两类Kampé de Fériet,级数的简化和求和公式

数学物理学报 ›› 2025, Vol. 45 ›› Issue (1): 136-152.

两类Kampé de Fériet,级数的简化和求和公式

刘红梅^*(),李阳

大连民族大学理学院辽宁大连 116600

收稿日期:2023-08-30 修回日期:2024-08-15 出版日期:2025-02-26 发布日期:2025-01-08
通讯作者: * 刘红梅, E-mail:liuhm7911@163.com

Reduction and Summation Formulas for Two Types of Kampé de Fériet Series

Liu Hongmei^*(),Li Yang

School of Science, Dalian Minzu University, Liaoning Dalian 116600

Received:2023-08-30 Revised:2024-08-15 Online:2025-02-26 Published:2025-01-08

摘要/Abstract

摘要：

基于两个 $ _3F_2 $-超几何级数求和公式, 该文建立了两个一般的双变量级数变换公式. 在经典超几何级数求和公式的帮助下, 这两个变换公式变形出一系列形如 $ F_{q:1;0}^{p:2;1} $ 的 Kampé de Fériet 级数求和公式. 另外, 利用四个 Saalschützian $ _4F_3[1] $-求和公式, 一些形如 $ F_{q:1;1}^{p:2;2} $ 的 Kampé de Fériet 级数的简化和变换公式也被推导出来.

关键词: 超几何级数, Kampé de Fériet 级数, 简化和求和公式

Abstract:

Two $ _3F_2[1] $-summation theorems are employed to establish two general transformation formulas for double infinite series. With the help of some classical hypergeometric series summation formulas, the two transformations yield a number of summation formulas for Kampé de Fériet series of type $ F_{q:1;0}^{p:2;1} $. Furthermore a list of reduction and transformation formulas for Kampé de Fériet series of type $ F_{q:1;1}^{p:2;2} $ are derived by utilizing four Saalschützian $ _4F_3[1] $-summation formulas.

Key words: hypergeometric series, Kampé de Fériet series, reduction and summation formulas

中图分类号:

O174.6

刘红梅, 李阳. 两类Kampé de Fériet,级数的简化和求和公式[J]. 数学物理学报, 2025, 45(1): 136-152.

Liu Hongmei, Li Yang. Reduction and Summation Formulas for Two Types of Kampé de Fériet Series[J]. Acta mathematica scientia,Series A, 2025, 45(1): 136-152.

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