Sums of powers via integration

2009/03/25 by Dashti, M. Torabi
#Discrete Mathematics (cs.DM) #FOS: Computer and information sciences

paper · doi:10.48550/arxiv.0903.4358

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.

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