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arXiv · 1105.4928

Complete monotonicity of a function involving the $p$-psi function and alternative proofs

Valmir Krasniqi·Feng Qi
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Abstract

In the paper the authors alternatively prove that the function $x^α\big[\ln\frac{px}{x+p+1}-ψ_p(x)\big]$ is completely monotonic on $(0,\infty)$ if and only if $α\le 1$, where $p\in\mathbb{N}$ and $ψ_p(x)$ is the $p$-analogue of the classical psi function $ψ(x)$. This generalizes a known result.

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Valmir Krasniqi, Feng Qi. 2011-12-28. Complete monotonicity of a function involving the $p$-psi function and alternative proofs. https://doi.org/10.14419/gjma.v2i3.3096

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