Summation of slowly convergent series

Volume 29 / 1994

Walter Gautschi Banach Center Publications 29 (1994), 7-18 DOI: 10.4064/-29-1-7-18

Abstract

Among the applications of orthogonal polynomials described briefly on my previous visit to this Center [9, §3.2] were slowly convergent series whose terms could be represented in terms of the Laplace transform at integer arguments. We proposed to sum such series by means of Gaussian quadrature rules applied to suitable integrals involving weight functions of Einstein and Fermi type (cf. [13]). In the meantime it transpired that the technique is applicable to a large class of numerical series and, suitably adapted, also to power series and Fourier series of interest in plate problems. In the following we give a summary of these new applications and the contexts in which they arise.

Authors

  • Walter Gautschi

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