On summation/integration methods for slowly convergent series

Abstract

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.