Differentiation identities for hypergeometric functions

被引：0

作者：

Motohashi, Hayato ^{[1
]}

机构：

[1] Kogakuin Univ, Div Liberal Arts, 2665-1 Nakano machi, Hachioji, Hachioji, Tokyo 1920015, Japan

来源：

EXPOSITIONES MATHEMATICAE | 2022年 / 40卷 / 04期

基金：

日本学术振兴会;

关键词：

Gauss hypergeometric function; Kummer confluent hypergeometric function; Generalized hypergeometric function;

D O I：

10.1016/j.exmath.2022.07.005

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

It is well-known that differentiation of hypergeometric function multiplied by a certain power function yields another hypergeometric function with a different set of parameters. Such differentiation identities for hypergeometric functions have been used widely in various fields of applied mathematics and natural sciences. In this expository note, we provide a simple proof of the differentiation identities, which is based only on the definition of the coefficients for the power series expansion of the hypergeometric functions.(c) 2022 The Author(s). Published by Elsevier GmbH. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

引用

页码：894 / 909

页数：16

共 11 条

[1]

Bailey W.N., 1935, GEN HYPERGEOMETRIC S

[2]

Bateman H., 1955, HIGHER TRANSCENDENTA, VI

[3]

Luke Y.L., 1969, SPECIAL FUNCTIONS TH, VVolume 1

[4]

Magnus W., 1966, Formulas and Theorems for the Special Functions of Mathematical Physics, Vthird