Stieltjes, Poisson and other integral representations for functions of Lambert $W$
Complex Variables
2011-03-30 v1
Abstract
We show that many functions containing are Stieltjes functions. Explicit Stieltjes integrals are given for functions , , and others. We also prove a generalization of a conjecture of Jackson, Procacci & Sokal. Integral representations of and related functions are also given which are associated with the properties of their being Pick or Bernstein functions. Representations based on Poisson and Burniston--Siewert integrals are given as well.
Keywords
Cite
@article{arxiv.1103.5640,
title = {Stieltjes, Poisson and other integral representations for functions of Lambert $W$},
author = {German A. Kalugin and David J. Jeffrey and Robert M. Corless},
journal= {arXiv preprint arXiv:1103.5640},
year = {2011}
}