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JOURNALS // Matematicheskie Zametki // Archive
Mat. Zametki, 2010 Volume 88, Issue 4, Pages 543–548 (Mi mzm8689)
This article is cited in 4 papers

Alternatives to the Euler–Maclaurin Formula for Calculating Infinite Sums

Yu. V. Matiyasevich

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences

Abstract: 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, quadrature formula, Stieltjes constant, Riemann zeta function, Simpson's formula.

UDC: 519.65+519.644.2

Received: 07.12.2009
Revised: 07.07.2010

DOI: 10.4213/mzm8689


 English version: Mathematical Notes, 2010, 88:4, 524–529

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© Steklov Math. Inst. of RAS, 2024