A Note on Some Generalized Hypergeometric Reduction Formulas

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