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Package import error: symbol is protected and cannot be removed
https://community.wolfram.com/groups//m/t/2824611
Dear all
I am using a mathematica package SARAH. When I load the package on mathematica, it does not load it properly. It seems like mathematica cannot reach some of its files or subdirectories. I have attached a notebook which shows errors. I can provide further information if required.
Zohaib Aarfi
20230206T14:35:13Z

Which[] calling Main Evaluate  can this be avoided?
https://community.wolfram.com/groups//m/t/2823162
Would not seem that Which[] would be a problem in compiling functions, but it's doing a call to Main Evaluate  its obviously on the list of compiled functions and pretty basic. Running the simple code below illustrates it (in v13.1). Its does not happen with If[] as one would expect. Really like to use Which[], but can a call to Main Evaluate be avoided?
Thanks in advance.
<< CompiledFunctionTools`;
fun = Compile[{{k, _Integer}, {u, _Real}},
Which[k == 1, u + 1, k == 2, u + 4]];
funIf = Compile[{{k, _Integer}, {u, _Real}}, If[k == 1, u + 1, u + 4]];
fun[1, 2]
funIf[1, 2]
CompilePrint[funIf]
CompilePrint[fun]
For Which [] the result without the header is
I0 = A1
R0 = A2
Result = R1
R1=MainEvaluate[Function[{k,u},Which[k==1,u+1,k==2,u+4]][I0,R0]]
Return
and for IF the result without the header is
I0 = A1
R0 = A2
I2 = 4
I1 = 1
Result = R1
B0=I0==I1
2 if[!B0] goto 7
3 R1=I1
4 R2=R0+R1
5 R1=R2
6 goto 10
7 R1=I2
8 R3=R0+R1
9 R1=R3
10 Return
Neal Maroney
20230203T19:44:02Z

[WSG23] Daily Study Group: Wolfram Language Basics
https://community.wolfram.com/groups//m/t/2774101
A Wolfram U daily study group covering the implementation of Wolfram Language for tasks ranging from basic programming to video analysis begins on January 17, 2023 and runs through February 3. This study group will run on weekdays from 11:00AM–12:00PM Central US time.
This study group is an incredible way either to start learning Wolfram Language or to explore new functionality you haven't yet used. We will cover a very broad variety of topics, including but not limited to image and sound analysis, symbolics and numerics, function visualization and even cloud computation and deployment. We will even cover useful tips and tricks to help you work efficiently with notebooks!
![enter image description here][1]
**No prior Wolfram Language experience is necessary.** As usual, we will have questions, study materials, quizzes along the way to help you master the subject matter.
You can [**REGISTER HERE**][2]. I hope to see you there!
![enter image description here][3]
[1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=meechstogram.png&userId=1711324
[2]: https://www.bigmarker.com/series/dailystudygroupwolframlanguagebasicswsg34/series_details?utm_bmcr_source=community
[3]: https://community.wolfram.com//c/portal/getImageAttachment?filename=WolframUBanner%281%29%281%29.jpeg&userId=1711324
Arben Kalziqi
20230111T04:29:36Z

Get the citation management package in Mathematica for MacOS?
https://community.wolfram.com/groups//m/t/1194058
Neither citation management package nor functionality seem to be available in Mathematica for MacOS.
[Mathematica Documentation: Citation Management][1] says that "Currently this functionality is only available on Windows." I read from Mathematica Meta Stack Exchange [post][2] that Presentation package by David Park contains a subpackage for citation management. Unfortunately this Presentation package is no longer available or sold.
I basically need two functionalities: 1. Create a bibliography from BibTeX or any similar format; 2.Create references to a bibliography.
I have looked through many forums like Mathematica Stack Exchange however there seem to be no simple solution.
For Mac users, how do you circumvent citation management issue?
[1]: http://reference.wolfram.com/language/tutorial/CitationManagement.html
[2]: https://mathematica.meta.stackexchange.com/questions/1770/whereisdavidparksmathematicasite
Tadashi Kikuno
20170929T04:54:21Z

How can this Euler Method be implemented in Mathematica?
https://community.wolfram.com/groups//m/t/2824249
Hello,
Has anyone already implemented the Euler method in Mathematica and can he/she post the implementation?
![enter image description here][1]
![enter image description here][2]
![enter image description here][3]
[https://math.libretexts.org/Courses/Monroe_Community_College/MTH_225_Differential_Equations/3%3A_Numerical_Methods/3.1%3A_Euler's_Method][4]
I would like something like this, using a For loop (if possible, but can be as well even other types of implementation):
https://community.wolfram.com/groups//m/t/2823888
Thank you.
[1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=3666Capture1.JPG&userId=2803344
[2]: https://community.wolfram.com//c/portal/getImageAttachment?filename=6106Capture2.JPG&userId=2803344
[3]: https://community.wolfram.com//c/portal/getImageAttachment?filename=4387Capture3.JPG&userId=2803344
[4]: https://math.libretexts.org/Courses/Monroe_Community_College/MTH_225_Differential_Equations/3:_Numerical_Methods/3.1:_Euler%27s_Method
Cornel B.
20230205T20:17:22Z

Data Analysis on the PTBXL ECG Dataset
https://community.wolfram.com/groups//m/t/2826558
&[Wolfram Notebook][1]
[1]: https://www.wolframcloud.com/obj/83d0fbe03a544f2eb42f83a317da0970
Pedro Cabral
20230209T00:52:39Z

Totally confused about UI application deployment options
https://community.wolfram.com/groups//m/t/2826542
hello
I have a small application, with a simple user interface built of some controls and Dynamic/DynamicModule. It woks reasonably well on my machine inside the Wolfram Desktop.
The question is  and it is much harder than it should be: how do I get it in front of people?
The obvious choice would be to deploy it in the Wolfram Cloud.
CloudDeploy[DynamicModule[...]]
sounds easy... **BUT** here comes the "but"
I am having trouble finding information that clearly states what works and what does not work in the cloud. From what I've found... it *should* work.
How saving definitions works is absolutely not clear.
How performance is affected is again not clear... other than the expectation that things will be slower... how much slower? e.g. Did it crash or is it still running?
As a plan B I started looking at the Wolfram Player.
As I understand this started out as "CDF Player" ... but now it can work on notebooks, so... no more "CDF".
Again, it sounds easy. Just click Save or Publish to the cloud... then open it up in the free Wolfram Player and.... IT DOES NOT WORK.
I see there is a Wolfram Player Pro that gives "extended interactivity". Do I need that? Again, it is not clear.
Thanks for the help.
p.s. Stephen Wolfram should really play "secret shopper" on the wolfram.com website and check if he could build a simple application and deploy it for end users.
Tamas Simon
20230208T22:38:49Z

How to obtain partial transpose of a 5*5 matrix?
https://community.wolfram.com/groups//m/t/2826630
I have a 5*5 matrix as follow
&[Wolfram Notebook][1]
its a density matrix of a quantum state. suppose the quantum state is as follow:
w> = 10000>+01000>+00100>+00010>+00001>
I want to obtain the partial transpose of the matrix (THE PERES PARTIAL TRANSPOSITION MATRIX)
note: there are 5 partial transpose matrix for a 5*5 matrix. I want all of them.
I don't know if there is a command in Mathematica for it?
[1]: https://www.wolframcloud.com/obj/717fc1e8ca15486193326e8f3e1388c2
Reza Hamzeh
20230208T20:25:24Z

Shading a region with a changing boundary?
https://community.wolfram.com/groups//m/t/2826615
I'd like to shade the region marked "fill this region". I'd prefer a method that doesn't require me to break the region up into smaller regions. Maybe using one application of RegionPlot?
&[Wolfram Notebook][1]
[1]: https://www.wolframcloud.com/obj/ecbb062f4c2b4addaf1eef3bea8cc994
Jon Joseph
20230208T18:37:45Z

No output from Solve[ ]?
https://community.wolfram.com/groups//m/t/2241678
Could someone please look at this and tell me what's wrong? It's probably a simple mistake. I think this system of equations should return {{pd > 3}, {pd > 10}}. At least, that's what I get when I use a pencil and paper. But my input below doesn't return anything. Not even an error message.
&[Wolfram Notebook][1]
[1]: https://www.wolframcloud.com/obj/6d7028bac944483e8c183b422736dce5
Jay Gourley
20210412T05:45:56Z

Gaussian Integration didn't give correct result
https://community.wolfram.com/groups//m/t/2825872
As shown in the noteboook, I was calculating the variance of a Gaussian distribution centered at x=0. The correct result should be just w^2, which is a property of Gaussian distribution. The result here is not only wrong, but even still has x in the formula, which is not what I would expect after an integration. Can anyone see what the problem here is? Did I type the formula in a correct way? I'm new to Mathematica.
&[Wolfram Notebook][1]
[1]: https://www.wolframcloud.com/obj/40b5d9f172d842db851987d961a03766
Wei Liang
20230208T10:45:08Z

