A Note on Some Generalized Hypergeometric Reduction Formulas

Abstract

Herein, we calculate reduction formulas for some generalized hypergeometric functions m+1Fmz in terms of elementary functions as well as incomplete beta functions. For this purpose, we calculate the n-th order derivative of the function zγBzα,β with respect to z. As corollaries, we obtain reduction formulas of these m+1Fmz functions for argument unity in terms of elementary functions, as well as beta functions.