Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: New integral representations of the polylogarithm function   Maximon has recently given an excellent summary of the properties of the
Euler dilogarithm function and the frequently used generalizations of the
dilogarithm, the most important among them being the polylogarithm function
$Li_(z)$. The polylogarithm function appears in several fields of mathematics
and in many physical problems. We, by making use of elementary arguments,
deduce several new integral representations of the polylogarithm for any
complex z for which $|z|$ < 1. Two are valid for all complex s, whenever
$\Re(s)>1$ . The other two involve the Bernoulli polynomials and are valid in
the important special case where the parameter s is an positive integer. Our
earlier established results on the integral representations for the Riemann
zeta function $\zeta(2n+1)$ ,$n\in\mathbb{N}$, follow directly as corollaries
of these representations.

23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys