Some summation theorems and transformations for q-series

Mourad E.H. Ismail; Mizan Rahman; Sergei K. Suslov

doi:10.4153/CJM-1997-025-6

Some summation theorems and transformations for q-series

Mourad E.H. Ismail, Mizan Rahman, Sergei K. Suslov

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

11 Scopus citations

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 ₆φ₅ 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.

Original language	English (US)
Pages (from-to)	543-567
Number of pages	25
Journal	Canadian Journal of Mathematics
Volume	49
Issue number	3
DOIs	https://doi.org/10.4153/CJM-1997-025-6
State	Published - Jun 1997
Externally published	Yes

Keywords

Al-Salam-Chihara polynomials
Balanced series
Basic hypergeomctric series
Integral representations
Very well-poised series

ASJC Scopus subject areas

General Mathematics

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AU - Ismail, Mourad E.H.

AU - Rahman, Mizan

AU - Suslov, Sergei K.

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AB - 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 6φ5 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.

KW - Al-Salam-Chihara polynomials

KW - Balanced series

KW - Basic hypergeomctric series

KW - Integral representations

KW - Very well-poised series

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SP - 543

EP - 567

JO - Canadian Journal of Mathematics

JF - Canadian Journal of Mathematics

IS - 3

ER -

Some summation theorems and transformations for q-series

Abstract

Keywords

ASJC Scopus subject areas

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