A LOGARITHMICALLY COMPLETELY MONOTONIC FUNCTION INVOLVING THE $q$-GAMMA FUNCTION

Feng Qi (1, 2, 3, 4)

1 Henan Polytechnic University
2 Tianjin Polytechnic University
3 Inner Mongolia University for Nationalities
4 UESTC - University of Electronic Science and Technology of China [Chengdu]

In the paper, the author proves the logarithmically complete monotonicity of a function involving the q-gamma function and derives some inequalities for the $q$-multinomial coefficient and the q-multivariate beta function. These conclusions generalize corresponding ones for the gamma function, the multinomial coefficient, and the multivariate beta function respectively.

Mots clés: logarithmically completely monotonic function; $q$-gamma function; inequality; $q$-multinomial coefficient; $q$-multivariate beta function

Domaines: Combinatoire [math.CO]; Théorie des nombres [math.NT]; Analyse classique [math.CA]; Probabilités [math.PR]; Statistiques [math.ST]

Feng Qi. A LOGARITHMICALLY COMPLETELY MONOTONIC FUNCTION INVOLVING THE $q$-GAMMA FUNCTION: A monotonic function involving $q$-gamma function. 2018. ⟨hal-01803352⟩