A simple approach to the summation of certain slowly convergent series
Author:
Stanisław Lewanowicz
Journal:
Math. Comp. 63 (1994), 741-745
MSC:
Primary 65B10
DOI:
https://doi.org/10.1090/S0025-5718-1994-1250774-0
MathSciNet review:
1250774
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Abstract | References | Similar Articles | Additional Information
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.
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- 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 https://doi.org/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.
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Additional Information
Keywords:
Slowly convergent series,
Euler-Maclaurin formula,
Gauss’ hypergeometric function
Article copyright:
© Copyright 1994
American Mathematical Society