ARTICLE | doi:10.20944/preprints202304.0844.v1
Subject: Computer Science And Mathematics, Mathematics Keywords: Extended Beta function; Extended hypergeometric function; Extended confluent hypergeometric function; Extended Appell function; Mellin transforms; Inverse Mellin transforms; H-functions; Laguerre polynomials; Transformation formulas; Recurrence relation; Generating function; Bounding inequalities
Online: 24 April 2023 (09:45:32 CEST)
This paper introduces extensions H4,p and X8,p of Horn’s double hypergeometric function H4 and Exton’s triple hypergeometric function X8, taking into account recent extensions of Euler’s beta function, hypergeometric function, and confluent hypergeometric function. Among the numerous extended hypergeometric functions, the primary rationale for choosing H4 and X8 is their comparable extension type. Next, we present various integral representations of Euler and Laplace type, Mellin and inverse Mellin transforms, Laguerre polynomial representation, transformation formulae and a recurrence relation for the extended functions. In particular, we provide a generating function for the X8,p and several bounding inequalities for the H4,p and X8,p.