A harmonic mean inequality for the digamma function and related results
نویسندگان
چکیده
منابع مشابه
A harmonic mean inequality for the digamma function and related results
We present some inequalities and a concavity property of the digamma function ψ = Γ′/Γ, where Γ denotes Euler’s gamma function. In particular, we offer a new characterization of Euler’s constant γ = 0.57721.... We prove that −γ is the minimum of the harmonic mean of ψ(x) and ψ(1/x) for x > 0. Mathematics Subject Classification (2010). 33B15, 39B62, 41A44.
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Let ψ(x) denote the digamma function, that is, the logarithmic derivative of Euler’s -function. Let q be a positive integer greater than 1 and γ denote Euler’s constant. We show that all the numbers ψ(a/q)+ γ, (a, q)= 1, 1 a q, are transcendental. We also prove that at most one of the numbers γ, ψ(a/q), (a, q)= 1, 1 a q, is algebraic. © 2007 Elsevier Inc. All rights reserved. MSC: primary 11J81...
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ژورنال
عنوان ژورنال: Rendiconti del Seminario Matematico della Università di Padova
سال: 2017
ISSN: 0041-8994
DOI: 10.4171/rsmup/137-10