# InverseSeries of Gauss HyperGeometric Function

Posted 6 years ago
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 I have an equation that describes the exact solution to a non-linear 2nd order ODE that contains Guass' Hypergeometric2F1 function. m := n + 1 z := c/c0 x := 1/Phi*Sqrt[m/2/c0^(m - 2)]*2/(2 - m)*(z^(1 - m/2)*Hypergeometric2F1[1/2 - 1/m, 1/2, 3/2 - 1/m, z^-m] - Hypergeometric2F1[1/2 - 1/m, 1/2, 3/2 - 1/m, 1]) I would like to generate a series expansion of that equation and then take the InverseSeries to generate the final solution. This is described in a publication by Eugen Magyari in some detail using Mathematica. I cannot reproduce his results despite talking to the author and getting his detailed Mathematica file. Our results match until I use the InverseSeries command where I get:SeriesData::scmp: The constant term of series c^2 + O[c]^34 does not match the expansion point of {Series generated from above}The author used Mathematica v4 and did not get this error. Is there a bug or has something changed with HyperGeometric2F1 or with InverseSeries that keeps it from generating a solution as it did in v4? I've attached the output file from v4. Attachments:
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Posted 6 years ago
 Clear[x, m, n, z, c, c0, fi]; c := 1/4 c0 := 1/8 fi := 5/8 n := 3/4 m := n + 1 z := c/c0 x := 1/Phi* Sqrt[m/2/c0^(m - 2)]*2/(2 - m)*(z^(1 - m/2)* Hypergeometric2F1[1/2 - 1/m, 1/2, 3/2 - 1/m, z^-m] - Hypergeometric2F1[1/2 - 1/m, 1/2, 3/2 - 1/m, 1]) Series[Hypergeometric2F1[c, c0, 8, x], {x, 0, 1}] 
Posted 6 years ago
 Simon,I saw your reply but it appears to be missing portions of your reply. I see in the first lines you reproduced my function and then I see the Length[%27] function. I'm not sure the purpose of that command and it appears ti reference line %27 which is not visible in you post. If there was more can you, please, re-post.Thanks