Geodesic
An extended version of Faulhaber's formula
Journal of integer sequences, Tome 19 (2016) no. 4
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 
@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/}
}
TY  - JOUR
AU  - Schumacher,  Raphael
TI  - An extended version of Faulhaber's formula
JO  - Journal of integer sequences
PY  - 2016
VL  - 19
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/JIS_2016__19_4_a7/
LA  - en
ID  - JIS_2016__19_4_a7
ER  - 
%0 Journal Article
%A Schumacher,  Raphael
%T An extended version of Faulhaber's formula
%J Journal of integer sequences
%D 2016
%V 19
%N 4
%U http://geodesic.mathdoc.fr/item/JIS_2016__19_4_a7/
%G en
%F JIS_2016__19_4_a7
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/