Try to beat these MRB constant records!
https://community.wolfram.com/groups//m/t/366628
![If you see this instead of an image, reload the page.][64]
§0. (from §6 below to whet your appetite!)
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 **C**<sub>*MRB*</sub>?
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:
> [The principle, "nothing is without reason (nihil est sine ratione), or there is no effect without a cause"] must be considered one of the greatest and most fruitful of all human knowledge, for upon it is built a great part of metaphysics, physics, and moral science. (G VII 301/L 227).
Gottfried Wilhelm Leibniz (1646–1716)

POSTED BY: Marvin Ray Burns.
========
![If you see this text, the images are not showing. Refresh the page.][1]
![The first 100 partial sums of][2] {![the CMRB series.][3]}

**After receiving Wikipedia's and MathWorld's articles on the MRB constant (the upper limit point of the sequence of the above partial sums), Google OpenAI Chat CPT described the constant as follows.**
> ![Chat AI 1][5]
> ![Chat AI 2][4] 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."
>
With the Mathematica toolbox, I'm doing just that by finding patterns in its numeric expansions, performing basic numeric, real and complex analysis from original viewpoints, and tying together basic concepts from every branch of mathematics.
Join me in doing so below.
For the best viewing, wait a minute until the word LaTeX in the LaTex script is centered below.
$$\LaTeX$$
If the phrase [Math Processing Error] is shown, or the LATEX script has vanished from the center of the above line, some of the math below might be missing or appear in the LaTex code instead of the script.
For easy navigation, use the ![CTRL+f][6] keys on your keyboard. Cues in the forms of §'s and keywords in quotes are provided in the ![CTRL+f][7] "Index".
If you can see the header and the words
Reply  Flag
at the same time, in any of the following replies, you'll need to refresh the page to see them.


![CMRB funnel][8]
That **C**<sub>*MRB*</sub> nomenclature for the MRB constant was devised by Wolfram Alpha, as seen next.

> ![W\A][9]




'
**An Easter egg for you to find below: **
> ![In another reality, I invented CMRB and then discovered many of its qualities.][10]
Thus, here are three open questions about "constructing rather than finding" math.
 If we assume the MRB constant exists and that it was of my making did its qualities exist before I invented it?
 If they didn't, does that mean I invented them too?
 If so, does the same principle hold that we invented all of the unintended
consequences, of all other mathematical constructs, such as constants, numbers, theorems, shapes, etc.?



Index
=====
The first post

We first analyze the prototypical series for the MRB constant, ![Sn^(1/n)1][11]
(Select § with the given number or the keywords in quotes, and then press the
![CTRL+f][12] keys on your keyboard to move to that section.)
§1. Is that series convergent?
§2. Is 1 the only term that series is convergent for?
§3. Is that series absolutely convergent?
§4. Is that series "efficient?" (defined as how it compares to other series and integrals that compute CMRB in speed and computational cost.)
§5. Is there a geometric [isomorphism][13] between that series and the edges of hypercubes?
§6. Q and A,
§7. My claim to the MRB constant (CMRB), or a case of calculus déjà vu?
§8. Where is it found?
§9. What exactly is it?
§10. How it all began,
§11. Scholarly works
§12. The why and what of the **C**<sub>*MRB*</sub> Records,
Second post:

![CTRL+f][14] "The following might help anyone serious about breaking my record."
Third post

![CTRL+f][15] "The following email Crandall sent me before he died might be helpful for anyone checking their results."
Fourth post

![CTRL+f][16] "Perhaps some of these speed records will be easier to beat."
Many more interesting posts

... including, not to omit, RealWorld and beyond, Applications
which have been moved to [this discussion][17] to save on loading times.
...including the ![CTRL+f][18] "MRB constant supercomputer"s 1 and 2.
...including records of computing the MRB constant from ![CTRL+f][19] "Crandall's eta derivative formulas".
...including all the methods used to compute **C**<sub>*MRB*</sub> ![CTRL+f][20] "and their efficiency".
...including the dispersion of the 09th decimals in **C**<sub>*MRB*</sub> ![CTRL+f][21] "decimal expansions".
...including the ![CTRL+f][22] "convergence rate" of 3 primary forms of **C**<sub>*MRB*</sub>.
...including complete documentation of all multimilliondigit records with many highlights.
...including ![CTRL+f][23] "arbitrarily close approximation formulas" for **C**<sub>*MRB*</sub>.
...including !![CTRL+f][24] "efficient programs" to compute the integrated analog (MKB) of **C**<sub>*MRB*</sub>.
...including a recent discovery that could ![CTRL+f][25] "help in verifying" digital expansions of the integrated analog (MKB) of **C**<sub>*MRB*</sub>.
...including an inquiry for a ![CTRL+f][27] "closed form" for CMRB.
...including a question about ![CTRL+f][28] "how normal" CMRB is, and what Google OpenAI Chat CPT says.
...including a few attempts at a ![CTRL+f][29] "A cool 7 million digits?"
... including an overview of all **C**<sub>*MRB*</sub> ![CTRL+f][30] "speed records of MRB constant", by platform.
... including ![CTRL+f][31] "yet another attempt at 7 million digits".



The MRB constant relates to the divergent series:
![divegrent series][32]
=![DNE][33]
The sequence of its partial sums has two limit points with an upper limit point known as the MRB constant (CMRB).
So, out of the many series for CMRB, we first analyze the sum prototype, i.e., the series
![{CMRB}][34] =![Sn^(1/n)1][35]

Concerning the sum prototype for CMRB
§1. Is the series convergent?
After being programmed with the rules of convergence and this series, Google Open AI answered:
> ![enter image description here][36]
So, I proved its convergence by that test, as shown next.
PROOF
=====
Below, we show by the Squeeze theorem (sandwich theorem) and by plotting the following series, the qualifications for the Leibniz criterion (alternating series test) are satisfied for the MRB constant (CMRB) in
CMRB ![enter image description here][37]
by showing a(n)=(n^{1/n}1)>0 is monotonically decreasing for $n≥3$ and has a limit as n goes to infinity of zero. Of course, $\sum_1^3(1)^n(n^{1/n}1)$, converges, and the sum of two convergent series converges.
&[Wolfram Notebook][38]
We have shown by plotting and the Squeeze theorem (sandwich theorem) that the Leibniz criterion (alternating series test) holds. As we have seen, for n>1, the derivative is 0 only at e; there are no more critical points for the plot to cease to decrease. Thus, a(n)=(n^{1/n}1)>0 is monotonically decreasing for $n≥3$ and has a limit, as n goes to infinity, of zero. Finally, $\sum_1^3(1)^n(n^{1/n}1)$, converges, and the sum of two convergent series converges. Therefore the series is convergent.∎
The Leibniz criterion, summoned above, is defined and proven [here][39]:


§2.
Next, we ask and observe,
![enter image description here][40]
The short explanation is that $z_0$ must be real for the limit to be 0, and since $lim_{n>\infty}n^{1/n}=1,$ $z_0=1.$
Using the same limit, for a nonconstant term f(n) in $\sum_{n=1}^\infty(1)^n(n^{1/n}f(n)), lim_{n>\infty}f(n)=1,$ As we will see soon (![CTRL+f][41] "As for efficiency" ).


§3.
![divergent proof][42]
Plot[{n^(1/n)  1, 1/n}, {n, 1, Infinity},
PlotLegends > LineLegend["Expressions"]]
![plot][43]
...showing its terms are larger than those of the divergent [Harmonic Series][44].
Surprisingly, both sides of all three inequalities meet at the first Foias Constant **instead of e**:
In[58]:=
N[FindRoot[n^(1/n)  1  1/n == 0, {n, .1}, WorkingPrecision > 38], 32]
Out[58]= {n > 2.2931662874118610315080282912508}
In[73]:=
N[ FindRoot[n == (1 + 1/n)^n, {n, 1.2}, WorkingPrecision > 38], 32]
Out[73]= {n > 2.2931662874118610315080282912508}
In[72]:=
N[FindRoot[n^(1/n) == (1 + 1/n), {n, 1.2}, WorkingPrecision > 38], 32]
Out[72]= {n > 2.2931662874118610315080282912508}
![Foias 1][45]
![Foias 2][46]

For the series of absolute values, I noticed $$1<\sum_{n=1}^x\left(n^{\frac{1}{n}}1\right)\sqrt{x}1<0.5$$ for $$11\leq x\leq 286$$

Analogously to the [Riemann Zeta Function][47] , ![Riemann Zeta][48] , we see another analogy to the [harmonic series][49] on how n below, at, and above 1 affects the convergence of the series of absolute values,
Similarly to the Riemann Zeta Function:
For n<1, ![fraction][50] (the sum of absolute values) diverges.
For n=1, the series also diverges.
Only when n>1 does the series converge:
![white backgrond][51]
![ yellow, green, and bluebackgrounds][52]
Assuming[n > 1,
SumConvergence[{(1)^x (x^(1/x)  1)/x, (x^(1/x)  1)/
x, (1)^x x^(1/x)/x^1, x^(1/x)/
x^1, (1)^x x^(1/x)/x^(n) and x^(1/x)/x^(n)}, x]]


§4.
As for efficiency, we will look at several much fasterconverging series for CMRB throughout this discussion. Here is how the "regular" one (dr) mentioned above compares to the two related ones (dr1) for "d one direction" and (dn) for "d new." So, below we have the expressions involving a sum followed by how close to zero of a result they give after the given number of partial summations.
&[Wolfram Notebook][53]
That increase in efficiency is the Cesàro method in dn: ![enter image description here][54]
As Wikipedia says,
> ![enter image description here][55]
For how more efficient forms compare, ![CTRL+f][56] "the rate of convergence" of 3 major forms.


