A further q-analogue of Gosper's strange series
arXiv:2603.24845
Abstract
Recently, the second author [Ramanujan J. 2026] introduced and proved a -series identity that appears to provide the first known -analogue of an evaluation for a -series known as \emph{Gosper's strange series}. Yamaguchi's derivation of this -analogue relies on three-term relations for -series along with Heine's transformation of -series. In this note, we introduce and prove, using a -analogue of a series evaluation technique relying on an Abel-type summation lemma, a further -analogue of Gosper's -identity that is inequivalent to Yamaguchi's -analogue, and we also apply this technique to construct an alternative and simplified proof of Yamaguchi's -analogue, together with a -series variant of Heine's -analogue of Gauss's hypergeometric formula, a -series variant and two -series variants of the -analogue of Kummer's identity due to Bailey and Daum, along with a -analogue of a result obtained by Cantarini [Ramanujan J. 2022] via Fourier-Legendre theory and related to Ramanujan's first series for .
9 pages