An Appell series over finite fields

TL;DR

This paper introduces a finite field analogue of an Appell series, deriving its transformations, reduction formulas, and generating functions to extend classical special functions into finite field contexts.

Contribution

It provides the first finite field analogue of an Appell series, including key properties and formulas not previously established.

Findings

Derived transformations for the finite field Appell series

Established reduction formulas for the series

Developed generating functions for the finite field analogue

Abstract

In this paper we present a finite field analogue for one of the Appell series. We shall derive its transformations, reduction formulas as well as generating functions.