Euler-Maclaurin Formula

The Euler-Maclaurin formula is a formula for the difference between an integral and a closely related sum, which allows an integral to be approximated by a finite sum, or conversely lets a finite sum or an infinite series be evaluated using integrals and the techniques of calculus. Many asymptotic expansions are derived from the formula, and Faulhaber's formula for sums of powers follows from it as an immediate consequence. Leonhard Euler and Colin Maclaurin discovered the formula independently around 1735, Euler using it to compute slowly converging infinite series and Maclaurin using it to evaluate integrals, and the formula was later generalized into Darboux's formula. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/