Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A note on additivity of polygamma functions   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 $2\abs{\psi^{(i)}(\theta)}=\abs{\psi^{(i)}(\theta^2)}$.

32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
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The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics