Parameter Augmentation for Basic Hypergeometric Series, II

William Y.C. Chen; Zhi Guo Liu

doi:10.1006/jcta.1997.2801

Parameter Augmentation for Basic Hypergeometric Series, II

William Y.C. Chen^*
, Zhi Guo Liu

^*Corresponding author for this work

Los Alamos National Laboratory
Nankai University
Xinxiang Education College

Research output: Contribution to journal › Article › peer-review

87 Scopus citations

Abstract

In a previous paper, we explored the idea of parameter augmentation for basic hypergeometric series, which provides a method of provingq-summation and integral formula based special cases obtained by reducing some parameters to zero. In the present paper, we shall mainly deal with parameter augmentation forq-integrals such as the Askey-Wilson integral, the Nassrallah-Rahman integral, theq-integral form of Sears transformation, and Gasper's formula of the extension of the Askey-Roy integral. The parameter augmentation is realized by another operator, which leads to considerable simplications of some well knownq-summation and transformation formulas. A brief treatment of the Rogers-Szegö polynomials is also given.

Original language	English
Pages (from-to)	175-195
Number of pages	21
Journal	Journal of Combinatorial Theory. Series A
Volume	80
Issue number	2
DOIs	https://doi.org/10.1006/jcta.1997.2801
State	Published - Nov 1997
Externally published	Yes

Access to Document

10.1006/jcta.1997.2801

Cite this

@article{169aeb3ff8f14695a536d5180385c699,

title = "Parameter Augmentation for Basic Hypergeometric Series, II",

abstract = "In a previous paper, we explored the idea of parameter augmentation for basic hypergeometric series, which provides a method of provingq-summation and integral formula based special cases obtained by reducing some parameters to zero. In the present paper, we shall mainly deal with parameter augmentation forq-integrals such as the Askey-Wilson integral, the Nassrallah-Rahman integral, theq-integral form of Sears transformation, and Gasper's formula of the extension of the Askey-Roy integral. The parameter augmentation is realized by another operator, which leads to considerable simplications of some well knownq-summation and transformation formulas. A brief treatment of the Rogers-Szeg{\"o} polynomials is also given.",

author = "Chen, \{William Y.C.\} and Liu, \{Zhi Guo\}",

year = "1997",

month = nov,

doi = "10.1006/jcta.1997.2801",

language = "英语",

volume = "80",

pages = "175--195",

journal = "Journal of Combinatorial Theory. Series A",

issn = "0097-3165",

publisher = "Academic Press Inc.",

number = "2",

}

TY - JOUR

T1 - Parameter Augmentation for Basic Hypergeometric Series, II

AU - Chen, William Y.C.

AU - Liu, Zhi Guo

PY - 1997/11

Y1 - 1997/11

N2 - In a previous paper, we explored the idea of parameter augmentation for basic hypergeometric series, which provides a method of provingq-summation and integral formula based special cases obtained by reducing some parameters to zero. In the present paper, we shall mainly deal with parameter augmentation forq-integrals such as the Askey-Wilson integral, the Nassrallah-Rahman integral, theq-integral form of Sears transformation, and Gasper's formula of the extension of the Askey-Roy integral. The parameter augmentation is realized by another operator, which leads to considerable simplications of some well knownq-summation and transformation formulas. A brief treatment of the Rogers-Szegö polynomials is also given.

AB - In a previous paper, we explored the idea of parameter augmentation for basic hypergeometric series, which provides a method of provingq-summation and integral formula based special cases obtained by reducing some parameters to zero. In the present paper, we shall mainly deal with parameter augmentation forq-integrals such as the Askey-Wilson integral, the Nassrallah-Rahman integral, theq-integral form of Sears transformation, and Gasper's formula of the extension of the Askey-Roy integral. The parameter augmentation is realized by another operator, which leads to considerable simplications of some well knownq-summation and transformation formulas. A brief treatment of the Rogers-Szegö polynomials is also given.

UR - https://www.scopus.com/pages/publications/0038877325

U2 - 10.1006/jcta.1997.2801

DO - 10.1006/jcta.1997.2801

M3 - 文章

AN - SCOPUS:0038877325

SN - 0097-3165

VL - 80

SP - 175

EP - 195

JO - Journal of Combinatorial Theory. Series A

JF - Journal of Combinatorial Theory. Series A

IS - 2

ER -

Parameter Augmentation for Basic Hypergeometric Series, II

Abstract

Access to Document

Other files and links

Fingerprint

Cite this