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arXiv · 0902.0065

Real-variables characterization of generalized Stieltjes functions

Alan D. Sokal
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Abstract

We obtain a characterization of generalized Stieltjes functions of any order λ> 0 in terms of inequalities for their derivatives on (0,\infty). When λ=1, this provides a new and simple proof of a characterization of Stieltjes functions first obtained by Widder in 1938.

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Alan D. Sokal. 2009-05-06. Real-variables characterization of generalized Stieltjes functions. https://doi.org/10.1016/j.exmath.2009.06.004

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