Watson resummation of a class of Hausdorff-transformed power series |
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Authors: | Enrico De Micheli Giovanni Alberto Viano |
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Affiliation: | a IBF-Consiglio Nazionale delle Ricerche, Via De Marini 6, 16149 Genova, Italy b Dipartimento di Fisica, Università di Genova, Istituto Nazionale di Fisica Nucleare, sez. di Genova, Via Dodecaneso 33, 16146 Genova, Italy |
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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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