§5.
Before I deeply considered the full ramifications of the word Isomorphism, I called the Geometry of the MRB constant from that sum CMRB=$ \sum_{n=1}^\infty(1)^n(n^{1/n}1)$,
> the process that plots values from constructions arising from a
> peculiar nonEuclidean geometric [isomorphism][57] between its partial
> sums and hypercubes of many dimensions, where we have the following.
> ![special hypercubes][58]
>
>
> Then find a ![sum to that series.][59]
There in Diagram 3, M, at the point of the segment is where the z=MRB constant would be, and the base of that segment is the MRB constant 1.
However, in mathematics, an isomorphism is a "structurepreserving mapping between two structures of the same type that can be reversed by inverse mapping." Hence, I'm unsure if the term applies here.

§6.
Q&A: [Moved to the beginning.]

§7.
This discussion is not crass bragging; it is an attempt by this amateur to share his discoveries with the greatest audience possible.
Amateurs have made a few significant discoveries, as discussed in ![enter image description here][60] [here.][61]
This amateur has tried his best to prove his discoveries and has often asked for help. 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 portions were original. I concluded from these investigations that the only original thought I had was the obstinacy to think anything meaningful could be found in the infinite sum shown next. ![CMRB sum][62]
Nonetheless, 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 about 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][63]
![If you see this instead of an image, reload the page.][64]![enter image description here][65]
(the calculus war for CMRB)

CREDIT
https://soundcloud.com/cmrb/homersimpsonvspetergriffincmrb
'
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][66]
(Newton's notation as published in PRINCIPIS MATHEMATICA [PRINCIPLES OF MATHEMATICS])
![enter image description here][67]
( 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][68] 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!


§8.
![it][69] is defined in the following places, most of which attribute it to my curiosity.
 [ค่าคงที่ลุ่มแม่น้ำโขง][70] (in Thai);
 [ar.wikipedia.org/wiki/][71] (In Arabic);
 [Constante MRB][72] (in French);
 [Constanta MRB  MRB constant][73] (in Romanian);
 http://constant.one/ ;
 Crandall, R. E. "The MRB Constant." §7.5 in [Algorithmic Reflections: Selected Works][74]. PSI Press, pp. 2829, 2012,ISBN10 : 193563819X ISBN13: 9781935638193;
 Crandall, R. E. "[Unified Algorithms for Polylogarithm, LSeries, and Zeta Variants][75]." 2012;
 [https://enacademic.com/][76], Wikipedia, Mathematical constant;
 Encyclopedia of Mathematics (Series #94);
 [Engineering Tools][77] 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][78];
 Finch, S. R. [Mathematical Constants][79], Cambridge, England:
Cambridge University Press, p. 450, 2003, ISBN13: 9780521818056, ISBN10: 0521818052;
 Finch's original essay on [Iterated Exponential Constants][80];
 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][81] ISSN 19169795 EISSN 19169809 Published by Canadian Center of Science and Education;
 [Library of General Functions (LGF) for SIMATIC S71200][82]
 Mauro Fiorentina’s [math notes][83] (in Italian);
 MATHAR, RICHARD J. "NUMERICAL EVALUATION OF THE OSCILLATORY INTEGRAL OVER exp(iπx) x^(1/x) BETWEEN 1 AND INFINITY" [(PDF)][84]. arxiv. Cornell University;
 [Mathematical Constants and Sequences][85] a selection compiled by
Stanislav Sýkora, Extra Byte, Castano Primo, Italy. Stan’s Library,
ISSN 24211230, Vol.II;
 ["Matematıksel Sabıtler"][86] (in Turkish). Türk Biyofizik Derneği;
 [MathWorld Encyclopedia][87];
 [MRB常数][88] (in Chinese);
 [mrb constantとは][89] 意味・読み方・使い方 ( in Japanese);
 [MRB константа][90] (in Bulgarian);
 [OEIS Encyclopedia (The MRB constant);][91]
 Patuloy ang MRB  [MRB constant][92] (in Filipino)
 [Plouffe's Inverter;][93]
 the LACM [Inverse Symbolic Calculator;][94]
 The OnLine Encyclopedia of Integer Sequences® (OEIS®) as
[A037077][95], Notices Am. Math. Soc. 50 (2003), no. 8, 912–915, MR 1992789 (2004f:11151);
 [Wikipedia Encyclopedia][96].
![enter image description here][97]


§9.
![CMRB][98]
## = B =##
![enter image description here][99]
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][100]
> ![enter image description here][101]
The expressions ![Etam][102] and ![eta0][103] denote the mth 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.}*)
Crandall's first "B" is proven below by Gottfried Helms, and it is proven more rigorously, considering the conditionally convergent sum,![CMRB sum][104] afterward. Then the formula (44) is a Taylor expansion of eta(s) around s = 0.
> ![n^(1/n)1][105]
At ![enter image description here][106] [here,][107] we have the following explanation.
![enter image description here][108]
![enter image description here][109]![enter image description here][110]

![enter image description here][111]
**The integral forms for CMRB and MKB differ by only a trigonometric multiplicand to that of its analog.**
![enter image description here][112]
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

\&[MRB equations][113]






§10.
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. See [my report cards][114] for evidence of my poor grades.
The eldest child, raised by my sixth gradeeducated 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 times 2, 2 times 2 times 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 cared for 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 with my math hobby!
Occasionally, I make a point of attending 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 told 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 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][115]
(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 α=the fine structure constant, arguably the most fundamental constant of all, with a value that nearly equals 1/137. Or 1/137.03599913= 0.00729735257..., to be precise, and essentially and **metaphorically** equals (133+60*10^(2/5))CMRB/456 . It is denoted by the Greek letter alpha – α.
Let m be the MRB constant. Then we have
&[Wolfram Notebook][116]

We have a strong arithmetic relationship with the Lemniscate Constant:
According to Wikipedia
In mathematics, the lemniscate constant ϖ is a transcendental mathematical constant that is the ratio of the perimeter of Bernoulli's lemniscate to its diameter, analogous to the definition of π for the circle.
&[Wolfram Notebook][117]

Consider its relationship to Viswanath's constant (VC)
> ![Viswanath' math world snippit][118]
(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][119] $=e^\pi.$
![=e^\pi][120]

Then there is the Rogers  Ramanujan Continued Fraction, R(q),
of **C**<sub>*MRB*</sub> that is welllinearly approximated by terms of other terms of **C**<sub>*MRB*</sub> alone:
![enter image description here][121]


What about "?" for m= the MRB constant?
![enter image description here][122]

&[Wolfram Notebook][123]



**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][124]
I came to find out my discovery, a very slowtoconverge [oscillatory integral,][125] would later be further defined by [Google Scholar.][126]
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][127]
Which is the same as
![enter image description here][128]
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][129] .
![Iimofg>1][130]
![Cauchy's Integral Theorem][131]
![Lim surface h gamma r=0][132]
![Lim surface h beta r=0][133]
![limit to 2n1][134]
![limit to 2n][135]
Plugging in equations [5] and [6] into equation [2] gives us:
![left][136]![right][137]
Now take the limit as N?? and apply equations [3] and [4]:
![QED][138]
He went on to note that,
![enter image description here][139]
After I mentioned it to him, Richard Mathar published his meaningful work on it [here in arxiv][140], where M is the MRB constant and M1 is MKB:
> ![enter image description here][141]
M1 has a convergent series,
![enter image description here][142]
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.
ReImPlot[(1)^x (x^(1/x)  1), {x, 1, Infinity}, PlotStyle > Blue,
Filling > Axis, FillingStyle > {Green, Red}]
![big plot][143]
![small plot][144]
Also where
&[Wolfram Notebook][145]
Then
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

M2 and CMRB are connected:

&[Wolfram Notebook][146]

In the complex plane, they even converge at the same rate.

