# Euler-Maclaurin summation formula

Let $B_{r}$ be the $r\mbox{th}$ Bernoulli number, and $B_{r}(x)$ be the $r\mbox{th}$ Bernoulli periodic function. For any integer $k\geq 0$ and for any function $f$ of class $C^{k+1}$ on $[a,b],a,b\in\mathbb{Z}$, we have

 $\sum_{a
Title Euler-Maclaurin summation formula EulerMaclaurinSummationFormula 2013-03-22 11:46:01 2013-03-22 11:46:01 KimJ (5) KimJ (5) 9 KimJ (5) Theorem msc 65B15 msc 00-02 BernoulliNumber