An Extended Version of Faulhaber's Formula

摘要

This paper presents an extended version of the well-known Faulhaber formula, which is used to compute the sum of the m-th powers of the first n natural numbers, where m and n are two natural numbers. Our expression is analogous to Faulhaber's formula, but sums the m-th powers of the natural numbers x for any non-negative real number x.