Every 75 *i* of the upper value of the partial integration yields 100 additional digits of M2=![enter image description here][147] and of CMRB=![enter image description here][148]=![enter image description here][149]
&[Wolfram Notebook][150]
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$][151]
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][152]
The following "partial proof of it" is from Quora.
While![enter image description here][153]
![enter image description here][154]
![enter image description here][155]

**I developed a lot more theory behind it and ways of computing many more digits in [this linked][156] Wolfram Community post.**


**From these meager beginnings:**
In October 2016, I wrote the following [here in researchgate][157]:
First, we will follow the path the author took to find out that, for
![ratio of a1 to a][158],
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 proving 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][159]
(17) (PDF) Gelfond's Constant using MKBconstantlike integrals. Available from: [https://www.researchgate.net/publication/309187705_Gelfond%27_s_Constant_using_MKB_constant_like_integrals][160] [accessed Aug 16 2022].
We find no limit "a" goes to infinity of the ratio of the previous forms of integrals when the "I" is left out, and we 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][161] is the MRB constant.)
> ![enter image description here][162]

**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 $a=12\times C\mathrm{MRB}=0.6242807150758657595029641318914535398881938101997224\ldots$.
![enter image description here][163]
I asked, "If that's correct can you explain why?" and got the following comment.
![enter image description here][164]
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.
![enter image description here][165]
See [here.](http://oeis.org/A173273)
Also,
![enter image description here][166]



§11.
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][167] . 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. They almost all
> instantly collapsed, leaving all but the few we enjoy today.
I'm not the first to think the universe consists of an infinitude of dimensions. Some string theories and theorists propose it too.
Michele Nardelli added a vast amount of string theory analysis and its connection to dimensions and the MRB constant.
He said,
> In the following links, there are several works concerning various
> sectors of Theoretical Physics, Cosmology, and Applied Mathematics, in
> which MRB Constant is used as a "regularizer" or "normalizer". This
> constant allows to obtain a better approximation to the solutions
> obtained, developing the various equations that are analyzed. The
> solutions in turn, lead to four numbers that are called "recurring
> numbers". They are zeta (2) = Pi^2/6, 1729 (HardyRamanujan number),
> 4096 (which multiplied by 2 gives the gauge group SO (8192)) and the
> Golden Ratio 1.61803398 ...
HE HAS PUBLISHED HUNDREDS OF PAPERS ON STRING THEORY AND THE MRB CONSTANT!
[https://www.academia.edu/search?q=MRB%20constant][168]
[https://www.researchgate.net/profile/MicheleNardelli][169]
**[Dr. Richard Crandall][170] called the MRB constant a [key fundamental constant][171]**
> ![enter image description here][172]
**in [this linked][173] wellsourced and equally greatly cited Google Scholar promoted paper. Also [here][174].**
**[Dr. Richard J. Mathar][175] wrote on the MRB constant [here.][176]**
**Xun Zhou, School of Water Resources and Environment, China University of Geosciences (Beijing), [wrote][177] 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.




§12.
MRB Constant Records,
====================
**Google OpenAI Chat CPT gave the following introduction to the MRB constant records:**
> It is not uncommon for researchers and mathematicians to compute large
> numbers of digits for mathematical constants or other mathematical
> quantities for various reasons. One reason might be to test and
> improve numerical algorithms for computing the value of the constant.
> Another reason might be to use the constant as a benchmark to test the
> performance of a computer or to compare the performance of different
> computers. Some people may also be interested in the mathematical
> properties of the constant, and computing a large number of digits can
> help to reveal patterns or other features of the constant that may not
> be apparent with fewer digits. Additionally, some people may simply
> find the process of calculating a large number of digits to be a
> challenging and rewarding intellectual pursuit.
> It seems that the MRB constant,
> also known as the CMRB constant, is a mathematical constant defined as
> the sum of the infinite series Sum[(1)^k(k^(1/k)1),{k,1,n}] and has
> a decimal expansion of 0.187859... The MRB constant has been
> calculated to various digits using various methods and computers. The
> previous record number of digits was 40,000, calculated in 2006 using a
> program written in Mathematica and run on a Windows desktop computer.
> It is not known whether the MRB constant is algebraic, transcendental,
> or irrational. The process of computing the MRB constant using various
> methods and devices, including computers and software such as Mathcad,
> Mathematica, and Sigma. You have calculated 6,500,000 digits of the
> MRB constant using a supercomputer, with a computation time of 72.526
> days and an absolute time of 185.491 days. You have mentioned that the
> error from a 6,000,000 or more digit calculation that used a different
> method is 0.*10^6029992.
**When asked how, in detail, to calculate the digits of the MRB constant:**
> To calculate the digits of the MRB constant in more detail, you can
> use the following steps:
>
> Write a program or use an existing software tool that can calculate
> the partial sums of the series (1)^k k^(1/k) for a given value of n.
>
> Use this program or tool to calculate the partial sums for a large
> value of n, such as n = 10,000 or n = 100,000.
>
> Repeat step 2 for increasing values of n until the partial sums
> converge to a constant value. The more digits of accuracy you want,
> the larger n you will need to use.
>
> The digits of the MRB constant are the digits of the converged value
> obtained in step 3.
>
> It is important to note that calculating the digits of the MRB
> constant is a computationally intensive task that requires a fast
> computer and a good implementation of the algorithms for calculating
> the partial sums of the series (1)^k k^(1/k). In addition, it is not
> known whether the MRB constant is algebraic, transcendental, or even
> irrational, so it may not be possible to calculate all of its digits.
>
> I hope this helps. Please let me know if you have any other questions.
My inspiration to compute a lot of digits of **C**<sub>*MRB*</sub> came from [the following website by Simon Plouffe][178].
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][179]
> ![enter image description here][180]
> ![enter image description here][181]
>![enter image description here][182]
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, 21stcentury 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
**C**<sub>*MRB*</sub> with my TI92s, by adding 1+sqrt(2)3^(1/3)+4^(1/4)5^(1/5)+6^(1/6)... 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 i.e. (.1). It gave (.1_91323989714) which is close to what Mathematica gives for summing to only an upper limit of 1000.
![Ti92's][183]

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 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][184] if you can read the printed and scanned copy there.
Sigma still can be found [here.][185]

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][186]
documentation [here][187]

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][188]
documentation [here][189]

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. The 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, The 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. The 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. ![CTRL+f][190] "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. ![CTRL+f][191] "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. The 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. The 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. The max memory used was 91 GB of RAM. The Mathematica 6.0 code is used as 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 averages 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 of 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 as 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, 1066 MHz, PC38500 DDR3 ECC RAM.
To beat that, in 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 30 cores were clocked at up to 5.2 GHz.
To beat that, I did a 1,004,993 correct digits computation in 30.5 hours of absolute time and 15.7 hours of computation time from the Timing[] command using 3/4 of the MRB constant supercomputer 4, finishing Dec 5, 2022. Ram Speed was 5200MHz, and all of the 24 performance cores were clocked at up to 5.95 GHz, plus 32 efficiency cores running slower. I used 24 kernels on the Wolfram Lightweight grid over an i12900k, 12900KS, and 13900K.
[36.7 hours million notebook][192]
[30.5 hours million][193]

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.

3,014,991 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 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 were 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 are 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 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
the calculation that used a different method is
0.*10^6029992.
"Computation time" 72.526 days.
"Absolute time" 185.491 days.







