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arXiv · 0903.0888

A note on additivity of polygamma functions

Feng Qi·Bai-Ni Guo
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Abstract

In the note, the functions $\abs{ψ^{(i)}(e^x)}$ for $i\in\mathbb{N}$ are proved to be sub-additive on $(\lnθ_i,\infty)$ and super-additive on $(-\infty,\lnθ_i)$, where $θ_i\in(0,1)$ is the unique root of equation $2\abs{ψ^{(i)}(θ)}=\abs{ψ^{(i)}(θ^2)}$.

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Feng Qi, Bai-Ni Guo. 2009-03-05. A note on additivity of polygamma functions. https://doi.org/10.2298/fil1505063g

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