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

 

Bilateral $ q$-Watson and $ q$-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: Watson and Whipple (1925) discovered two summation formulae for a $ _3F_2(1)$-series. Their terminating $ q$-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 $ q$-analogue of the $ _3H_3$-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: http://dx.doi.org/10.1090/S0002-9939-2010-10701-3
PII: S 0002-9939(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.