Corrected Euler-Maclaurin's formulae
type: Item
instance of: scholarly article
title: Corrected Euler-Maclaurin's formulae
zbMATH Open document ID: 1117.26016
DOI: 10.1007/BF02874640
publication date: 2007-02-02T00:00:00Z
review text: Quadrature formulas are proposed of the form \[ \int_a^b f(x)\,dx = D(a,b)+T_n(a,b)+R_n \] where \(D(a,b)=\lambda_1f(x_1)+\lambda_2f(x_2)+\lambda_3f(x_3)\) is an open formula with \(x_2=(a+b)/2\) and \(x_1,x_3 = x_2 \pm (b-a)/3\), while \(T_n=\sum_{k=1}^n \mu_k [f^{(k-1)}(b)-f^{(k-1)}(a)]\) gives a correction term in the end points involving derivatives. All the weights \(\lambda_k,\mu_k\) are positive. Bernoulli polynomials are used in the construction of the formulas. Depending on conditions for the integrand \(f\), several expressions and estimates for the error term \(R_n\) are given.
Mathematics Subject Classification ID: 26D15
Mathematics Subject Classification ID: 65B15
Mathematics Subject Classification ID: 65D32
zbMATH DE Number: 5121519
zbMATH Keywords: Open type quadrature formulae
zbMATH Keywords: Corrected Maclaurin's formulae
zbMATH Keywords: Bernoulli polynomials
zbMATH Keywords: Functions of bounded variation
zbMATH Keywords: Lipschitzian functions
author: Iva Franjić
author: J. Pečarić
reviewed by: Adhemar Bultheel
MaRDI profile type: Publication
cites work: Q4060253
cites work: Euler-Maclaurin formulae
cites work: Q3429142
cites work: On generalizations of Ostrowski inequality via some Euler-type identities
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cites work: Some inequalities of Euler-Grüss type
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published in: Rendiconti del Circolo Matematico di Palermo
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description: scientific article; zbMATH DE number 5121519