Symmetries of coefficients of three-term relations for basic hypergeometric series

2025/05/27 by Yuka Yamaguchi, Yamaguchi, Yuka
Mathematics · #advanced mathematical theories #Differential Equations and Boundary Problems

paper · pdf · doi:10.48550/arxiv.2505.20798

Abstract

Any three basic hypergeometric series ₂ϕ₁ whose respective parameters a, b, c and a variable x are shifted by integer powers of q are linearly related with coefficients that are rational functions of a, b, c, q, and x. This relation is called a three-term relation for ₂ϕ₁. In this paper, we prove that the coefficients of the three-term relation for ₂ϕ₁ considered in the author's earlier paper (2022) have ninety-six symmetries, and present explicit formulas describing these symmetries.

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