Asymptotic expansions of Kummer hypergeometric functions with three asymptotic parameters a,b and z期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Asymptotic expansions of Kummer hypergeometric functions with three asymptotic parameters a,b and z

Affiliation:	1. Institut de Mathématiques de Bordeaux, 351, cours de la Libération, 33 405 Talence, France;2. Copenhagen Centre for Geometry and Topology, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark;3. Department of Mathematics, 155 South 1400 East, JWB 233, Salt Lake City, UT 84112, USA;1. Mathematisches Institut, Endenicher Allee 60, D-53115 Bonn, Germany;2. Alfréd Rényi Institute of Mathematics, POB 127, Budapest H-1364, Hungary;3. MTA Rényi Intézet Lendület Automorphic Research Group, POB 127, Budapest H-1364, Hungary;4. Bryn Mawr College, Department of Mathematics, 101 North Merion Avenue, Bryn Mawr, PA 19010, USA

Abstract:	In a recent paper (Temme, 2021) new asymptotic expansions are given for the Kummer functions $M (a, b, z)$ and $U (a, b + 1, z)$ for large positive values of $a$ and $b$ , with $z$ fixed and special attention for the case $a ～ b$ . In this paper we extend the approach and also accept large values of $z$ . The new expansions are valid when at least one of the parameters $a$ , $b$ , or $z$ is large. We provide numerical tables to show the performance of the expansions.

Keywords:	Asymptotic expansions Kummer functions Confluent hypergeometric functions
本文献已被 ScienceDirect 等数据库收录！