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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



A simple approach to the summation of certain slowly convergent series

Author: Stanisław Lewanowicz
Journal: Math. Comp. 63 (1994), 741-745
MSC: Primary 65B10
MathSciNet review: 1250774
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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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Keywords: Slowly convergent series, Euler-Maclaurin formula, Gauss’ hypergeometric function
Article copyright: © Copyright 1994 American Mathematical Society