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

Rok, strany: 2013, 469 - 478

The di-gamma function $ψ(x)$ is defined on $(0,∞)$ by $ψ(x)=((Γ'(x)) / (Γ(x)))$ and $ψ⁽ⁱ⁾(x)$ for $i\in\mathbb{N}$ 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 $(0,∞)$.

ISO 690:

Guo, B., Zhao, J., Qi, F. 2013. A completely monotonic function involving the tri- and tetra-gamma functions. In Mathematica Slovaca, vol. 63, no.3, pp. 469-478. 0139-9918. DOI: https://doi.org/10.2478/s12175-013-0109-2

APA:

Guo, B., Zhao, J., Qi, F. (2013). A completely monotonic function involving the tri- and tetra-gamma functions. Mathematica Slovaca, 63(3), 469-478. 0139-9918. DOI: https://doi.org/10.2478/s12175-013-0109-2