A q-analogue of Gosper's strange evaluation of the hypergeometric series
Abstract
In 1977, Gosper conjectured many strange evaluations of hypergeometric series. One of them is a 2F1-series identity with two free parameters, which was proved by Ebisu (2013), Chu (2017), and Campbell (2023) in different ways. In this paper, we present a q-analogue of the 2F1-series identity, along with its generalization, by using three-term relations for the 2φ1 basic hypergeometric series.
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