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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Semi-finite forms of bilateral basic hypergeometric series


Authors: William Y. C. Chen and Amy M. Fu
Journal: Proc. Amer. Math. Soc. 134 (2006), 1719-1725
MSC (2000): Primary 33D15
Published electronically: December 5, 2005
MathSciNet review: 2204284
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Abstract | References | Similar Articles | Additional Information

Abstract: We show that several classical bilateral summation and transformation formulas have semi-finite forms. We obtain these semi-finite forms from unilateral summation and transformation formulas. Our method can be applied to derive Ramanujan's $ _{1}\psi _{1}$ summation, Bailey's $ _{2}\psi _{2}$ transformations, and Bailey's $ _{6}\psi _{6}$ summation.


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Additional Information

William Y. C. Chen
Affiliation: Center for Combinatorics, LPMC, Nankai University, Tianjin 300071, People’s Republic of China
Email: chen@nankai.edu.cn

Amy M. Fu
Affiliation: Center for Combinatorics, LPMC, Nankai University, Tianjin 300071, People’s Republic of China
Email: fu@nankai.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-05-08173-6
PII: S 0002-9939(05)08173-6
Keywords: Bilateral hypergeometric summation, semi-finite forms, Ramanujan's ${}_{1}\psi _{1}$ summation, Bailey's ${}_{2}\psi _{2}$ transformations, Bailey's ${}_{6}\psi _{6}$ summation.
Received by editor(s): December 8, 2004
Received by editor(s) in revised form: January 11, 2005
Published electronically: December 5, 2005
Communicated by: John R. Stembridge
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.