UNIFORM ASYMPTOTIC EXPANSIONS FOR HYPERGEOMETRIC FUNCTIONS WITH LARGE PARAMETERS I-Reference-Cited by-同舟云学术

UNIFORM ASYMPTOTIC EXPANSIONS FOR HYPERGEOMETRIC FUNCTIONS WITH LARGE PARAMETERS I

Published:2003-01 Issue:01 Volume:01 Page:111-120
ISSN:0219-5305
Container-title:Analysis and Applications
language:en
Short-container-title:Anal. Appl.

Author:

OLDE DAALHUIS A. B.¹

Affiliation:

1. School of Mathematics, King's Buildings, University of Edinburgh, Edinburgh EH9 3JZ, UK

Abstract

In this paper, we obtain an asymptotic expansion for the Gauss hypergeometric function 2F1(a, b - λ; c + λ; -z), as |λ| → ∞. The expansion holds for fixed values of a, b, and c, and is uniformly valid for z in the domain | ph z| < π.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Analysis

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219530503000028

Reference10 articles.

1. Nat. Bur. Standards Appl. Math. Series;Abramowitz M.,1964

2. Uniform asymptotic expansions of integrals with stationary point near algebraic singularity

3. Asymptotics of the hypergeometric function

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