Watson resummation of a class of Hausdorff-transformed power series
Copyright policy )Watson resummation of a class of Hausdorff-transformed power series
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.
18 pages, 4 Postscript figures
- University of Genoa Italy
- Istituto di Biofisica Italy
- National Research Council Italy
- National Research Council Sri Lanka
- National Institute for Nuclear Physics Italy
65B10; 30B10; 40G05, Applied Mathematics, 40G05, 30B10, Numerical Analysis (math.NA), Moment problems and interpolation problems in the complex plane, Applications of hypergeometric functions, Moment problems, Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, 65B10, Mathematics - Numerical Analysis, Analysis
65B10; 30B10; 40G05, Applied Mathematics, 40G05, 30B10, Numerical Analysis (math.NA), Moment problems and interpolation problems in the complex plane, Applications of hypergeometric functions, Moment problems, Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, 65B10, Mathematics - Numerical Analysis, Analysis
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