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Some summation theorems and transformations for $q$-series

  Published:1997-06-01
 Printed: Jun 1997
  • Mourad E. H. Ismail
  • 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. Basic hypergeometric series, balanced series, very well-poised series, integral representations, Al-Salam-Chihara polynomials.
MSC Classifications: 33D20, 33D60 show english descriptions unknown classification 33D20
Basic hypergeometric integrals and functions defined by them
33D20 - unknown classification 33D20
33D60 - Basic hypergeometric integrals and functions defined by them
 

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