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Watson resummation of a class of Hausdorff-transformed power series

Enrico De Micheli·Giovanni Alberto Viano
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Abstract

In this paper we study a class of Hausdorff--transformed power series whose convergence is extremely slow for large values of the argument. We perform a Watson-type resummation of these expansions, and obtain, by the use of the Pollaczek polynomials, a new representation whose convergence is much faster. We can thus propose a new algorithm for the numerical evaluation of these expansions, which include series playing a relevant role in the computation of the partition function in statistical mechanics. By the same procedure we obtain also a solution of the classical Hausdorff moment problem.

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BibTeXRIS

Enrico De Micheli, Giovanni Alberto Viano. 2006-01-13. Watson resummation of a class of Hausdorff-transformed power series. https://arxiv.org/abs/math/0601316

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