The Euler-Maclaurin formula for functions with singularities
type: Item
instance of: scholarly article
title: The Euler-Maclaurin formula for functions with singularities
zbMATH Open document ID: 0883.40004
DOI: 10.1007/BF02473975
published in: Lithuanian Mathematical Journal
publication date: 1997-10-29T00:00:00Z
review text: Asymptotic formulas for the sum \((1/n)\sum^{n- 1}_{k= 1}\Phi(k/n)\) as \(n\to\infty\) are obtained, where \(\Phi\) is a function of the form \(\Phi(x)= x^{-\alpha_1}(\log x)^{d_1}(1- x)^{-\alpha_2}(\log(1- x))^{d_2}\phi(x)\), and \(\phi(x)\) is sufficiently smooth on \([0, 1]\).
Mathematics Subject Classification ID: 40A25
Mathematics Subject Classification ID: 65B15
zbMATH DE Number: 1059799
zbMATH Keywords: Euler-Maclaurin formula
author: Birutė Kryžienė
reviewed by: Gerald A. Heuer
MaRDI profile type: Publication
cites work: Q5788558
cites work: Q3269298
cites work: Asymptotic expansion of densities of the maxima of sums of random variables. Large deviations
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cites work: Q5803461
full work available at URL: https://doi.org/10.1007/bf02473975
OpenAlex ID: W2159705930
description: scientific article; zbMATH DE number 1059799