MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Certain formulas I really enjoy looking at like the Euler-Maclaurin formula or the Leibniz integral rule. What's your favorite equation, formula, identity or inequality?

share|cite|improve this question

closed as no longer relevant by Robin Chapman, Akhil Mathew, Yemon Choi, Qiaochu Yuan, Pete L. Clark Aug 22 '10 at 9:00

This question is unlikely to help any future visitors; it is only relevant to a small geographic area, a specific moment in time, or an extraordinarily narrow situation that is not generally applicable to the worldwide audience of the internet. For help making this question more broadly applicable, visit the help center.If this question can be reworded to fit the rules in the help center, please edit the question.

There are numerous significant formula and laws from our mathematical legacy. It should be noticed while we are now enjoying them freely, there are still quite a lot of basic problems that we are not able to solve using the techniques we know. – Sunni Mar 4 '10 at 1:20
Voting to close. People are at the repeating-other-people's-answers stage now. – Qiaochu Yuan Aug 21 '10 at 18:23
The question has been closed as no longer relevant. It had a long and healthy life, but the large number of answers has become unwieldy. If the question had been asked more recently, it would probably have been closed sooner as being "overly broad". I encourage people who are interested in following up issues raised in the question or the answers with further questions. Please be specific! – Pete L. Clark Aug 22 '10 at 9:02
Sadly my favourite $\sum \frac{1}{n^2 +a^2} = \frac{\pi}{a} cth(\pi a)$ wasn't listed – Ostap Chervak May 1 '11 at 16:57

63 Answers 63

With the stuff I've seen in the literature of sequence transformations, I've started to love the formulae for Aitken's Δ² process:

$S_n^{\prime}=S_{n+1}-\frac{(\Delta S_n)^2}{\Delta^2 S_n}$

and its generalization the Wynn ε algorithm:


for the latter one especially because it is nicely represented as a lozenge diagram:

Wynn epsilon

share|cite|improve this answer

I like Riemann-Roch the most!!!

share|cite|improve this answer

I'm surprised that nobody said


share|cite|improve this answer
Perhaps because is a formula from physics. – Sunni Apr 25 '10 at 18:22
I love the "Einstein meets Pythagoras" version: $E=m(a^2+b^2)$ – Federico Poloni Aug 20 '10 at 20:46

Not the answer you're looking for? Browse other questions tagged or ask your own question.