Qi, F. Necessary and Sufficient Conditions for a Difference Constituted by Four Derivatives of a Function Involving Trigamma Function to Be Completely Monotonic. Mathematical Inequalities & Applications 2021, 845–855, doi:10.7153/mia-2021-24-58.
Qi, F. Necessary and Sufficient Conditions for a Difference Constituted by Four Derivatives of a Function Involving Trigamma Function to Be Completely Monotonic. Mathematical Inequalities & Applications 2021, 845–855, doi:10.7153/mia-2021-24-58.
Qi, F. Necessary and Sufficient Conditions for a Difference Constituted by Four Derivatives of a Function Involving Trigamma Function to Be Completely Monotonic. Mathematical Inequalities & Applications 2021, 845–855, doi:10.7153/mia-2021-24-58.
Qi, F. Necessary and Sufficient Conditions for a Difference Constituted by Four Derivatives of a Function Involving Trigamma Function to Be Completely Monotonic. Mathematical Inequalities & Applications 2021, 845–855, 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
Computer Science and Mathematics, Algebra and Number Theory
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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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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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
Commenter:
The commenter has declared there is no conflict of interests.
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.
Commenter:
Commenter's Conflict of Interests: I am the author of this paper