Semi-finite forms of bilateral basic hypergeometric series

被引：15

作者：

Chen, WYC ^{[1
]}

Fu, AM ^{[1
]}

机构：

[1] Nankai Univ, LPMC, Tianjin 300071, Peoples R China

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2006年 / 134卷 / 06期

关键词：

bilateral hypergeometric summation; semi-finite forms; Ramanujan's 1 psi 1 summation; Bailey's 2 psi 2 transformations; Bailey's 6 psi 6 summation;

D O I：

10.1090/S0002-9939-05-08173-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show that several classical bilateral summation and transformation formulas have semi-finite forms. We obtain these semi-finite forms from unilateral summation and transformation formulas. Our method can be applied to derive Ramanujan's 1 psi 1 summation, Bailey's 2 psi 2 transformations, and Bailey's 6 psi 6 summation.

引用

页码：1719 / 1725

页数：7

共 9 条

[1] APPLICATIONS OF BASIC HYPERGEOMETRIC FUNCTIONS [J].

ANDREWS, GE .

SIAM REVIEW, 1974, 16 (04) :441-484

[2]

Bailey W. N., 1936, Quart. J. Math. (Oxford), V7, P105, DOI DOI 10.1093/QMATH/OS-7.1.105

[3]

Chen W Y C., 1998, Parameter augmenting for basic hypergeometric series I//Sagan B E, P111

[4]

GASPER G, 2004, ENCY MATH ITS APPL, V0096

[5]

ISMAIL MEH, 1977, P AM MATH SOC, V63, P185

[6]

Schlosser M, 2005, DEV MATH, V13, P383

[7] A simple proof of Bailey's very-well-poised 6ψ6 summation [J].

Schlosser, M .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2002, 130 (04) :1113-1123

[8]

Slater L. J., 1956, Proc. Edinburgh Math. Soc., V9, P116, DOI DOI 10.1017/S0013091500024895

[9]

YOUHET F, 2005, AEQUATIONES MATH, V70, P43

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