%0 Journal Article
%T A note on additivity of polygamma functions
%A Feng Qi
%A Bai-Ni Guo
%J Mathematics
%D 2009
%I arXiv
%R 10.2298/FIL1505063G
%X 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 $2\abs{\psi^{(i)}(\theta)}=\abs{\psi^{(i)}(\theta^2)}$.
%U http://arxiv.org/abs/0903.0888v1