On an integral identity. (English) Zbl 1482.26013

Summary: We give three elementary proofs of a nice equality of definite integrals, recently proven by Ekhad, Zeilberger, and Zudilin. The equality arises in the theory of bivariate hypergeometric functions, and has connections with irrationality proofs in number theory. We furthermore provide a generalization together with an equally elementary proof and discuss some consequences.


26A42 Integrals of Riemann, Stieltjes and Lebesgue type
33C65 Appell, Horn and Lauricella functions
33F10 Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.)


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