Journal of Integer Sequences, Vol. 19 (2016), Article 16.4.2

An Extended Version of Faulhaber's Formula

Raphael Schumacher
Department of Mathematics
ETH Zurich
Rämistrasse 101
8092 Zurich


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.

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(Concerned with sequences A027641 A027642.)

Received November 7 2015; revised versions received November 9 2015; March 19 2016. Published in Journal of Integer Sequences, April 7 2016.

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