A q-series expansion formula and the Askey-Wilson polynomials

被引：38

作者：

Liu, Zhi-Guo ^{[1
]}

机构：

[1] E China Normal Univ, Dept Math, Shanghai 200241, Peoples R China

来源：

RAMANUJAN JOURNAL | 2013年 / 30卷 / 02期

基金：

美国国家科学基金会;

关键词：

q-series; Rogers' (6)phi(5) summation; Mock theta functions; Hecke type series; Askey-Wilson polynomials; Lambert series;

D O I：

10.1007/s11139-012-9450-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Previously, we proved a q-series expansion formula which allows us to recover many important classical results for q-series. Based on this formula, we derive a new q-formula in this paper, which clearly includes infinitely many q-identities. This new formula is used to give a new proof of the orthogonality relation for the Askey-Wilson polynomials. A curious q-transformation formula is proved, and many applications of this transformation to Hecke type series are given. Some Lambert series identities are also derived.

引用

页码：193 / 210

页数：18

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