COMPLETE MONOTONICITY FOR A NEW RATIO OF FINITE MANY GAMMA FUNCTIONS

Feng Qi (1, 2, 3)

1 Henan Polytechnic University
2 Tianjin Polytechnic University
3 Inner Mongolia University for Nationalities

In the paper, by deriving an inequality involving the generating function of the Bernoulli numbers, the author introduces a new ratio of finite many gamma functions, finds complete monotonicity of the second logarithmic derivative of the ratio, and simply reviews complete monotonicity of several linear combinations of finite many digamma or trigamma functions.

Mots clés: complete monotonicity; ratio; gamma function; digamma function; trigamma function; inequality; Bernoulli number; generating function; logarithmic derivative; linear combination

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

Feng Qi. COMPLETE MONOTONICITY FOR A NEW RATIO OF FINITE MANY GAMMA FUNCTIONS. 2020. ⟨hal-02511909v1⟩