Euler–Maclaurin formula
Fórmula de Euler-Maclaurin
- Date
- c. 1735 · confidence medium
- Place
- Saint Petersburg, Russia
- Credited to
- Leonhard Euler and Colin Maclaurin
- Field
- Knowledge & symbols
What was discovered
A formula relating a finite sum to the corresponding integral plus correction terms, useful both for approximating integrals by sums and for evaluating sums and series with calculus tools. Among other things, Faulhaber's formula for sums of powers follows from it.
Discovered independently by Euler, who needed it to sum slowly converging series, and by Maclaurin, who used it to compute integrals, around 1735.
What it led to
- computation of slowly converging series (Euler's original use)
- later generalisation to Darboux's formula
- numerical methods approximating integrals by finite sums