On generalized Stieltjes functions

2017/06/02 by Stamatis Koumandos, Koumandos, Stamatis, Henrik L. Pedersen +1
Mathematics · #44A10 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA #msc:44A10

paper · pdf · doi:10.48550/arxiv.1706.00606

17 pages

arxiv created 2017/06/02 · arxiv updated 2017/06/05

Abstract

It is shown that a function f is a generalized Stieltjes function of order λ>0 if and only if x^1-λ(x^λ-1+kf(x))^(k) is completely monotonic for all k≥ 0, thereby complementing a result due to Sokal. Furthermore, a characterization of those completely monotonic functions f for which x^1-λ(x^λ-1+kf(x))^(k) is completely monotonic for all k≤ n is obtained in terms of properties of the representing measure of f.

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