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Decreasing property and complete monotonicity of two functions constituted via three derivatives of a function involving trigamma function

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Published/Copyright: August 9, 2022
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Abstract

With the aid of 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 author presents decreasing property of a ratio constituted via three derivatives of a sum involving trigamma function and discovers necessary and sufficient conditions for a function constituted via three derivatives of a function involving trigamma function to be completely monotonic.


Dedicated to my father Shu-Gong Qi and my grandson Magnus Xi-Zhe Qi

https://qifeng618.wordpress.com


Acknowledgement

The author appreciate anonymous referees for their careful and valuable comments on the original version of this paper.

  1. (Communicated by Tomasz Natkaniec )

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Received: 2021-03-06
Accepted: 2021-05-24
Published Online: 2022-08-09
Published in Print: 2022-08-26

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