Geodesic
Alternatives to the Euler--Maclaurin Formula for Calculating Infinite Sums
Matematičeskie zametki, Tome 88 (2010) no. 4, pp. 543-548.

Voir la notice de l'article provenant de la source Math-Net.Ru

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 
@article{MZM_2010_88_4_a5,
     author = {Yu. V. Matiyasevich},
     title = {Alternatives to the {Euler--Maclaurin} {Formula} for {Calculating} {Infinite} {Sums}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {543--548},
     publisher = {mathdoc},
     volume = {88},
     number = {4},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2010_88_4_a5/}
}
TY  - JOUR
AU  - Yu. V. Matiyasevich
TI  - Alternatives to the Euler--Maclaurin Formula for Calculating Infinite Sums
JO  - Matematičeskie zametki
PY  - 2010
SP  - 543
EP  - 548
VL  - 88
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2010_88_4_a5/
LA  - ru
ID  - MZM_2010_88_4_a5
ER  - 
%0 Journal Article
%A Yu. V. Matiyasevich
%T Alternatives to the Euler--Maclaurin Formula for Calculating Infinite Sums
%J Matematičeskie zametki
%D 2010
%P 543-548
%V 88
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2010_88_4_a5/
%G ru
%F MZM_2010_88_4_a5
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