Geodesic
An extended version of Faulhaber's formula
Journal of integer sequences, Tome 19 (2016) no. 4
Zbl
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 $x$.
Classification : 11B68, 34M30
Keywords: extended faulhaber formula, floor function, sum of powers of the first few natural numbers, Bernoulli polynomial, Bernoulli number 
Schumacher,  Raphael. An extended version of Faulhaber's formula. Journal of integer sequences, Tome 19 (2016) no. 4. http://geodesic.mathdoc.fr/item/JIS_2016__19_4_a7/
@article{JIS_2016__19_4_a7,
     author = {Schumacher,  Raphael},
     title = {An extended version of {Faulhaber's} formula},
     journal = {Journal of integer sequences},
     year = {2016},
     volume = {19},
     number = {4},
     zbl = {1353.11044},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2016__19_4_a7/}
}
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