By Shalosh B. Ekhad, Doron Zeilberger, and Wadim Zudilin
published in The Mathematical Intelligencer ("Gems and Curiosities" column) v. 42 (2020), 10-11.
Written: Nov. 4, 2019.
Last update of this webpage: Dec. 14, 2019
We find this identity, that looks like an exercise in Calculus 1, surprising, and beautiful. We hope that you would too.
Added Nov. 8, 2019: Watch this neat animation, by Greg Egan.
Added Nov. 11, 2019: Alin Bostan found two beautiful alternative proofs. See here and also here.
Added Nov. 11, 2019: Mikael P. Sundqvist (from Lund, where Gert Almkvist used to be) found a quick change of variable proof, alas he had to be clever. In our proof, using the Almkvist-Zeilberger algorithm, we did not have to be clever.
Added Dec. 14, 2019: Read Fernando Chamizo's insightful note,
Added Feb. 26, 2020: Alin Bostan, Fernando Chamizo, and Mikael Sundqvist combined their insights into this very interesting article.