Multiplicate inverse forms of terminating hypergeometric series

Abstract

The multiplicate form of Gould–Hsu's inverse series relations enables to investigate the dual relations of the Chu–Vandermonde–Gauß’s, the Pfaff–Saalschütz's summation theorems and the binomial convolution formula due to Hagen and Rothe. Several identity and reciprocal relations are thus established for terminating hypergeometric series. By virtue of the duplicate inversions, we establish several dual formulae of Chu–Vandermonde–Gauß’s and Pfaff–Saalschütz's summation theorems in Section 3 and 4, respectively. Finally, the last section is devoted to deriving several identities and reciprocal relations for terminating balanced hypergeometric series from Hagen–Rothe's convolution identity in accordance with the duplicate, triplicate and multiplicate inversions.