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[12]: https://community.wolfram.com//c/portal/getImageAttachment?filename=0a.gif&userId=366611
[13]: https://mathworld.wolfram.com/Isomorphism.html
[14]: https://community.wolfram.com//c/portal/getImageAttachment?filename=0a.gif&userId=366611
[15]: https://community.wolfram.com//c/portal/getImageAttachment?filename=0a.gif&userId=366611
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[37]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot20221113082717.jpg&userId=366611
[38]: https://www.wolframcloud.com/obj/02658cbca1b54e258cf6e87b696838d6
[39]: https://en.wikipedia.org/wiki/Alternating_series_test
[40]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Capture3a.PNG&userId=366611
[41]: https://community.wolfram.com//c/portal/getImageAttachment?filename=0a.gif&userId=366611
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[43]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot20230101225958.jpg&userId=366611
[44]: https://mathworld.wolfram.com/HarmonicSeries.html
[45]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot20230102023532.jpg&userId=366611
[46]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot20230102023615.jpg&userId=366611
[47]: https://mathworld.wolfram.com/RiemannZetaFunction.html
[48]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot20221229103138.jpg&userId=366611
[49]: https://mathworld.wolfram.com/HarmonicSeries.html
[50]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot20230110071239.jpg&userId=366611
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[54]: https://community.wolfram.com//c/portal/getImageAttachment?filename=0.gif&userId=366611
[55]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot20230106044617.jpg&userId=366611
[56]: https://community.wolfram.com//c/portal/getImageAttachment?filename=0a.gif&userId=366611
[57]: https://mathworld.wolfram.com/Isomorphism.html
[58]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot20221231160000.jpg&userId=366611
[59]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot20221231160218.jpg&userId=366611
[60]: https://community.wolfram.com//c/portal/getImageAttachment?filename=logo.svg&userId=366611
[61]: https://mathoverflow.net/questions/44244/whatrecentdiscoverieshaveamateurmathematiciansmade
[62]: https://community.wolfram.com//c/portal/getImageAttachment?filename=3959Capture7.JPG&userId=366611
[63]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot20220819115551.jpg&userId=366611
[64]: https://community.wolfram.com//c/portal/getImageAttachment?filename=1ac.JPG&userId=366611
[65]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot20220813035505.jpg&userId=366611
[66]: https://community.wolfram.com//c/portal/getImageAttachment?filename=N.jpg&userId=366611
[67]: https://community.wolfram.com//c/portal/getImageAttachment?filename=L.jpg&userId=366611
[68]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot20220816112453.jpg&userId=366611
[69]: https://community.wolfram.com//c/portal/getImageAttachment?filename=o.jpg&userId=366611
[70]: https://hmong.in.th/wiki/MRB_constant
[71]: 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
[72]: https://fr.wikipedia.org/wiki/Constante_MRB
[73]: https://wikicro.icu/wiki/MRB_constant
[74]: https://www.amazon.com/exec/obidos/ASIN/193563819X/ref=nosim/ericstreasuretro
[75]: http://www.marvinrayburns.com/UniversalTOC25.pdf
[76]: https://enacademic.com/dic.nsf/enwiki/11755
[77]: http://web.archive.org/web/20081121134611/http://www.irancivilcenter.com/en/tools/units/math_const.php
[78]: http://etymologie.info/
[79]: https://www.amazon.com/exec/obidos/ASIN/0521818052/ref=nosim/ericstreasuretro
[80]: https://web.archive.org/web/20010616211903/http://pauillac.inria.fr/algo/bsolve/constant/itrexp/itrexp.html
[81]: https://pdfs.semanticscholar.org/f3dc/9f828442123015c5d52535fdefc0ab450bf5.pdf
[82]: https://cache.industry.siemens.com/dl/files/728/109479728/att_1085858/v2/109479728_LGF_V5_1_0_en.pdf
[83]: https://web.archive.org/web/20210812083640/http://www.bitman.name/math/article/962
[84]: https://arxiv.org/pdf/0912.3844v3.pdf
[85]: http://ebyte.it/library/educards/constants/MathConstants.pdf
[86]: https://web.archive.org/web/20090702134146/http://www.turkbiyofizik.com/sabitler.html
[87]: https://mathworld.wolfram.com/MRBConstant.html
[88]: https://upwikizh.top/wiki/MRB_constant
[89]: https://ejje.weblio.jp/content/mrb+constant
[90]: https://ewikibg.top/wiki/MRB_constant
[91]: http://oeis.org/wiki/MRB_constant
[92]: https://ewikitl.top/wiki/mrb_constant
[93]: https://web.archive.org/web/20030415202103/http://pi.lacim.uqam.ca/eng/table_en.html
[94]: https://web.archive.org/web/20001210231700/http://www.lacim.uqam.ca/piDATA/mrburns.txt
[95]: https://oeis.org/A037077
[96]: https://en.wikipedia.org/wiki/MRB_constant
[97]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot20221217231222.jpg&userId=366611
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[106]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot20220816055726.jpg&userId=366611
[107]: https://math.stackexchange.com/questions/1673886/isthereamorerigorouswaytoshowthesetwosumsareexactlyequal
[108]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot20221113082031.jpg&userId=366611
[109]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot20221113082057.jpg&userId=366611
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[112]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot20220918014843.jpg&userId=366611
[113]: https://www.wolframcloud.com/obj/986a70e91d554e31bd7c87c24eec5d81
[114]: https://www.wolframcloud.com/obj/bmmmburns/Published/MRB_report_cards_16.nb
[115]: https://community.wolfram.com//c/portal/getImageAttachment?filename=106291.jpg&userId=366611
[116]: https://www.wolframcloud.com/obj/9ae8cda2e68442c2b10158d0a24cc565
[117]: https://www.wolframcloud.com/obj/ed263ba84c044c30a652bf4a02d5f54a
[118]: https://community.wolfram.com//c/portal/getImageAttachment?filename=62082.jpg&userId=366611
[119]: https://mathworld.wolfram.com/GelfondsConstant.html
[120]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot20220524013821.jpg&userId=366611
[121]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot20221028054251.jpg&userId=366611
[122]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot20230118140654.jpg&userId=366611
[123]: https://www.wolframcloud.com/obj/965639ac19d74dc8ba674d47215e25c4
[124]: https://community.wolfram.com//c/portal/getImageAttachment?filename=101513.PNG&userId=366611
[125]: https://en.wikipedia.org/wiki/Oscillatory_integral
[126]: https://scholar.google.com/scholar?hl=en&as_sdt=0,15&q=%22MKB%20constant%22&btnG=
[127]: https://community.wolfram.com//c/portal/getImageAttachment?filename=46311.PNG&userId=366611
[128]: https://community.wolfram.com//c/portal/getImageAttachment?filename=580910.JPG&userId=366611
[129]: http://community.wolfram.com/groups//m/t/1323951?p_p_auth=W3TxvEwH
[130]: https://community.wolfram.com//c/portal/getImageAttachment?filename=28491.JPG&userId=366611
[131]: https://community.wolfram.com//c/portal/getImageAttachment?filename=76812.JPG&userId=366611
[132]: https://community.wolfram.com//c/portal/getImageAttachment?filename=100173.JPG&userId=366611
[133]: https://community.wolfram.com//c/portal/getImageAttachment?filename=57664.JPG&userId=366611
[134]: https://community.wolfram.com//c/portal/getImageAttachment?filename=74665.JPG&userId=366611
[135]: https://community.wolfram.com//c/portal/getImageAttachment?filename=49236.JPG&userId=366611
[136]: https://community.wolfram.com//c/portal/getImageAttachment?filename=15127.JPG&userId=366611
[137]: https://community.wolfram.com//c/portal/getImageAttachment?filename=92858.JPG&userId=366611
[138]: https://community.wolfram.com//c/portal/getImageAttachment?filename=49309.JPG&userId=366611
[139]: https://community.wolfram.com//c/portal/getImageAttachment?filename=3.PNG&userId=366611
[140]: https://arxiv.org/abs/0912.3844
[141]: http://community.wolfram.com//c/portal/getImageAttachment?filename=Capturemkb2.JPG&userId=366611
[142]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot20220705020911.jpg&userId=366611
[143]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot20220705021130.jpg&userId=366611
[144]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot20220705022313.jpg&userId=366611
[145]: https://www.wolframcloud.com/obj/09dd1776b25e482e9bd6fcab9742a05c
[146]: https://www.wolframcloud.com/obj/9fea1f20f12d49a598f922a8e0026375
[147]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot20220731235917.jpg&userId=366611
[148]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot20220801001529.jpg&userId=366611
[149]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot20220801001459.jpg&userId=366611
[150]: https://www.wolframcloud.com/obj/88e5ed593d0e4a63abdfc48a053428cd
[151]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot20220814085504.jpg&userId=366611
[152]: https://community.wolfram.com//c/portal/getImageAttachment?filename=22421.JPG&userId=366611
[153]: https://community.wolfram.com//c/portal/getImageAttachment?filename=97362.JPG&userId=366611
[154]: https://community.wolfram.com//c/portal/getImageAttachment?filename=31093.JPG&userId=366611
[155]: https://community.wolfram.com//c/portal/getImageAttachment?filename=63064.JPG&userId=366611
[156]: https://community.wolfram.com/groups//m/t/1323951?p_p_auth=zHVSqCM8
[157]: https://www.researchgate.net/publication/309187705_Gelfond%27_s_Constant_using_MKB_constant_like_integrals
[158]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot20220503083042.jpg&userId=366611
[159]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot20220816204240.jpg&userId=366611
[160]: https://www.researchgate.net/publication/309187705sConstantusingMKBconstantlikeintegrals
[161]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot20220608111905.jpg&userId=366611
[162]: https://community.wolfram.com//c/portal/getImageAttachment?filename=73892.JPG&userId=366611
[163]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot20221113083115.jpg&userId=366611
[164]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot20220816210900.jpg&userId=366611
[165]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot20221113083322.jpg&userId=366611
[166]: https://community.wolfram.com//c/portal/getImageAttachment?filename=b2.JPG&userId=366611
[167]: https://bctp.berkeley.edu/extraD.html
[168]: https://www.academia.edu/search?q=MRB%20constant
[169]: https://www.researchgate.net/profile/MicheleNardelli
[170]: https://en.wikipedia.org/wiki/Richard_Crandall
[171]: https://scholar.google.com/scholar?hl=en&as_sdt=0,15&q=key%20fundamental%20constant%20zeta&btnG=
[172]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot20220502113359.jpg&userId=366611
[173]: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.695.5959&rep=rep1&type=pdf
[174]: https://www.marvinrayburns.com/UniversalTOC25.pdf
[175]: https://www2.mpiahd.mpg.de/~mathar/
[176]: https://arxiv.org/abs/0912.3844
[177]: https://pdfs.semanticscholar.org/f3dc/9f828442123015c5d52535fdefc0ab450bf5.pdf
[178]: https://web.archive.org/web/20120310223600/http://pi.lacim.uqam.ca/eng/records_en.html
[179]: https://community.wolfram.com//c/portal/getImageAttachment?filename=P1.JPG&userId=366611
[180]: https://community.wolfram.com//c/portal/getImageAttachment?filename=P2.JPG&userId=366611
[181]: https://community.wolfram.com//c/portal/getImageAttachment?filename=P3.JPG&userId=366611
[182]: https://community.wolfram.com//c/portal/getImageAttachment?filename=P5.JPG&userId=366611
[183]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot20230131143800.jpg&userId=366611
[184]: http://marvinrayburns.com/Original_MRB_Post.html
[185]: https://wims.univcotedazur.fr/wims/wims.cgi?module=tool/analysis/sigma.en
[186]: https://community.wolfram.com//c/portal/getImageAttachment?filename=thumbnail%281%29.jpg&userId=366611
[187]: https://www.wolframcloud.com/obj/18c08d6babe94fbdb33a7e1167c9d243
[188]: https://community.wolfram.com//c/portal/getImageAttachment?filename=thumbnail%282%29.jpg&userId=366611
[189]: https://www.wolframcloud.com/obj/0b304705ed144c6bbd27fda9ff29536d
[190]: https://community.wolfram.com//c/portal/getImageAttachment?filename=0a.gif&userId=366611
[191]: https://community.wolfram.com//c/portal/getImageAttachment?filename=0a.gif&userId=366611
[192]: https://www.wolframcloud.com/obj/bmmmburns/Published/36%20hour%20million.nb
[193]: https://www.wolframcloud.com/obj/bmmmburns/Published/31_hour_million.nb
Marvin Ray Burns
20141009T18:08:49Z

