Hypergeometric functions as generalized Stieltjes transforms

TL;DR

This paper explores the application of generalized Stieltjes transforms to hypergeometric functions, deriving new integral representations, inequalities, and properties related to their conformal mapping behavior.

Contribution

It introduces novel integral representations and inequalities for hypergeometric functions using generalized Stieltjes transforms, advancing theoretical understanding.

Findings

New integral representations of hypergeometric functions

Derived inequalities and properties of the Padé table

Analyzed hypergeometric functions as conformal maps

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 Pad\'{e} table and the properties of the generalized hypergeometric function as a conformal map.