Hypergeometric functions as generalized Stieltjes transforms

2011/12/25 by Dmitry Karp, Karp, Dmitry, Elena Prilepkina +1
Mathematics · #26A48 #33C20 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA #msc:26A48 #msc:33C20

paper · pdf · doi:10.48550/arxiv.1112.5769

16 pages, no figures

arxiv created 2011/12/25 · arxiv updated 2011/12/30

Abstract

In this paper we apply generalized Stieltjes transform representation to study the generalized hypergeometric function. Among the results thus proved are new integral representations, inequalities, properties of the Padé table and the properties of the generalized hypergeometric function as a conformal map.

Related

• Applications of the Stieltjes and Laplace transform representations of the hypergeometric functions
• Representations and inequalities for generalized hypergeometric functions
• Generalized Stieltjes transforms: basic aspects
• Representations of hypergeometric functions for arbitrary parameter values and their use
• A Class of Extended Hypergeometric Functions and Its Applications