On the Euler-Maclaurin formula
type: Item
instance of: scholarly article
title: On the Euler-Maclaurin formula
zbMATH Open document ID: 0899.41019
author: R. Estrada
published in: Boletín de la Sociedad Matemática Mexicana. Third Series
publication date: 1997-09-17T00:00:00Z
review text: The classical Euler-Maclaurin formula \[ \sum^M_{k=N} \varphi (k)= \int^M_N \varphi (x)+ {\varphi(N) +\varphi(M) \over 2} +\sum^q_{j=2} c_j\bigl[ \varphi^{(j-1)} (M)-\varphi^{(j-1)} (N)\bigr] +Rq, \] relating the integral of a function \(\varphi\in C^q(N,M)\) to the relevant finite sum, is generalized to distributions. The case of a power behaviour of \(\varphi\) at the ends of the interval and the case when \(\varphi\) has discontinuities inside the interval are studied.
Mathematics Subject Classification ID: 41A60
Mathematics Subject Classification ID: 46F10
zbMATH DE Number: 1061848
zbMATH Keywords: asymptotic expansion
zbMATH Keywords: numerical quadrature
zbMATH Keywords: generalized functions
reviewed by: Boris Rubin
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1061848