SOME SUMMATION FORMULAS FOR THE HYPERGEOMETRIC SERIES

Abstract

The aim of this paper is to obtain explicit expressions of the generalizedhypergeometric function r+2Fr+1a, b, 1 2 (a + b + j + 1), (fr + mr) (fr) ; 1 2 for j = 0, ±1, . . . , ±5, where r pairs of numeratorial and denominatorialparameters differ by positive integers mr. The results are derived withthe help of an expansion in terms of a finite sum of 2F1( 1 2 ) functions anda generalization of Gauss' second summation theorem due to Lavoie etal. [J. Comput. Appl. Math. 72, 293-300 (1996)]. Some special andlimiting cases are also given.