COMPLETE MONOTONICITY AND MONOTONICITY OF TWO FUNCTIONS DEFINED BY TWO DERIVATIVES OF A FUNCTION INVOLVING TRIGAMMA FUNCTION

Feng Qi (1, 2, 3)

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

In the paper, by convolution theorem for the Laplace transforms, Bernstein's theorem for completely monotonic functions, some properties of a function involving exponential function, and other analytic techniques, the author finds necessary and sufficient conditions for two functions defined by two derivatives of a function involving trigamma function to be completely monotonic or monotonic. These results generalize corresponding known ones. The author also poses several guesses related to these results.

Mots clés: complete monotonicity; monotonicity; necessary and sufficient condition; derivative; trigamma function; Bernstein's theorem for completely monotonic functions; convolution theorem for the Laplace transforms; exponential function; inequality; guess

Domaines: Analyse classique [math.CA]

Feng Qi. COMPLETE MONOTONICITY AND MONOTONICITY OF TWO FUNCTIONS DEFINED BY TWO DERIVATIVES OF A FUNCTION INVOLVING TRIGAMMA FUNCTION. 2020. ⟨hal-02993723v1⟩