Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Two applications of polylog functions and Euler sums   Let $I(n):=\int_0^1 [x^n+(1-x)^n]^\frac1n dx.$ In this paper, we show that
$I(n)= \sum_0^\infty \frac{I_i}{n^i},n\rightarrow \infty$ and we compute $I_i,
i =0..5$, obtained by polylog functions and Euler sums. As a corollary, we
obtain explicit expressions for some integrals involving functions $ u^i,
exp(-u), (1 +exp(-u))^j , ln(1 + exp(-u))^k$ . As another asymptotic result,
let $S_0(z):=\frac{Li_m(1)}{Li_m(1)-Li_m(z)}$, where $Li_m(z)$ is the polylog
function. We provide the asymptotic behaviour of $S_n,n\rightarrow \infty$
where $S_n:=[z^n]S_0(z)$. This paper fits within the framework of analytic
combinatorics.

31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph