A finite field analogue of the Appell series $F_4$

TL;DR

This paper introduces a finite field analogue of the classical Appell series $F_4$ using Gauss sums and establishes identities for this new function that mirror those of the original series.

Contribution

The paper defines a new finite field version of the Appell series $F_4$ and proves identities analogous to the classical case, expanding the understanding of special functions over finite fields.

Findings

Defined the finite field analogue $F_4^{\

established identities similar to the classical Appell series $F_4$

Abstract

We define a function $F_4^{\ast}$ as a finite field analogue of the classical Appell series $F_4$ using Gauss sums. We establish identities for $F_4^{\ast}$ analogous to those satisfied by the classical Appell series $F_4$.