Watson resummation of a class of Hausdorff-transformed power series

Details Watson resummation of a class of Hausdorff-transformed power series Watson resummation of a class of Hausdorff-transformed power series

2006-01-13

arxiv.org/abs/math/0601316v1

J. Math. Anal. Appl. 299 (2004), 630-650

Mathematics

Classical Analysis and ODEs

18 pages, 4 Postscript figures

Scientific paper

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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