Bilateral -Watson and -Whipple sums

Authors:
Wenchang Chu and Chenying Wang

Journal:
Proc. Amer. Math. Soc. **139** (2011), 931-942

MSC (2010):
Primary 33D15; Secondary 05A30

Published electronically:
November 1, 2010

MathSciNet review:
2745645

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Abstract | References | Similar Articles | Additional Information

Abstract: Watson and Whipple (1925) discovered two summation formulae for a -series. Their terminating -analogues were found by Andrews (1976) and Jain (1981). As a common extension of these results, we prove a general bilateral series identity, which may also be considered as a full -analogue of the -series identity due to M. Jackson (1949). This will be accomplished by means of the modified Abel lemma on summation by parts.

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Additional Information

**Wenchang Chu**

Affiliation:
Institute of Combinatorial Mathematics, Hangzhou Normal University, Hangzhou 310036, People’s Republic of China

Address at time of publication:
Dipartimento di Matematica, Università del Salento, Via Provinciale Lecce–Arnesano, P.O. Box 193, Lecce 73100, Italy

Email:
chu.wenchang@unisalento.it

**Chenying Wang**

Affiliation:
College of Mathematics and Physics, Nanjing University of Information Science and Technology, Nanjing 210044, People’s Republic of China

Email:
wang.chenying@163.com

DOI:
https://doi.org/10.1090/S0002-9939-2010-10701-3

Keywords:
Abel’s lemma on summation by parts,
$q$-Whipple sum,
$q$-Watson sum.

Received by editor(s):
February 22, 2010

Published electronically:
November 1, 2010

Additional Notes:
The second author is the corresponding author

Communicated by:
Walter Van Assche

Article copyright:
© Copyright 2010
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.