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

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 gives explicit formulas describing symmetries of the coefficients of three-term relations.