Transformation Formulas for Bilinear Sums of Basic Hypergeometric Series

Canadian mathematical bulletin

Yasushi Kajihara¹ 

[1] Department of Mathematics, Kobe University, Rokko-dai, Kobe 657-8501, Japan

关键词: bilinear sums;    basic hypergeometric series;   

DOI  :  10.4153/CMB-2015-016-8

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

A master formula of transformation formulas for bilinear sumsof basic hypergeometric seriesis proposed. It is obtained from the author's previous results ona transformation formula for Milne's multivariate generalizationof basic hypergeometricseries of type $A$ with different dimensions and it can be consideredas a generalization of the Whipple-Sears transformation formula forterminating balanced ${}_4 phi_3$series. As an application of the master formula, the one variable casesof some transformation formulasfor bilinear sums of basic hypergeometric series are given asexamples.The bilinear transformation formulas seem to be new in the literature,even in one variable case.

【 授权许可】

Unknown