience than teach them to understand your terminology on the history of Mathematica.
I am not convinced by these recent developments. I still think: (1) that this is a twosided coin (but I am no physicist and do no know about electrons and such), (2) that it is advantageous to clarify to the world: (2a) that mathematics can be used for everything, and (2b) that doing mathematics by computer is a revolution for mankind, and (3) that one should beware of people without didactic training who want to ship computer technology into the classroom. My suggestion to Stephen Wolfram remains, as I did before in (2009, 2015a), that he turns WRI into a public utility like those that exist in Holland  while it already has many characteristics of this. It is curious to see the open source initiatives that apparently will not use the language of Mathematica, now by WRI (also) called the Wolfram Language, most likely because of copyright fears even while it is good mathematics.
Apparently there are legal concerns (but I am no lawyer) that issues like 1+1 = 2 or \[Pi] are not under copyright, but that choices for software can be. For example the use of h[x] with square brackets rather than parentheses h(x), might be presented to the copyright courts as a copyright issue. This is awkward, because it is good didactics of mathematics to use the square brackets. Not only computers but also kids may get confused by expressions a(2 + b) and f(x + h)  f(x). Let me refer to my suggestion that each nation sets up its own National Center for Mathematics Education. Presently we have a jungle that is no good for WRI, no good for the open source movement (e.g. R or https://www.python.org or http://jupyter.org), and especially no good for the students. Everyone will be served by clear distinctions between (i) what is in the common domain for mathematics and education of mathematics (the language) and (ii) what would be subject to private property laws (programs in that language, interpreters and compilers for the language) (though such could also be placed into the common domain).
Colignatus, Th. (2009, 2015a), Elegance with Substance,
(1) website: http://thomascool.eu/Papers/Math/Index.html
(2) PDF on Zenodo: https://zenodo.org/record/291974
Wolfram, S. (1991, 1998), Mathematica. A system for doing mathematics by computer, 2nd edition, AddisonWesley
Wolfram, S. (2013), What Should We Call the Language of Mathematica?, http://blog.stephenwolfram.com/2013/02/whatshouldwecallthelanguageofmathematica/
Wolfram, S. (2017), What Is a Computational Essay?, http://blog.stephenwolfram.com/2017/11/whatisacomputationalessay/
Wolfram, S. (2018), Launching the Wolfram Challenges Site, http://blog.stephenwolfram.com/2017/11/whatisacomputationalessay/
Thomas Colignatus
20180523T10:29:27Z

Data collector using SQL operators package
https://community.wolfram.com/groups//m/t/2619525
&[Wolfram Notebook][1]
[1]: https://www.wolframcloud.com/obj/aa72f721ee9e4730a813f1803af5215c
Damian Calin
20220919T19:25:41Z