Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Complete monotonicity of a difference constituted by four derivatives of a function involving trigamma function

Version 1 : Received: 10 November 2020 / Approved: 12 November 2020 / Online: 12 November 2020 (11:58:39 CET)

A peer-reviewed article of this Preprint also exists.

Journal reference: Mathematical Inequalities & Applications 2021, 24, 24-58
DOI: 10.7153/mia-2021-24-58

Abstract

In the paper, by virtue of convolution theorem for the Laplace transforms, Bernstein's theorem for completely monotonic functions, and other techniques, the author finds necessary and sufficient conditions for a difference constituted by four derivatives of a function involving trigamma function to be completely monotonic.

Keywords

complete monotonicity; necessary and sufficient condition; difference; derivative; trigamma function; convolution theorem for the Laplace transforms; Bernstein's theorem for completely monotonic functions

Subject

MATHEMATICS & COMPUTER SCIENCE, Algebra & Number Theory

Comments (2)

Comment 1
Received: 15 May 2021
Commenter: Feng Qi (Click to see Publons profile: )
The commenter has declared there is no conflict of interests.
Comment: This manuscript has been formally accepted, please cite it as follows:

Feng Qi, \textit{Necessary and sufficient conditions for a difference constituted by four derivatives of a function involving trigamma function to be completely monotonic}, Mathematical Inequalities \& Applications \textbf{24} (2021), in press.
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Comment 2
Received: 30 July 2021
Commenter: Feng Qi (Click to see Publons profile: )
Commenter's Conflict of Interests: I am the author of this paper
Comment: Feng Qi, Necessary and sufficient conditions for a difference constituted by four derivatives of a function involving trigamma function to be completely monotonic, Mathematical Inequalities & Applications 24 (2021), no. 3, 845--855; available online at http://dx.doi.org/10.7153/mia-2021-24-58
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