Stieltjes and other integral representations for functions of Lambert W

Author： Kalugin German A.  

Publisher： Taylor & Francis Ltd

ISSN： 1065-2469

Source： Integral Transforms and Special Functions, Vol.23, Iss.8, 2012-08, pp. : 581-593

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Abstract

We show that many functions containing the Lambert W function are Stieltjes functions. We extend the known properties of the set of Stieltjes functions and also prove a generalization of a conjecture of Jackson, Procacci and Sokal. In addition, we consider the relationship of functions of W with the class of completely monotonic functions and show that W is a complete Bernstein function.

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