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A simple proof of a new summation formula for a terminating r+3Fr+2(1)hypergeometric series, representing an extension of Saalschutz's formula for a3F2(1) series, is given for the case of r pairs of numeratorial anddenominatorial parameters differing by positive integers. Two applications ofthis extended summation theorem are discussed. The first application extendstwo identities given by Ramanujan and the second, which also employs a similarextension of the Vandermonde-Chu summation theorem for the 2F1 series, extendscertain reduction formulas for the Kamp?e de F?eriet function of two variablesgiven by Exton and Cvijovi?c and Miller.

An alternative proof of the extended Saalschutz summation theorem for the r+3Fr+2(1) series with applications

An alternative proof of the extended Saalschutz summation theorem for the r+3Fr+2(1) series with applications