Kamp\'e de F\'eriet hypergeometric functions over finite fields

TL;DR

This paper extends Kampé de Fériet hypergeometric functions to finite fields, establishing analogous reduction and summation formulas, thus broadening their theoretical framework and potential applications.

Contribution

It introduces the definition of Kampé de Fériet hypergeometric functions over finite fields and proves related formulas, a novel extension of classical functions.

Findings

Defined Kampé de Fériet hypergeometric functions over finite fields

Proved reduction formulas analogous to classical cases

Established summation formulas in the finite field context

Abstract

Kamp\'e de F\'eriet hypergeometric functions are two-variable hypergeometric functions, which are a generalization of Appell's functions. It is known that they satisfy many reduction and summation formulas. In this paper, we define Kamp\'e de F\'eriet hypergeometric functions over finite fields and show analogous formulas.