Two Definite Integrals That Are Definitely (and Surprisingly!) Equal
Classical Analysis and ODEs
2020-09-24 v2 Number Theory
Abstract
We find this identity, that looks like an exercise in Calculus 1, surprising, and beautiful. We hope that you would too.
Cite
@article{arxiv.1911.01423,
title = {Two Definite Integrals That Are Definitely (and Surprisingly!) Equal},
author = {Shalosh B. Ekhad and Doron Zeilberger and Wadim Zudilin},
journal= {arXiv preprint arXiv:1911.01423},
year = {2020}
}
Comments
1+epsilon pages. This version corrects a typo pointed out by Greg Egan, gives links to a beautiful animation that he did, announces a direct change of variable proof discovered by Mikael Sundquist, and gives references to two additional proofs by Alin Bostan