Abelian theorems for the stieltjes transform of functions, II

Abstract

An initial (final) value Abelian theorem concerning transforms of functions is a result in which known behavior of the function as its domain variable approaches zero (approaches∞) is used to infer the behavior of the transform as its domain variable approaches zero (approaches∞). We obtain such theorems in this paper concerning the Stieltjes transform. In our results all parameters are complex; the variablesof the transform is complex in the right half plane; and the initial (final) value Abelian theorems are obtained as|s|→0(|s|→∞)within an arbitrary wedge in the right half plane.