What is the Asymptotic expressions of Jacobi polynomial?

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Dudley J Benton

Everything you need to know about Jacobi functions can be found in Chapters 16 and 22 of Handbook of Mathematical Functions by Abramowitz and Stegun, which can be downloaded free online.

Ekwevugbe Omugbe

Thank you for the information. I think I have checked the recommended textbook and also Tables of integrals series and products by Gradshteyn and Ryzhik. I have not found the asymptotic expression for Jacobi function.

I have used Jacobi polynomials for a variety of applications and so have attached C code. Which function(s) are you interested in?

Thank you once again. I am in interested in Jacobi[n, a, b, x].

That is the function I provided in the code above. The declaration is:

double Jacobi(int n,double alpha,double beta,double x);

Here is the same thing in Excel with VBA code:

Thanks. I can write the series expansion using either Maple or Mathematica. I am only interested in the leading asymptotic expression. Also I am not familiar with the codes you sent. Is it possible to get the asymptotic expression from the codes?

Thanks for providing help