Sum representations of Appell-Lauricella functions over finite fields using confluent hypergeometric functions and their applications

TL;DR

This paper establishes sum representations of Appell-Lauricella functions over finite fields using confluent hypergeometric functions, and explores their transformation, summation, and reduction formulas for broader applications.

Contribution

It introduces novel sum representations and transformation formulas for Appell-Lauricella functions over finite fields, expanding their theoretical framework.

Findings

Derived sum representations using confluent hypergeometric functions

Proved transformation formulas for Appell-Lauricella functions

Established summation and reduction formulas

Abstract

We prove sum representations of Appell-Lauricella functions over a finite field using confluent hypergeometric functions over the finite field. As an application, we also prove transformation formulas, summation formulas and reduction formulas for Appell-Lauricella functions over the finite field.