Geodesic
A harmonic mean inequality for the q-gamma and q-digamma functions
Filomat, Tome 35 (2021) no. 12, p. 4105

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DOI

We prove among others results that the harmonic mean of Γ q (x) and Γ q (1/x) is greater than or equal to 1 for arbitrary x > 0, and q ∈ J where J is a subset of [0, +∞). Also, we prove that there is a unique real number p 0 ∈ (1, 9/2), such that for q ∈ (0, p 0), ψ q (1) is the minimum of the harmonic mean of ψ q (x) and ψ q (1/x) for x > 0 and for q ∈ (p 0 , +∞), ψ q (1) is the maximum. Our results generalize some known inequalities due to Alzer and Gautschi
DOI : 10.2298/FIL2112105B
Classification : 33B15, 26D15, 33D05, 33D15
Keywords: q-Digamma function, q-Psi function, q-Gamma function, Gamma function, Digamma function 
Mohamed Bouali. A harmonic mean inequality for the q-gamma and q-digamma functions. Filomat, Tome 35 (2021) no. 12, p. 4105 . doi: 10.2298/FIL2112105B
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     title = {A harmonic mean inequality for the q-gamma and q-digamma functions},
     journal = {Filomat},
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     year = {2021},
     volume = {35},
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     doi = {10.2298/FIL2112105B},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2112105B/}
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