Community RSS Feed https://community.wolfram.com RSS Feed for Wolfram Community showing any discussions in tag Wolfram|Alpha sorted by active Obtain series expansions using Frobenius Method https://community.wolfram.com/groups/-/m/t/1705566 ## Fail Cases ## Series[Exp[-2 Pi/Sqrt Hypergeometric2F1[1/2, 1/2, 1, 1 - x]/Hypergeometric2F1[1/2, 1/2, 1, x]], {x, 0, 5}] Series[Exp[-2 Pi/Sqrt Hypergeometric2F1[1/3, 2/3, 1, 1 - x]/Hypergeometric2F1[1/3, 2/3, 1, x]], {x, 0, 5}] Series[Exp[-2 Pi/Sqrt Hypergeometric2F1[1/4, 3/4, 1, 1 - x]/Hypergeometric2F1[1/4, 3/4, 1, x]], {x, 0, 5}] Series[Exp[-2 Pi Hypergeometric2F1[1/6, 5/6, 1, 1 - x]/Hypergeometric2F1[1/6, 5/6, 1, x]], {x, 0, 5}] ![Fail Cases] Looks like something is going wrong on your end. Or try typing one of these into Wolfram|Alpha: ![enter image description here] No response is slightly better than printing out nonsense, but why shouldn&#039;t we try and do better? I asked Bill Gosper, and he also thinks these expansions need to be fixed. We could try to do something like this: ## Frobenius Method ## TSol[PFCS_, nMax_] := With[{TAnsatz = { Dot[a1 /@ Range[0, nMax], x^Range[0, nMax]], Plus[Log[x] Dot[a1 /@ Range[0, nMax], x^Range[0, nMax]], Dot[a2 /@ Range[0, nMax], x^Range[0, nMax]]]} /. {a1 -&gt; 1, a2 -&gt; 0}}, TAnsatz /. Solve[# == 0 &amp; /@ Flatten[CoefficientList[#, {x, Log[x]}][[1 ;; nMax] ] &amp; /@ Dot[PFCS, D[TAnsatz, {x, #}] &amp; /@ Range[0, 2]]], Flatten[{a1 /@ Range[1, nMax], a2 /@ Range[1, nMax]}] ][] /. {a1[_] -&gt; 0, a2[_] -&gt; 0}] MapThread[With[{f1 = TSol[{#1 - 1, #1^2 (-1 + 2 x), #1^2 (-1 + x) x}, 14]}, Expand[1/#2 Normal[Series[Exp[f1[]/f1[]], {x, 0, 10}]] /. x -&gt; #2 x]] &amp;, {{2, 3, 4, 6}, {16, 27, 64, 432}}] Out[]:= { x + 8 x^2 + 84 x^3 + 992 x^4 + 12514 x^5 + 164688 x^6 + 2232200 x^7 + 30920128 x^8 + 435506703 x^9 + 6215660600 x^10, x + 15 x^2 + 279 x^3 + 5729 x^4 + 124554 x^5 + 2810718 x^6 + 65114402 x^7 + 1538182398 x^8 + 36887880105 x^9 + 895303119303 x^10, x + 40 x^2 + 1876 x^3 + 95072 x^4 + 5045474 x^5 + 276107408 x^6 + 15444602248 x^7 + 878268335296 x^8 + 50588345910799 x^9 + 2944021398570264 x^10, x + 312 x^2 + 107604 x^3 + 39073568 x^4 + 14645965026 x^5 + 5609733423408 x^6 + 2182717163349896 x^7 + 859521859502348352 x^8 + 341679883727799750159 x^9 + 136868519056531319862408 x^10 } I&#039;m also willing to give a talk as to why I think these are important evaluations and how they fit into the wider context of what we can possibly hope to accomplish using Mathematica. Cheers --Brad PS. Don&#039;t feel too bad, other than A005797, these expansions are not in OEIS either. : https://community.wolfram.com//c/portal/getImageAttachment?filename=FailCases.png&amp;userId=234448 : https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshotfrom2019-06-1603-14-17.png&amp;userId=234448 Brad Klee 2019-06-16T08:39:24Z Wolfram|Alpha says "invalid appid"... how to rectify? https://community.wolfram.com/groups/-/m/t/957549 On my Samsung s6, my wolfram alpha app (and even the Web version in the chrome app) continually responds to my queries with &#034;invalid appid&#034;. Does anyone know how to overcome this technical difficulty? Thanks for your time everyone! Aaron Bondy 2016-11-06T07:33:39Z [✓] Solve an equation for peptide deletion sequences? https://community.wolfram.com/groups/-/m/t/1704239 Hi there, I am trying to solve the equation [known value]=a*113+b*147+c*99+d*163+e*106+f*101+g*186+h*97+i*103 for a number of different [known values], where each variable is limited to its individual small set of positive integers up to 4, including 0. However, I am unable to input this into Wolfram Alpha. I have tried 635=a*113+b*147+c*99+d*163+e*106+f*101+g*186+h*97+i*103 ; a=0,1,2 ; b=0,1 ; c=0,1 ; d=0,1 ; e=0,1 ; f=0,1,2,3,4 ; g=0,1,2,3 ; h=0,1 ; i=0,1 solve [635=a*113+b*147+c*99+d*163+e*106+f*101+g*186+h*97+i*103] over a=0,1,2 ; b=0,1 ; c=0,1 ; d=0,1 ; e=0,1 ; f=0,1,2,3,4 ; g=0,1,2,3 ; h=0,1 ; i=0,1 solve [635=a*113+b*147+c*99+d*163+e*106+f*101+g*186+h*97+i*103] over [a,b,c,d,e,f,g,h,i] where [a=0,1,2 ; b=0,1 ; c=0,1 ; d=0,1 ; e=0,1 ; f=0,1,2,3,4 ; g=0,1,2,3 ; h=0,1 ; i=0,1] 635=a*113+b*147+c*99+d*163+e*106+f*101+g*186+h*97+i*103 AND a=0,1,2 AND b=0,1AND c=0,1 AND d=0,1 AND e=0,1 AND f=0,1,2,3,4 AND g=0,1,2,3 AND h=0,1 AND i=0,1 635=a*113+b*147+c*99+d*163+e*106+f*101+g*186+h*97+i*103 ; a={0,1,2}... ...and a bunch of other guesses. Basically I need someone to tell me how to limit different variables to individual sets of numbers. Wolfram Alpha examples and Google are not of much help. For those interested in the background: I work as a chemist synthesizing peptides. Sometimes in complicated sequences some amino acids won&#039;t give full conversion during coupling, leading to deletion sequences in the final product mixture. The number left of the = is the mass differential to the expected product, the variables&#039; factors are masses of individual amino acid building blocks. By finding out which of the amino acids are missing, I&#039;ll be able to take measures to improve coupling yields in following attempts. Lutz Adam 2019-06-13T15:35:11Z