Large Parameter Cases of the Gauss Hypergeometric Function
经典分析与常微分方程
2015-06-26 v1
摘要
We consider the asymptotic behaviour of the Gauss hypergeometric function when several of the parameters a, b, c are large. We indicate which cases are of interest for orthogonal polynomials (Jacobi, but also Krawtchouk, Meixner, etc.), which results are already available and which cases need more attention. We also consider a few examples of 3F2-functions of unit argument, to explain which difficulties arise in these cases, when standard integrals or differential equations are not available.
引用
@article{arxiv.math/0205065,
title = {Large Parameter Cases of the Gauss Hypergeometric Function},
author = {Nico M. Temme},
journal= {arXiv preprint arXiv:math/0205065},
year = {2015}
}
备注
21 pages, 4 figures