English Dictionary

Faulhaber's formula

固有名詞

(mathematics) A formula expressing the sum of the pth powers of the first n positive integers as a (p + 1)th-degree polynomial function of n, the coefficients involving Bernoulli numbers.

日本語の意味

数学において、最初のn個の正の整数のp乗の和を、nの(p+1)次の多項式で表現する公式であり、その多項式の各係数にはベルヌーイ数が含まれる。

Faulhaber's formula allows one to express the sum of the pth powers of the first n positive integers as a (p + 1)th-degree polynomial in n whose coefficients involve Bernoulli numbers.

べき乗和の公式は、最初のn個の正の整数のp乗の和を、係数にベルヌーイ数を含むnの(p+1)次多項式として表すことを可能にします。

意味（1）

(mathematics) A formula expressing the sum of the pth powers of the first n positive integers as a (p + 1)th-degree polynomial function of n, the coefficients involving Bernoulli numbers.