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arXiv · 1001.4611

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

Feng Qi·Bai-Ni Guo
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Abstract

The psi function $ψ(x)$ is defined by $ψ(x)=\frac{Γ'(x)}{Γ(x)}$ and $ψ^{(i)}(x)$ for $i\in\mathbb{N}$ denote the polygamma functions, where $Γ(x)$ is the 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 $(0,\infty)$.

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Feng Qi, Bai-Ni Guo. 2010-01-26. A completely monotonic function involving the tri- and tetra-gamma functions. https://doi.org/10.2478/s12175-013-0109-2

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