Transformation Formulas for Bilinear Sums of Basic Hypergeometric Series

被引：1

作者：

Kajihara, Yasushi ^{[1
]}

机构：

[1] Kobe Univ, Dept Math, Kobe, Hyogo 6578501, Japan

来源：

CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES | 2016年 / 59卷 / 01期

关键词：

bilinear sums; basic hypergeometric series; ORTHOGONAL POLYNOMIALS;

D O I：

10.4153/CMB-2015-016-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A master formula of transformation formulas for bilinear sums of basic hypergeometric series is proposed. It is obtained from the author's previous results on a transformation formula for Milne's multivariate generalization of basic hypergeometric series of type A with different dimensions and it can be considered as a generalization of the Whipple-Sears transformation formula for terminating balanced 4 phi 3 series. As an application of the master formula, the one-variable cases of some transformation formulas for bilinear sums of basic hypergeometric series are given as examples. The bilinear transformation formulas seem to be new in the literature, even in the one-variable case.

引用

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页码：136 / 143

页数：8

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