On an Integral Identity

Alin Bostan; Fernando Chamizo; Mikael Persson Sundqvist

doi:10.1080/00029890.2021.1944754

On an Integral Identity

Alin Bostan, Fernando Chamizo, Mikael Persson Sundqvist

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Sammanfattning

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.

Originalspråk	engelska
Sidor (från-till)	737-743
Antal sidor	7
Tidskrift	American Mathematical Monthly
Volym	128
Nummer	8
DOI	https://doi.org/10.1080/00029890.2021.1944754
Status	Published - 2021

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10.1080/00029890.2021.1944754

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title = "On an Integral Identity",

abstract = "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.",

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AB - 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.

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M3 - Article

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On an Integral Identity

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