English

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

R2 v1 2026-06-23T12:04:29.990Z