Transformation formula of Dwork's $p$-adic hypergeometric function

TL;DR

This paper establishes a transformation formula for Dwork's $p$-adic hypergeometric function relating values at $t$ and $t^{-1}$, and introduces a finite analogue that supports this transformation.

Contribution

The paper provides the first explicit transformation formula for Dwork's $p$-adic hypergeometric function between $t$ and $t^{-1}$, including a finite analogue as an appendix.

Findings

Transformation formula between $t$ and $t^{-1}$ for Dwork's $p$-adic hypergeometric function

Finite analogue of the transformation formula

Implication for special cases of the transformation

Abstract

In this paper, we give a transformation formula of Dwork's $p$-adic hypergeometric function between $t$ and $t^{-1}$. As an appendix, we introduce a finite analogue of this transformation formula, which implies the special case of the above transformation formula.