Gautschi, Walter Summation of slowly convergent series. (English) Zbl 0799.65005 Kowalski, Jan Krzysztof (ed.) et al., Numerical analysis and mathematical modelling. Warszawa: Polish Academy of Sciences, Inst. of Mathematics, Banach Cent. Publ. 29, 7-18 (1994). The author starts with the assumption that it is possible to find a function, whose Laplace transforms at integer arguments correspond to terms of a given series. Now, the summation of these terms leads to integrals containing the Einstein or Fermi kernels. Gaussian quadrature is used to evaluate those integrals. Some examples of slowly convergent series illustrate the above method.For the entire collection see [Zbl 0790.00003]. Reviewer: J.Gilewicz (Marseille) Cited in 1 Document MSC: 65B10 Numerical summation of series 65R10 Numerical methods for integral transforms 44A10 Laplace transform Keywords:summation of series; Einstein kernel; numerical examples; Laplace transforms; Fermi kernels; Gaussian quadrature PDFBibTeX XMLCite \textit{W. Gautschi}, Banach Cent. Publ. 29, 7--18 (1994; Zbl 0799.65005)