Multiplicate inverse forms of terminating hypergeometric series

Christian Lavault (1)

1 LIPN - Laboratoire d'Informatique de Paris-Nord

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 identitity 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~\ref{ChuVanGauss} and~\ref{PfaffSaalsch}, 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.

Mots clés: Hagen--Rothe's convolution identity.; Generalized hypergeometric serie; Gould--Hsu inverse series relations; Multiplicate inversions; Chu--Vandermonde--Gauß's summation formula; Pfaff--Saalschütz's summation theorem; Hagen--Rothe's convolution identity

Domaines: Combinatoire [math.CO]; Mathématique discrète [cs.DM]; Théorie des nombres [math.NT]; Calcul parallèle, distribué et partagé [cs.DC]

Christian Lavault. Multiplicate inverse forms of terminating hypergeometric series. Integral Transform and Special Functions (Ed. Taylor \& Francis), 2014, 25 (9), pp.730-749. ⟨10.1080/10652469.2014.905933⟩. ⟨hal-00905887⟩