Euler-Maclaurin summation formula


Let Br be the rth Bernoulli numberMathworldPlanetmathPlanetmath, and Br(x) be the rth Bernoulli periodic function. For any integer k0 and for any function f of class Ck+1 on [a,b],a,b, we have

a<nbf(n)=abf(t)𝑑t+r=0k(-1)r+1Br+1(r+1)!(f(r)(b)-f(r)(a))+(-1)k(k+1)!abBk+1(t)f(k+1)(t)𝑑t.
Title Euler-Maclaurin summation formula
Canonical name EulerMaclaurinSummationFormula
Date of creation 2013-03-22 11:46:01
Last modified on 2013-03-22 11:46:01
Owner KimJ (5)
Last modified by KimJ (5)
Numerical id 9
Author KimJ (5)
Entry type Theorem
Classification msc 65B15
Classification msc 00-02
Related topic BernoulliNumber