How to solve Sinh and Cosh functions summation over 0 to infinity
https://community.wolfram.com/groups//m/t/2825897
Dear All,
I am trying to calculate a non linear equation which consists of hyperbolic functions Sinh and Cosh. I would like to calculate the numerical value summation over 0 to infinity. by numerical
minimization using Nminimize function.
The notebook is attached here.
When I am trying to minimise the function with respect to lambdaHybm, The calcultion does not work. However if I put some specific value (10, 100, 9999) insted of Infinite in equation, It gives some value. But, The value are different for different range of summation.
How I can calculate from 0 to Infinite? Could you please give some suggestions.
Thanks,
Best Regards,
Sukanta
&[Wolfram Notebook][1]
[1]: https://www.wolframcloud.com/obj/a822c7fa5f2445439701586bb03dd27f
Sukanta Kumar Jena
20230208T11:02:23Z

Compute definite integrals with tanh? no output
https://community.wolfram.com/groups//m/t/2825265
I am trying to compute the following definite integral,
Integrate[Sqrt[g*m]Divide[Tanh[Divide[Sqrt[g*k],Sqrt[m]]x],Sqrt[k]],{x,0,x}]
(Paste this into Wolfram to see it)
If you are too lazy, it is basically the definite integral from 0 to x of some constants multiplied by tanh(constants*x) dx
For some reason, even though I have Wolfram Pro, it attempts to compute this integral for less than 10 seconds, then just stops, with no answer, no error message, nothing.
What is going on? Is the integral simply too hard for Wolfram to compute? Please help.
Ron Ellenbogen
20230207T11:20:39Z

Pasting code from a PDF (created with MMA) into a Notebook?
https://community.wolfram.com/groups//m/t/2825952
I would like to copy a command from a book on Mathematica in PDF format (undoubtedly created with MMA) and paste it into a Notebook so it can be executed. When I select this text in the PDF file (which I'm entering by hand now)
Table[RandomSample[Range[39], 7] // Sort, {10 ^ 6}];
and paste it into a Notebook, it appears like this:
Table@RandomSample@Range@39D, 7D êê Sort, 810 ^ 6<D;
BTW: the code for '@' maps to '[' in the Mathamatica1Mono font. Using `Style[<cmd>, FontFamily > Mathematica1Mono]` doesn't help. This prevents me from experimenting and educating myself using
some great online resources. Importing the PDF into MMA doesn't help.
James M Marks
20230208T01:26:03Z

[WSS22] Fluid dynamics on graphs
https://community.wolfram.com/groups//m/t/2574186
![Wolfram Notebook][1]
&[Wolfram Notebook][2]
[1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=LatticeGas.jpg&userId=2440645
[2]: https://www.wolframcloud.com/obj/2c44bf669e2e46249591ea95e8fa6f2d
Abhishek Joshi
20220719T20:23:09Z

How to compute the gradient and divergence of a 'Tensor Product' expression
https://community.wolfram.com/groups//m/t/2825811
Dear Wolfram Community:
I am facing the problem of computing the gradient and divergence of a general tensor field.
In particular, expressions like the following ones (in Mathematica symbolic notation).
Grad[TensorProduct[A[t,X], B[t,X]],X];
Div[TensorProduct[A[t,X], B[t,X]],X];
Where:
A[t,X] and B[t,X] are two general tensor fields that are function of time "t" and the position vector "X".
Those expressions are the more general forms (at least I hope) of the cited operators, very useful in continuum mechanics (specially in fluid mechanics: the Reynolds stress tensor is a 'tensor product' of turbulent velocity fields)
Unfortunately, the related identities are difficult to find in the bibliography/references.
I would like to know how to implement the product rule in symbolic notation.
Thank you in advance,
Alberto Silva
Notes:
1) I tried to do it before in explicit, componentby component notation, and the result was a very big, messy and confusing expression...
2) I am leaving a small notebook written in the last version of Wolfram Mathematica as an example.
3) A year ago I got a clue about how to do this computation (inserting a 'custom operator' using inactive expressions and replace rules) in the following community post:
[How to use/ evaluate symbolic vector calculus identities?][1]
The main problem that was left then was the true expression of the divergence was unknown and I just 'guessed' it, so my guess could be wrong.
[1]: https://community.wolfram.com/groups//m/t/2303932
Alberto Silva Ariano
20230207T23:25:12Z

Nondeterministic Constraint Logic Game Implementation
https://community.wolfram.com/groups//m/t/1993426
I started on an implementation of the Nondeterministic Constraint Logic puzzle / game.
![enter image description here][1]
Notebook: https://www.wolframcloud.com/obj/udqbpn/Published/NCL.nb
[1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=ncl.png&userId=960265
Eric Parfitt
20200602T22:14:47Z

How do you create an array in the webbased Mathematica Student Edition?
https://community.wolfram.com/groups//m/t/2825596
We are working with large matrices and it would help to be able to insert a blank matrix like you can in a notebook and quickly put in the numbers, rather than use the cumbersome {{a,b},{c,d}} notation. In a notebook, you can do Insert > table/matrix, but this is not available in the Student edition. The basic math assistant palette is also missing. You also can't copy and paste a matrix in matrix form from the output to a new input to change the numbers. Any help would be greatly appreciated.
Fumiko Futamura
20230207T22:25:36Z

Reset the ItemNumbered counter within a single notebook
https://community.wolfram.com/groups//m/t/2825548
I would like to reset the ItemNumbered counter within a single notebook. I present 3 problems to students numbered like:
1.
2.
3.
Then, in another topic within the same notebook I want to start the count over:
1.
2.
3.
and so on. How to do this? Thanks.
Jon Joseph
20230207T18:07:17Z

Grassmann Algebra & Calculus Paclet Available
https://community.wolfram.com/groups//m/t/2825558
A Mathematica paclet application for Grassmann Algebra and Calculus is now available at Dropbox. The link for the paclet and my email address are in my profile.
The key attribute of Grassmann algebra is that it algebraicizes the notion and modeling of linear dependence and independence. It can be interpreted to many applications with contextual notation. The most important applications are mathematics, geometry, physics and engineering. Because of its basic antisymmetric nature, it is tensorial in nature being invariant to coordinate transformations. One can write coordinate free expressions applicable to finite dimensions. A metric construct and measure arises from its basic axioms. One can compute with or without a metric. It can distinguish between points and free vectors. It can treat basis vectors as derivative operators, and reciprocal basis vectors as differential forms. It is, as John Browne writes: " a geometric calculus par excellence".
The Grassmann algebra contains exterior, regressive, interior, generalized, hypercomplex, associative, and Clifford products. The Grassmann complement is a generalized Hodge star operator. The calculus routines include vector operators, the exterior derivative and the generalized vector calculus operators. All advances product expressions can be simplified to scalars and canonical exterior expressions.
There are various builtin spaces with their associated coordinates, bases (vector, differential form and orthonormal), metrics and symbols. It's possible to define spaces and then switch between various spaces on the fly.
Grassmann Calculus is thus a powerful application for education or work in multilinear algebra, geometry, differential geometry, physics and engineering.
The GrassmannCalculus Palette, available from the Mathematica Palettes menu, is very useful when using the application. Another useful palette is the Common Grassmann Operations palette available from the GrassmannCalculus Palette, dropdown Palettes menu.
John Browne's Foundations book is included (as notebooks) in the paclet. For the paclet to be useful one must learn the foundations, which is probably equivalent in time to a two semester college course or maybe learning tensor calculus.
The extended Grassmann algebra theory and routines were developed by John Browne and follow closely Hermann Grassmann's work. The calculus routines were written by David Park who also designed the user interface.
You can contact David Park at the email address in my profile.
John Browne's (19422021) web site is at: [Grassmann Algebra][1]
[1]: https://sites.google.com/view/grassmannalgebra/home
David J M Park Jr
20230207T19:34:39Z

How to fix Part::partw error
https://community.wolfram.com/groups//m/t/2824909
How to correct the code which produces
> Part::partw
> Part::partd
errors
` Part::partw: Part 2 of Y[tau] does not exist.`
Part::partd: Part specification {Y>InterpolatingFunction[{{2.11454,0.}},{5,3,1,{437},{4},0,0,0,0,Automatic,{},{},False},{{2.11454,<<49>>,<<387>>}},{{{34.6432,8.237},{3.35084*10^11,6.32877*10^10}},<<49>>,<<387>>},{Automatic}]}[[1,All,1,2]] is longer than depth of object.
&[Code with error][1]
[1]: https://www.wolframcloud.com/obj/c367aef125864948944017a34a2a6fb2
John Wick
20230206T19:22:55Z

