In mathematics, Faulhaber's formula, named after Johann Faulhaber, expresses the sum
as a (p + 1)th-degree polynomial function of n, the coefficients involving Bernoulli numbers Bj.
The formula says
Faulhaber himself did not know the formula in this form, but only computed the first seventeen polynomials; the general form was established with the discovery of the Bernoulli numbers (see History section below). The derivation of Faulhaber's formula is available in The Book of Numbers by John Horton Conway and Richard K. Guy.
Read more about Faulhaber's Formula: Alternate Expression, Examples, Proof, Relation To Bernoulli Polynomials, Umbral Form, Faulhaber Polynomials, History
Famous quotes containing the word formula:
“Ideals possess the strange quality that if they were completely realized they would turn into nonsense. One could easily follow a commandment such as “Thou shalt not kill” to the point of dying of starvation; and I might establish the formula that for the proper functioning of the mesh of our ideals, as in the case of a strainer, the holes are just as important as the mesh.”
—Robert Musil (1880–1942)