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An Extended Version of Faulhaber's Formula
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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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