Bilateral $q$-Watson and $q$-Whipple sums

Abstract

Watson and Whipple (1925) discovered two summation formulae for a 3 F 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 3 H 3 -series identity due to M. Jackson (1949). This will be accomplished by means of the modified Abel lemma on summation by parts.