Watson resummation of a class of Hausdorff-transformed power series

[摘要] 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. (C) 2004 Elsevier Inc. All rights reserved.

[发布日期] 2004-11-15