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 summation, Bailey's transformations, and Bailey's 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

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.