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These are replies submitted by ahmadtalaei

Thanks a lot for your help.

@dharr  Thank you so much. Min...

Thank you so much. Mine is 2016 and that is probably the issue. Anyway, could you please convert two hypergeom functions to given in the attached file to the LagendreP?

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@dharr I was able to upload th...

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I was able to upload the file. Thank you.

I find on the following page where these two functions can be converted to each other. Please see equation 14.3.1 in the following page:

https://dlmf.nist.gov/14.3

But the problem is that I couldn't find value for ν in the hypergeom function F(ν+1,−ν;1−μ;1/2−1/2x) that could result in the Legendre(ν,μ,x) where x=cos($\psi$).

@Mariusz Iwaniuk I always get a pro...

I always get a problem copy&paste from maple. Here is the link provided to the question:

https://math.stackexchange.com/questions/3254765/how-to-convert-a-hypergeom-function-to-the-legendre-function