2025/07/02 by Yuka Yamaguchi, Yamaguchi, Yuka
Mathematics · #Advanced Mathematical Identities #Mathematical functions and polynomials #Algebraic structures and combinatorial models
paper · pdf · doi:10.48550/arxiv.2507.01499
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.