A harmonic mean inequality for the q-gamma and q-digamma functions
نویسندگان
چکیده
We prove among others results that the harmonic mean of ?q(x) and ?q(1/x) is greater than or equal to 1 for arbitrary x > 0, q ? J where a subset [0,+?). Also, we there unique real number p0 (1, 9/2), such (0, p0), ?q(1) minimum q(1/x) 0 (p0,+?), maximum. Our generalize some known inequalities due Alzer Gautschi.
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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ژورنال
عنوان ژورنال: Filomat
سال: 2021
ISSN: ['2406-0933', '0354-5180']
DOI: https://doi.org/10.2298/fil2112105b