An extension of trapezoidal type product integration rules
type: Item
instance of: scholarly article
title: An extension of trapezoidal type product integration rules
zbMATH Open document ID: 1175.65036
published in: Journal of Computational and Applied Mathematics
publication date: 2009-09-29T00:00:00Z
review text: Let \(-\infty < a < b< \infty\) and let \(F_0 \in C[a,b]\) be a positive weight function. The author presents a generalized Euler-Maclaurin summation formula for an integral \[ \int_a^b F_0(x) \,g(x)\,{\mathrm d}x\,, \] where \(g\in C^2[a,b]\). This method can be seen as a generalization of the trapezoidal rule. The order of the corresponding error is estimated. Numerical examples are given.
Mathematics Subject Classification ID: 65D30
Mathematics Subject Classification ID: 65D32
Mathematics Subject Classification ID: 65B15
zbMATH DE Number: 5608854
zbMATH Keywords: numerical integration
zbMATH Keywords: generalization of trapezoidal rule
zbMATH Keywords: product integration
zbMATH Keywords: generalized Euler-Maclaurin summation formula
zbMATH Keywords: Bernoulli functions
zbMATH Keywords: numerical examples
author: Grzegorz Rządkowski
reviewed by: Manfred Tasche
MaRDI profile type: Publication
full work available at URL: j.cam.2009.07.001
OpenAlex ID: W2133271503
cites work: Q5533688
cites work: An introduction to numerical methods and analysis
cites work: Asymptotic Expansions for Product Integration
cites work: Hybrid Gauss-Trapezoidal Quadrature Rules
cites work: Generalized Gaussian Quadrature Rules for Systems of Arbitrary Functions
cites work: A generalization of the Euler-Maclaurin summation formula: an application to numerical computation of the Fermi-Dirac integrals
cites work: Asymptotic expansions for trapezoidal type product integration rules
cites work: A circular interpretation of the Euler-Maclaurin formula.
cites work: A new transformation technique for evaluating nearly singular integrals
DOI: 10.1016/J.CAM.2009.07.001
description: scientific article; zbMATH DE number 5608854