Sum representations of Appell-Lauricella functions over finite fields using confluent hypergeometric functions and their applications (2306.15936v4)

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.