A note on additivity of polygamma functions

Details A note on additivity of polygamma functions A note on additivity of polygamma functions

2009-03-05

arxiv.org/abs/0903.0888v1

Mathematics

Classical Analysis and ODEs

3 pages

Scientific paper

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

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