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# Mathematica Slovaca

Editor-in-Chief: Pulmannová, Sylvia

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Volume 63, Issue 3

# A completely monotonic function involving the tri- and tetra-gamma functions

Bai-Ni Guo
/ Jiao-Lian Zhao
• Department of Mathematics and Informatics, Weinan Teachers University, Weinan City, Shaanxi Province, 714000, China
• Email
• Other articles by this author:
/ Feng Qi
Published Online: 2013-06-28 | DOI: https://doi.org/10.2478/s12175-013-0109-2

## Abstract

The di-gamma function ψ(x) is defined on (0,∞) by $\psi (x) = \frac{{\Gamma '(x)}} {{\Gamma (x)}}$ and ψ (i)(x) for i ∈ ℕ denote the polygamma functions, where Γ(x) is the classical Euler’s gamma function. In this paper we prove that a function involving the difference between [ψ′(x)]2 + ψ″(x) and a proper fraction of x is completely monotonic on (0,∞).

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Published Online: 2013-06-28

Published in Print: 2013-06-01

Citation Information: Mathematica Slovaca, Volume 63, Issue 3, Pages 469–478, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918,

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