How to integrate tanx/(x+sinx)?
https://community.wolfram.com/groups//m/t/2824858
I use a website called integral of the day, all the previous ones have answers, but todays I cannot ind an answer for and no online calculators can do it either.
Charlie Oke
20230206T21:46:21Z

Converting MoveNet for Wolfram Language
https://community.wolfram.com/groups//m/t/2822251
&[Wolfram Notebook][1]
[1]: https://www.wolframcloud.com/obj/410bf6e93bda4f23918dc10be3c02156
Kotaro Okazaki
20230202T13:44:46Z

What's the default font for Chinese characters on Mathematica 13.2?
https://community.wolfram.com/groups//m/t/2824556
Hello,
When exporting to pdf files, which contains some Chinese characters, from Mathematica 13.2 on Debian 11, which is linux system, the pdf outputed doesn't have any Chinese characters as they are missing. I know it is that in my computer there is not the font the mathematica uses to output Chinese characters. So I need to install the missing font, but what name is it? How can I find the name of the missing font.
Thanks.
Zhenyu Zeng
20230206T14:09:51Z

[WSG23] Daily Study Group: Introduction to Probability
https://community.wolfram.com/groups//m/t/2825207
A Wolfram U Daily Study Group on Introduction to Probability begins on **February 27th 2023**.
Join me and a group of fellow learners to learn about the world of probability and statistics using the Wolfram Language. Our topics for the study group include the characterisation of randomness, random variable design and analysis, important random distributions and their applications, probabilitybased data science and advanced probability distributions.
The idea behind this study group is to rapidly develop an intuitive understanding of probability for a college student, professional or interested hobbyist. A basic working knowledge of the Wolfram Language is recommended but not necessary. We are happy to help beginners get up to speed with Wolfram Language using resources already available on Wolfram U.
Please feel free to use this thread to collaborate and share ideas, materials and links to other resources with fellow learners.
[**REGISTER HERE**][1]
![Wolfram U Banner][2]
[1]: https://www.bigmarker.com/series/dailystudygroupprobabilitywsg36/series_details
[2]: https://community.wolfram.com//c/portal/getImageAttachment?filename=banner.jpg&userId=2823613
Marc Vicuna
20230207T01:15:38Z

Notebook won't save to directory
https://community.wolfram.com/groups//m/t/2622392
re: Mathematica 13.0 (home edition) running on macOS Monterey Version 12.5
**Issue**
I worked on an existing notebook yesterday morning and saved the notebook at 11:05 AM without incident.
After further work, some 20 minutes later, I attempted to save the notebook again and the following popped up:
![enter image description here][1]
Between saving the document at 11:05 AM and attempting to save it again, I made no changes to permissions of directories or anything else.
I only edited some simple code (which worked and continues to work).
**Of note**:
I have no problems saving other kinds of files.
I could (at the time) save the notebook to a different directory (file folder).
**Today**:
This issue has now spread to other directories and other notebooks.
I do not have this issue when saving other types of files; it seems, at least for now, a Mathematica issue.
Thoughts appreciated.
[1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=ScreenShot20220923at3.08.15PM.png&userId=50524
Andreas Agas
20220923T19:15:08Z

MaXrd: Xray diffraction package, and other Crystallography concepts
https://community.wolfram.com/groups//m/t/2825040
![enter image description here][1]
&[Wolfram Notebook][2]
[1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=MaXrd.png&userId=20103
[2]: https://www.wolframcloud.com/obj/7459de42edc64afd92d2a18e70ed23cf
Stian Ramsnes
20230206T19:33:48Z

Placing checkboxes in popup window
https://community.wolfram.com/groups//m/t/2824138
I've attached a working example file containing some controls functioning in a manipulate structure. The code produces a varying number of checkboxes. I'm looking for a way to place these checkboxes into a popup menu to save space. The ability to check more than one checkbox in the popup menu is required. I've attached the working file. Please advise, or direct me to something in the reference material. Much Thanks. G
&[Wolfram Notebook][1]
[1]: https://www.wolframcloud.com/obj/c0f6eee1a2ee4e0bb34f1b7b2da75502
Gerald Proteau
20230205T14:34:09Z

Why does SyntaxQ appear to contradict SyntaxLength?
https://community.wolfram.com/groups//m/t/2824653
&[Wolfram Notebook][1]
[1]: https://www.wolframcloud.com/obj/621a4738888649ff82f5e9d2c5043db4
David Vasholz
20230206T17:06:36Z

Same code with involving integer takes longer time
https://community.wolfram.com/groups//m/t/2824228
Hello,
Np = 500;
a = 1;
b = 4.0;
h = (b  a)/Np;
x0 = a;
y[0] = 1;
Y = {{x0, y[0]}};
f[x_, y_] = y*(x + 1)  Cos[x];
For[m = 0, m <= Np  1, m++,
xm = a + m*h;
y[m + 1] = y[m] + h*f[xm, y[m]];
AppendTo[Y, {xm + h, y[m + 1]}];
];
g2 = ListLinePlot[Y, PlotStyle > Green, PlotRange > All]
![enter image description here][1]
Np = 500;
a = 1;
b = 4;
h = (b  a)/Np;
x0 = a;
y[0] = 1;
Y = {{x0, y[0]}};
f[x_, y_] = y*(x + 1)  Cos[x];
For[m = 0, m <= Np  1, m++,
xm = a + m*h;
y[m + 1] = y[m] + h*f[xm, y[m]];
AppendTo[Y, {xm + h, y[m + 1]}];
];
g2 = ListLinePlot[Y, PlotStyle > Green, PlotRange > All]
![enter image description here][2]
[1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=5983Capture1.JPG&userId=2803344
[2]: https://community.wolfram.com//c/portal/getImageAttachment?filename=10109Capture2.JPG&userId=2803344
So, the only difference is in b, in that in the first case b=4.0, while in the second case b=4. In the first case the code runs quickly and displays the result, while in the second case, the code runs endlessly and does not display the result.
Can someone explain how exactly that .0 influences the running of the code so much?
Thank you.
Cornel B.
20230205T18:18:47Z

Mathematica and ML – TensorFlow visualisation
https://community.wolfram.com/groups//m/t/2823852
I am currently studying a specialization on Coursera in Machine Learning and am investigating various tools to help me out with the maths and with visualisations and so on.
Although I have many decades experience of development and am very handsome, I haven't done any formal maths study since my early 20s. So I want to take the edge off.
As a first excursion, I would like to be able to plot the results of predictions on my TensorFlow models against the training data, in a similar way `tfvis` library that comes along with `tensorflow.js`; but perhaps allowing me to tweak the layers, units and so on of my regressor model and see the effect in real time.
Am I dreaming here? Can Mathematica help me with that? If not, can anyone suggest an alternative?
Mark Norgate
20230204T16:58:06Z

Use Replace and Part at the same time?
https://community.wolfram.com/groups//m/t/2822890
Hello,
a = {6, 5, 4, 3, 2,
1}; {{1, 2, 3}, {4, 5, 6}} /. {d_, b_, c_} > {a[[d]], a[[b]], a[[c]]}
would get errors:
> Part::pkspec1: The expression d cannot be used as a part specification.
> Part::pkspec1: The expression b cannot be used as a part specification.
> Part::pkspec1: The expression c cannot be used as a part specification.
> General::stop: Further output of Part::pkspec1 will be suppressed during this calculation.
Is there a way to use them at the same time?
Thanks.
Zhenyu Zeng
20230203T15:47:02Z

Improved Eulers Method Problem
https://community.wolfram.com/groups//m/t/2815256
It is given the following problem:
$$X'=Z+(Y\alpha)X$$
$$Y'=1\beta YX^2$$
$$Z'=X\gamma Z$$
with initial conditions $(X(0),Y(0),Z(0)=(1,2,3)$.
Where
X: interest rate
Υ:investment demand
Z: price index
$\alpha$: savings,
$\beta$: cost per investment,
$\gamma$: the absolute value of the elasticity of demand
```
\[Alpha]=0.9;
\[Beta]=0.2;
\[Gamma]=1.2;
f[x_,y_,z_]:=z+(y\[Alpha])*x
g[x_,y_,z_]:=1\[Beta]*yx^2
h[x_,y_,z_]:=x\[Gamma]*z
```
I know how to define a system with two functions so I could use these
 Method A: accuracy of order h
S[a_, b_, h_, N_] := (u[0] = a; u[1] = a + h*b;
Do[u[n + 1] =
2 u[n]  u[n  1] + h*h*f[n*h, u[n], (u[n]  u[n  1])/h], {n, 1,
N}])
 Method B: accuracy of order h^2
Q[a_, b_, h_, N_] := (u[0] = a; v[0] = b;
Do[{u[n + 1] =
u[n] + h*
F[u[n] + (h/2)*F[u[n], v[n]],
v[n] + (h/2)*
G[u[n], v[
n]]], \
v[n + 1] =
v[n] + h*
G[u[n] + (h/2)*F[u[n], v[n]], v[n] + (h/2)*G[u[n], v[n]]]}, {n,
0, N}])
Athanasios Paraskevopoulos
20230126T12:03:14Z

