Open Access

ARTICLE

Complete Monotonicity of Functions Related to Trigamma and Tetragamma Functions

Mona Anis¹, Hanan Almuashi², Mansour Mahmoud^3,*
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).

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Keywords

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

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