Certain transformations for hypergeometric series in the p-adic setting

Abstract

In [The trace of Frobenius of elliptic curves and the p-adic gamma function, Pacific J. Math. 261(1) (2013) 219–236], McCarthy defined a function nGn[⋯] 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 nGn[⋯] which are not implied from the analogous hypergeometric functions over finite fields.