Certain Transformations for Hypergeometric series in $p$-adic setting

Abstract

In \cite{mccarthy2}, McCarthy defined a function ${}_n{G}_n[\cdots ]$ using the Teichmüller character of finite fields and quotients of the $p$-adic gamma function. This function extends hypergeometric functions over finite fields to the $p$-adic setting. In this paper, we give certain transformation formulas for the function ${}_n{G}_n[\cdots ]$ which are not implied from the analogous hypergeometric functions over finite fields.

12 pages