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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.

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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}]

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

Simon,

Thanks for the follow-up but it still appears that I cannot see your entire post. I see all "In" lines but no "Out" lines so I'm not sure what the results are of any of your commands. IN addition I see that you see values for c, c0, fi, and n. These need to remain as variables so in the end I get c(x, c0, n, fi). Just for your information....c is the reaction concentration at any point along the radius of the catalyst bead, x is the radial position in a bead of catalysts, c0 is the reactant concentration at the core of the bead, n is the kinetic order of the reaction (2 for my case) and fi is the Thiele Modulus. The resulting InverseSeries will allow me to calculate the concentration profile of a reactant in a bead of catalyst.

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