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Some Summation Theorems and Transformations for Q-Series

Published online by Cambridge University Press:  20 November 2018

Mourad E. H. Ismail ,
Mizan Rahman  and
Sergei K. Suslov
Mourad E. H. Ismail
Affiliation:
Department of Mathematics, University of South Florida, Tampa, Florida 33620, USA
Mizan Rahman
Affiliation:
Department of Mathematics and Statistics, Carleton University, Ottawa, Ontario, K1S 5B6
Sergei K. Suslov
Affiliation:
Department of Mathematics, Arizona State University, Tempe, Arizona 85287, USA
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Abstract

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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 ϕ 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

33D2033D60Basic hypergeometric seriesbalanced seriesvery well-poised seriesintegral representationsAl-Salam-Chihara polynomials

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 49 , Issue 3 , 01 June 1997 , pp. 543 - 567
Copyright
Copyright © Canadian Mathematical Society 1997

References

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