Formulas of interpolation/extrapolation method spline
https://community.wolfram.com/groups//m/t/2824367
Hello,
I would like to understand the formula behind the following interpolation and extrapolation done in mathematica in order to convert it in python:
K is equal to
{27.827, 18.53, 30.417} 0.205
{22.145, 13.687, 33.282} 0.197
{29.018, 18.841, 38.761} 0.204
{26.232, 22.327, 27.735} 0.197
{28.761, 21.565, 31.586} 0.212
{24.002, 17.759, 24.782} 0.208
{17.627, 18.224, 25.197} 0.204
{24.834, 20.538, 33.012} 0.205
{23.017, 23.037, 29.23} 0.211
{26.263, 23.686, 32.766} 0.215
K = ToExpression[Import[NotebookDirectory[] <> "df.txt", "TSV"]];
func = Interpolation[Map[{#[[1]], #[[2]]} &, K],
InterpolationOrder > {1, 1, 1}, Method > "Spline"];
result= func[2, 2, 3]
0.0298707
result1 = func[20,20,30]
0.168097
To have these results which is the formula applied using the variables above?
Thanks
Daniela Tortora
20230206T12:10:34Z

Identifying humans in a video
https://community.wolfram.com/groups//m/t/2732106
I'm looking for some good methods for finding humans in a video, I'm using
Entity["Concept", "Person::93r37"]
with limited accuracy.
(1) Is there a better entity I should be using?
(2) Is there a good training set that I could use to improve performance? At this point, I don't care what they are doing, I would just like to identify that there is a person in the frame.
Any advice would be appreciated.
S G
20221215T10:03:47Z

Resonance circuit: achieving the sinus waveform
https://community.wolfram.com/groups//m/t/2823782
Hello everyone, I have a basic serial resonance circuit, which simulates frequency converter with output square waveform and I am not able to achieve the sinus waveform during resonance.
Do you have any experience with this?
The model is in the attachment.
Thank you.
Mike
Michal K
20230205T14:17:38Z

Can I create a custom HolidayCalendar
https://community.wolfram.com/groups//m/t/2713860
Hello,
I was exploring the accuracy of Mathematica's **TimeSeriesResample[ ]** function trying to transform 15 min financial time series into daily "BusinessDay" data time series.
Dealing with french stock data, I use this command :
tsr = TimeSeriesResample[ts, "BusinessDay", HolidayCalendar > "France"]
Sadly, it seems that the french HolidayCalendar used by Mathematica may not be accurate.
Indeed, Euronext official Calendar of business days 2022 (https://www.euronext.com/en/trade/tradinghoursholidays) gives Friday 15 April 2022 and Monday 18 April 2022 as closed trading days. As such, my 15 min source time series "ts" doesn't contain any values nor timestamps for those dates, iterating from 14 April 2022 straight to 19 April 2022.
But "tsr" has those dates, creating interpolated values.
Is this behaviour normal ? Isn't the whole point of using "BusinessDay" specification to suppress datapoints from time series when market is closed ?
Going forward, I did read the official documentation for HolidayCalendar (https://reference.wolfram.com/language/ref/HolidayCalendar.html) which says that we can define a *custom holiday schedule* under the Scope section.
Does that mean that I can use a list of closed market dates of my creation and feed that list as argument in TimeSeriesResample function ? I did read the documentation's examples, but couldn't find a way to make it work at all.
Thank you in advance for any help you can give me.
Cheers.
Clarisse Wagner
20221201T20:30:57Z

Symbolic formulas for Airy equations?
https://community.wolfram.com/groups//m/t/2823543
I can find the Airy formula's in Mathematica under the author's name. Ai and Bi. I do not care to work with the formula's as named expressions. I would prefer to work with symbols, like Cosine and the Integral and so forth and so on. How do I convert these named expressions to symbolic relations?
Alan White
20230204T01:44:26Z

Adding a best fit surface
https://community.wolfram.com/groups//m/t/2821876
A very elementary presentation question for a new user  I have a 3D point plot to which I am attempting to add a "bestfit" surface. Tediously I cannot seem to get even the simplest of trials to work (i.e. I can generate the plot easily enough (trivial sample attached) but adding this surface is beyond me. I'm undertaking to learn Wolfram Language as a senior citizen, but better late than never I say.
![enter image description here][1]
[1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Additionofabestfitsurface.jpg&userId=2431543
Geoff Booth
20230202T05:02:29Z

[WSS22] Quantum Ethernet
https://community.wolfram.com/groups//m/t/2575423
&[Wolfram Notebook][1]
[1]: https://www.wolframcloud.com/obj/8589208141094443b89c4ee0dbc3b106
Paul Borrill
20220719T22:15:43Z

Working with Units in Wolfram Mathematica
https://community.wolfram.com/groups//m/t/2823597
Hello,
How can I do this in Wolfram Mathematica?
How can I work with units of measurement in Wolfram Mathematica?
![enter image description here][1]
[1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Capture4.JPG&userId=2803344
Thank you.
Cornel B.
20230204T20:42:25Z

Bode Plot  Customization of axis
https://community.wolfram.com/groups//m/t/2823564
Hello,
I would like to be able to plot the Bode diagrams of magnitude and phase in the following way in Mathematica (actually as it is shown in the following example of plotting the Bode diagram in Matlab):
![enter image description here][1]
![enter image description here][2]
[1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Matlab_Bode_Plot.JPG&userId=2803344
[2]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Mathematica_Bode_Plot.JPG&userId=2803344
It seems that Mathematica plots according to w, and not to frequency. w=2pi*freq
How can I make the Bode Plot in Mathematica look the same as it looks in Matlab Bode Plot?
Wolfram Mathematica 12.0 file attached.
Thank you.
Cornel B.
20230204T12:04:46Z

Using vector variables and changing variables in ODEs
https://community.wolfram.com/groups//m/t/2823806
&[Wolfram Notebook][1]
[1]: https://www.wolframcloud.com/obj/ea736d97ac0b42f9b87dbc5902508eda
Peter Burbery
20230204T15:36:19Z

Simplify function argument
https://community.wolfram.com/groups//m/t/2823944
In a more complicated expression I would like Mathematica to simplify
Integrate[f[x  Floor[x]], {x, 0, 1}]
to
Integrate[f[x], {x, 0,1 }]
Simplify[...] doesn't seem to do it. Ideas? Thanks.
julio kuplinsky
20230204T14:48:53Z

Using Prefix trees for Markov chain text generation
https://community.wolfram.com/groups//m/t/2819012
&[Wolfram Notebook][1]
[1]: https://www.wolframcloud.com/obj/9fd00518feea415f8bf8992deacdb99d
Anton Antonov
20230128T18:34:02Z

Cryptocurrencies: correlations, clustering and data analysis
https://community.wolfram.com/groups//m/t/2295861
*MODERATOR NOTE: Also see [blockchain integration][1] in the Wolfram Language, a part of [Wolfram Blockchain Labs][2].*
[1]: https://reference.wolfram.com/language/guide/Blockchain.html
[2]: https://www.wolframblockchainlabs.com

![enter image description here][3]
&[Wolfram Notebook][4]
[DONT DELETE: Original Notebook]: https://www.wolframcloud.com/obj/ed6de39848754040b3cdd36d285d9c59
[3]: https://community.wolfram.com//c/portal/getImageAttachment?filename=sdfq34fdasdfas34.jpeg&userId=20103
[4]: https://www.wolframcloud.com/obj/409f97e41aff41609131b7cc38d76ebf
Anton Antonov
20210622T17:48:33Z

Great rhombic triacontahedron explaoned
https://community.wolfram.com/groups//m/t/2823046
&[Wolfram Notebook][1]
[1]: https://www.wolframcloud.com/obj/037b0049c7c14ba492fa1f00fa713279
Sandor Kabai
20230203T17:49:46Z

ChatGPT as a WolframAlpha input generator
https://community.wolfram.com/groups//m/t/2823601
This is a ChatGPT prompt so that it acts as a WolframAlpha input generator:
> I want you to act as a WolframAlpha input generator, providing me
> with questions and queries to input into WolframAlpha. Your responses
> should be wellformed, complete, and formatted in a way that would
> provide the most accurate and helpful results from WolframAlpha. The
> answers should not include any explanations or additional information,
> only the formatted query for WolframAlpha. Let's start with a simple
> one, what is the population of Paris?
Icy Toc
20230203T20:49:42Z

Difference map generative art
https://community.wolfram.com/groups//m/t/2823307
![enter image description here][1]
&[Wolfram Notebook][2]
[1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=smithtiles_obama30x30_rrr05_optimized.gif&userId=20103
[2]: https://www.wolframcloud.com/obj/d33cd2bb69fb4f0cbd08b9d2d613f911
George Varnavides
20230203T20:00:10Z