English

Sums of powers via integration

Discrete Mathematics 2009-03-26 v1

Abstract

Sum of powers 1^p+...+n^p, with n and p being natural numbers and n>=1, can be expressed as a polynomial function of n of degree p+1. Such representations are often called Faulhaber formulae. A simple recursive algorithm for computing coefficients of Faulhaber formulae is presented. The correctness of the algorithm is proved by giving a recurrence relation on Faulhaber formulae.

Cite

@article{arxiv.0903.4358,
  title  = {Sums of powers via integration},
  author = {M. Torabi Dashti},
  journal= {arXiv preprint arXiv:0903.4358},
  year   = {2009}
}

Comments

4 pages

R2 v1 2026-06-21T12:44:22.883Z