Some new formulas for Appell series over finite fields

TL;DR

This paper introduces finite field analogues of Appell series, providing new transformation, reduction formulas, and generating functions, extending Greene's hypergeometric series framework over finite fields.

Contribution

It presents the first finite field analogues of Appell series, along with transformation, reduction formulas, and generating functions, advancing the theory of hypergeometric functions over finite fields.

Findings

Derived finite field analogues of Appell series

Established transformation and reduction formulas

Developed generating functions for these series

Abstract

In 1987 Greene introduced the notion of the finite field analogue of hypergeometric series. In this paper we give a finite field analogue of Appell series and obtain some transformation and reduction formulas. We also establish the generating functions for Appell series over finite fields.