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Some Generalizations of Beukers' Integrals
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Abstract
Beukers[3] used some double integrals to give an elegant proof to Apery's result, which states that ζ(3) is irrational. In this paper, based on his methods, we generalize Beukers' integrals (although we do not prove the irrationality of ζ(2n+1) for positive integer n). The evaluaton of these integrals is achieved by using an expansion of an infinite geometric series and differentiating under the integral sign.
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