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 -