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Complete Monotonicity of Functions Related to Trigamma and Tetragamma Functions

Mona Anis1, Hanan Almuashi2, Mansour Mahmoud3,*
1 Faculty of Science, Mathematics Department, Mansoura University, Mansoura, 35516, Egypt
2 Faculty of Science, Mathematics Department, Jeddah University, Jeddah, 21589, Saudi Arabia
3 Faculty of Science, Mathematics Department, King Abdulaziz University, Jeddah, 21589, Saudi Arabia
* Corresponding Author: Mansour Mahmoud. Email:
(This article belongs to this Special Issue: Trend Topics in Special Functions and Polynomials: Theory, Methods, Applications and Modeling)

Computer Modeling in Engineering & Sciences 2022, 131(1), 263-275. https://doi.org/10.32604/cmes.2022.016927

Received 11 April 2021; Accepted 20 October 2021; Issue published 24 January 2022

Abstract

In this paper, we study the completely monotonic property of two functions involving the function △(x) = and deduce the double inequality , x > 0
which improve some recent results, where ψ(x) is the logarithmic derivative of the Gamma function. Also, we deduce the completely monotonic degree of a function involving ψ'(x).

Keywords

Trigamma function; tetragamma function; completely monotonic function; completely monotonic degree; inequality

Cite This Article

Anis, M., Almuashi, H., Mahmoud, M. (2022). Complete Monotonicity of Functions Related to Trigamma and Tetragamma Functions. CMES-Computer Modeling in Engineering & Sciences, 131(1), 263–275.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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