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# Some summation theorems and transformations for $q$-series

Published:1997-06-01
Printed: Jun 1997
• Mizan Rahman
• Sergei K. Suslov
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## Abstract

We introduce a double sum extension of a very well-poised series and extend to this the transformations of Bailey and Sears as well as the ${}_6\f_5$ summation formula of F.~H.~Jackson and the $q$-Dixon sum. We also give $q$-integral representations of the double sum. Generalizations of the Nassrallah-Rahman integral are also found.
 Keywords: Basic hypergeometric series, balanced series, very well-poised series, integral representations, Al-Salam-Chihara polynomials.
 MSC Classifications: 33D20 - unknown classification 33D2033D60 - Basic hypergeometric integrals and functions defined by them