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
Switzerland

Abstract:

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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