On the coefficients of power sums of arithmetic progressions

András Bazsó; István Mező

On the coefficients of power sums of arithmetic progressions

Number Theory 2015-01-09 v1

Authors: András Bazsó , István Mező

Abstract

We investigate the coefficients of the polynomial $S_{m,r}^n(\ell)=r^n+(m+r)^n+(2m+r)^n+\cdots+((\ell-1)m+r)^n.$ We prove that these can be given in terms of Stirling numbers of the first kind and $r$ -Whitney numbers of the second kind. Moreover, we prove a necessary and sufficient condition for the integrity of these coefficients.

Keywords

arithmetic progressions power sums polynomial coefficients Stirling numbers of the first kind r-Whitney numbers of the second kind integrity condition

Cite

@article{arxiv.1501.01843,
  title  = {On the coefficients of power sums of arithmetic progressions},
  author = {András Bazsó and István Mező},
  journal= {arXiv preprint arXiv:1501.01843},
  year   = {2015}
}

Related papers

View all related →