On summation/integration methods for slowly convergent series
Dedicated to Professor Gheorghe Coman on the occasion of his 80th anniversary
Keywords:
Slowly convergent series, Gaussian quadrature, weight function, three-term recurrence relation, convergence, Laplace transform, contour integration.Abstract
A survey on summation/integration methods for computation of slowly convergent series is presented. Methods are based on some transformations of series to integrals, with respect to certain nonclassical weight functions over R+, and an application of suitable quadratures of Gaussian type for numerical calculating of such integrals with a high accuracy. In particular, applications to some series with irrational terms are considered. Several numerical examples are included in order to illustrate the efficiency of these methods.
Mathematics Subject Classification (2010): 65B10, 65D30, 65D32, 40A25.
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