×

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].

MSC:

65B10 Numerical summation of series
65R10 Numerical methods for integral transforms
44A10 Laplace transform
PDFBibTeX XMLCite