An alternative to the Euler-Maclaurin summation formula: approximating sums by integrals only

DOI10.1007/s00211-018-0978-yzbMath1478.65005arXiv1511.03247OpenAlexW2810056370WikidataQ129646787 ScholiaQ129646787MaRDI QIDQ1616027

Iosif Pinelis

Publication date: 31 October 2018

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1511.03247

Mathematics Subject Classification ID

Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities) (41A17) Approximate quadratures (41A55) Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.) (68Q17) Euler-Maclaurin formula in numerical analysis (65B15) One-variable calculus (26A06) Antidifferentiation (26A36)

Related Items (4)

Euler–Maclaurin expansions without analytic derivatives ⋮ On the efficient computation of large scale singular sums with applications to long-range forces in crystal lattices ⋮ Exact bounds on the inverse Mills ratio and its derivatives ⋮ Approximating sums by integrals only: multiple sums and sums over lattice polytopes

Uses Software

• Mathematica
• MathOverflow

Cites Work

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• The SIAM 100-Digit Challenge: a decade later. Inspirations, ramifications, and other eddies left in its wake
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• Ramanujan summation and the exponential generating function \(\sum_{k=0}^{\infty}\frac{z^{k}}{k!}\zeta'(-k)\)
• A multimodular algorithm for computing Bernoulli numbers
• Faster computation of Bernoulli numbers
• The SIAM 100-Digit Challenge
• Explicit Formulas for Bernoulli Numbers
• Euler's Constant to 1271 Places
• Quantum field theory

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