A simple proof of Bailey's very-well-poised 6ψ6 summation

被引：16

作者：

Schlosser, M ^{[1
]}

机构：

[1] Ohio State Univ, Dept Math, Columbus, OH 43210 USA

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2002年 / 130卷 / 04期

关键词：

bilateral basic hypergeometric series; q-series; Ramanujan's 1 psi 1 summation; Dougall's H-2(2) summation; Bailey's 6 psi 6 summation;

D O I：

10.1090/S0002-9939-01-06175-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We give elementary derivations of some classical summation formulae for bilateral (basic) hypergeometric series. In particular, we apply Gau ss' 2(F)1 summation and elementary series manipulations to give a simple proof of Dougall's H-2(2) summation. Similarly, we apply Rogers' nonterminating (6)phi (5) summation and elementary series manipulations to give a simple proof of Bailey's very-well-poised (6)psi (6) summation. Our method of proof extends M. Jackson's first elementary proof of Ramanujan's (1)psi (1) summation.

引用

页码：1113 / 1123

页数：11

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