Symmetries of Coefficients of Three-Term Relations for the Hypergeometric Series

TL;DR

This paper investigates the symmetries of the coefficients in three-term relations for hypergeometric series, providing explicit formulas and enhancing understanding of their algebraic structure.

Contribution

It introduces explicit formulas for the symmetries of coefficients in three-term relations of hypergeometric series, a novel insight into their algebraic properties.

Findings

Coefficients exhibit specific symmetry properties.

Explicit formulas for these symmetries are derived.

Enhances understanding of hypergeometric series relations.

Abstract

Any three hypergeometric series whose respective parameters, a, b and c, differ by integers satisfy a linear relation with coefficients that are rational functions of a, b, c and the variable x. These relations are called three-term relations. This paper shows that the coefficients of three-term relations have properties called symmetries, and gives explicit formulas describing the symmetries.