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On the arithmetic nature of the values of the gamma function, Euler's constant, and Gompertz's constant

2012
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The Michigan mathematical journal
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We prove new results concerning the arithmetic nature values of the Gamma function Γ at algebraic points and Euler's constant γ. We prove that for any α ∈ Q\Z, α > 0, at least one of the numbers Γ is an irrational number. Similarly, at least one of the numbers γ = − ∞ 0 log(t)e −t dt and Gompertz's constant ∞ 0 e −t /(1 + t)dt is an irrational number. Quantitative statements, obtained by means of Nesterenko's linear independence criterion, strengthen these irrationality assertions. G α (z) := z

doi:10.1307/mmj/1339011525
fatcat:u67stsevkreq3hweh67ilgatwa