A simple approach to the summation of certain slowly convergent series
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- by Stanisław Lewanowicz PDF
- Math. Comp. 63 (1994), 741-745 Request permission
Abstract:
Summation of series of the form $\sum \nolimits _{k = 1}^\infty {k^{\nu - 1}}r(k)$ is considered, where $0 \leq \nu \leq 1$ and r is a rational function. By an application of the Euler-Maclaurin summation formula, the problem is reduced to the evaluation of Gauss’ hypergeometric function. Examples are given.References
- Milton Abramowitz and Irene A. Stegun, Handbook of mathematical functions with formulas, graphs, and mathematical tables, National Bureau of Standards Applied Mathematics Series, No. 55, U. S. Government Printing Office, Washington, D.C., 1964. For sale by the Superintendent of Documents. MR 0167642
- Philip J. Davis, Spirals: from Theodorus to chaos, A K Peters, Ltd., Wellesley, MA, 1993. With contributions by Walter Gautschi and Arieh Iserles. MR 1224447
- Walter Gautschi, A class of slowly convergent series and their summation by Gaussian quadrature, Math. Comp. 57 (1991), no. 195, 309–324. MR 1079017, DOI 10.1090/S0025-5718-1991-1079017-5 I. S. Gradshteyn and I. M. Ryzhik, Tables of integrals, series and products, Academic Press, New York, 1980.
Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Math. Comp. 63 (1994), 741-745
- MSC: Primary 65B10
- DOI: https://doi.org/10.1090/S0025-5718-1994-1250774-0
- MathSciNet review: 1250774