Bilateral 𝑞-Watson and 𝑞-Whipple sums

Chu, Wenchang; Wang, Chenying

doi:10.1090/S0002-9939-2010-10701-3

Bilateral $q$-Watson and $q$-Whipple sums
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by Wenchang Chu and Chenying Wang PDF

Proc. Amer. Math. Soc. 139 (2011), 931-942 Request permission

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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