Several transformation formulas for basic hypergeometric series

被引：0

作者：

Wei, Chuanan ^{[1
]}

Gong, Dianxuan ^{[2
]}

机构：

[1] Hainan Med Univ, Sch Biomed Informat & Engn, Haikou, Hainan, Peoples R China

[2] North China Univ Sci & Technol, Coll Sci, Tangshan, Peoples R China

来源：

JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS | 2021年 / 27卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Basic hypergeometric series; Ramanujan's (1)psi(1) summation formula; Andrews' identity; Ramanujan's reciprocity theorem;

D O I：

10.1080/10236198.2021.1876683

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In 1981, Andrews gave a four-variable generalization of Ramanujan's (1)psi(1) summation formula. Weestablish a six-variable generalization of Andrews' identity according to the transformation formula for two (8)phi(7) series and Bailey's transformation formula for three (8)phi(7) series. Then, it is used to find a six-variable generalization of Ramanujan's reciprocity theorem, which is different from Liu's formula. We derive the generalizations of Bailey's two (3)psi(3) summation formulas in terms of two limiting relations and Bailey's another transformation formula for three (8)phi(7) series. Based on the two limiting relations, some different results involving bilateral basic hypergeometric series are also deduced from the Guo-Schlosser transformation formula and other two transformation formulas.

引用

页码：157 / 171

页数：15

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