MONOTONICITY AND COMPLETE MONOTONICITY OF TWO FUNCTIONS DEFINED BY THREE DERIVATIVES OF A FUNCTION INVOLVING TRIGAMMA FUNCTION - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year : 2020

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

Abstract

In the paper, by convolution theorem of the Laplace transforms, a monotonicity rule for the ratio of two Laplace transforms, Bernstein's theorem for completely monotonic functions, and other analytic techniques, the authors (1) verify decreasing monotonicity of a ratio between three derivatives of a function involving trigamma function; (2) find necessary and sufficient conditions for a function defined by three derivatives of a function involving trigamma function to be completely monotonic. These results confirm previous guesses posed by the first author and generalize corresponding known conclusions.
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Dates and versions

hal-02998203 , version 1 (10-11-2020)

Identifiers

  • HAL Id : hal-02998203 , version 1

Cite

Feng Qi, Ling-Xiong Han, Hong-Ping Yin. MONOTONICITY AND COMPLETE MONOTONICITY OF TWO FUNCTIONS DEFINED BY THREE DERIVATIVES OF A FUNCTION INVOLVING TRIGAMMA FUNCTION. 2020. ⟨hal-02998203⟩
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