A Nonterminating q -Clausen Formula and Some Related Product Formulas

This paper uses Gasper-s proof of Rogers- linearization formula for the continuous $q$-ultraspherical polynomials and a quadratic transformation formula for well-poised basic hypergeometric _2 \phi _1 $ series to derive a nonterminating $q$-analogue of Clausen-s formula for the square of a certain h...

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Bibliographic Details
Published in:SIAM journal on mathematical analysis Vol. 20; no. 5; pp. 1270 - 1282
Main Authors: Gasper, George, Rahman, Mizan
Format: Journal Article
Language:English
Published: Philadelphia, PA Society for Industrial and Applied Mathematics 01.09.1989
Subjects:
Applied mathematics
Exact sciences and technology
Function theory, analysis
Mathematical methods in physics
Physics
Mathematical function
Special function
Hypergeometric series
ISSN:0036-1410, 1095-7154
Online Access:Get full text
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Summary:This paper uses Gasper-s proof of Rogers- linearization formula for the continuous $q$-ultraspherical polynomials and a quadratic transformation formula for well-poised basic hypergeometric _2 \phi _1 $ series to derive a nonterminating $q$-analogue of Clausen-s formula for the square of a certain hypergeometric series. This formula is extended to a $q$-analogue of the Ramanujan and Bailey extension of Clausen-s formula by employing the Gasper and Rahman nonterminating $q$-extension of the Sears-Carlitz quadratic transformation formula. Additional product formulas are derived.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
content type line 14
ISSN:0036-1410
1095-7154
DOI:10.1137/0520084