Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sums of powers of integers and hyperharmonic numbers   In this paper, we derive a formula for the sums of powers of the first $n$
positive integers, $S_k(n)$, that involves the hyperharmonic numbers and the
Stirling numbers of the second kind. Then, using an explicit representation for
the hyperharmonic numbers, we generalize this formula to the sums of powers of
an arbitrary arithmetic progression. Moreover, we express the Bernoulli
polynomials in terms of hyperharmonic polynomials and Stirling numbers of the
second kind. Finally, we extend the obtained formula for $S_k(n)$ to negative
values of $n$.

9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph