A proof of symmetry of the power sum polynomials using a novel Bernoulli number identity
Journal of integer sequences, Tome 20 (2017) no. 6
The problem of finding formulas for sums of powers of natural numbers has been of interest to mathematicians for many centuries. Among these is Faulhabers well-known formula expressing the power sums as polynomials whose coefficients involve Bernoulli numbers. In this paper we give an elementary proof that the sum of $p$-th powers of the first $n$ natural numbers can be expressed as a polynomial in $n$ of degree $p + 1$. We also prove a novel identity involving Bernoulli numbers and use it to show the symmetry of this polynomial.
@article{JIS_2017__20_6_a6,
author = {Newsome, Nicholas J. and Nogin, Maria S. and Sabuwala, Adnan H.},
title = {A proof of symmetry of the power sum polynomials using a novel {Bernoulli} number identity},
journal = {Journal of integer sequences},
year = {2017},
volume = {20},
number = {6},
zbl = {1422.11052},
language = {en},
url = {http://geodesic.mathdoc.fr/item/JIS_2017__20_6_a6/}
}
TY - JOUR AU - Newsome, Nicholas J. AU - Nogin, Maria S. AU - Sabuwala, Adnan H. TI - A proof of symmetry of the power sum polynomials using a novel Bernoulli number identity JO - Journal of integer sequences PY - 2017 VL - 20 IS - 6 UR - http://geodesic.mathdoc.fr/item/JIS_2017__20_6_a6/ LA - en ID - JIS_2017__20_6_a6 ER -
%0 Journal Article %A Newsome, Nicholas J. %A Nogin, Maria S. %A Sabuwala, Adnan H. %T A proof of symmetry of the power sum polynomials using a novel Bernoulli number identity %J Journal of integer sequences %D 2017 %V 20 %N 6 %U http://geodesic.mathdoc.fr/item/JIS_2017__20_6_a6/ %G en %F JIS_2017__20_6_a6
Newsome, Nicholas J.; Nogin, Maria S.; Sabuwala, Adnan H. A proof of symmetry of the power sum polynomials using a novel Bernoulli number identity. Journal of integer sequences, Tome 20 (2017) no. 6. http://geodesic.mathdoc.fr/item/JIS_2017__20_6_a6/