Geodesic
Alternatives to the Euler–Maclaurin Formula for Calculating Infinite Sums
Matematičeskie zametki, Tome 88 (2010) no. 4, pp. 543-548 Cet article a éte moissonné depuis la source Math-Net.Ru

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We propose a new class of formulas, which, just as the Euler–Maclaurin formula, can be used to calculate the approximate value of an infinite sum by approximating the corresponding integral.
Keywords: Euler–Maclaurin formula, Bernoulli number, Riemann zeta function, Simpson's formula.
Mots-clés : quadrature formula, Stieltjes constant 
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     title = {Alternatives to the {Euler{\textendash}Maclaurin} {Formula} for {Calculating} {Infinite} {Sums}},
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Yu. V. Matiyasevich. Alternatives to the Euler–Maclaurin Formula for Calculating Infinite Sums. Matematičeskie zametki, Tome 88 (2010) no. 4, pp. 543-548. http://geodesic.mathdoc.fr/item/MZM_2010_88_4_a5/

[1] http://www.17centurymaths.com/contents/euler/e025tr.pdf

[2] C. MacLaurin, A Treatise of Fluxions, v. 1, 2, T. W. and T. Ruddimans, Edinburgh, 1742 http://www.archive.org/details/atreatisefluxio00conggoog

[3] H. Monien, Gaussian Summation: An Exponentially Converging Summation Scheme, arXiv: math.NA/0611057

[4] Yu. V. Matijasevich, “The Riemann hypothesis from a logician's point of view”, Number Theory (Banff, AB, 1988), de Gruyter, Berlin, 1990, 387–400 | MR | Zbl