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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 the 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

## 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

APA Style
Anis, M., Almuashi, H., Mahmoud, M. (2022). Complete monotonicity of functions related to trigamma and tetragamma functions. Computer Modeling in Engineering & Sciences, 131(1), 263-275. https://doi.org/10.32604/cmes.2022.016927
Vancouver Style
Anis M, Almuashi H, Mahmoud M. Complete monotonicity of functions related to trigamma and tetragamma functions. Comput Model Eng Sci. 2022;131(1):263-275 https://doi.org/10.32604/cmes.2022.016927
IEEE Style
M. Anis, H. Almuashi, and M. Mahmoud "Complete Monotonicity of Functions Related to Trigamma and Tetragamma Functions," Comput. Model. Eng. Sci., vol. 131, no. 1, pp. 263-275. 2022. https://doi.org/10.32604/cmes.2022.016927

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