English Dictionary

Bernoulli number

名詞

(mathematical analysis, number theory) Any one of the rational numbers in a sequence of such that appears in numerous contexts, including formulae for sums of integer powers and certain power series expansions.

日本語の意味

数学解析や数論の文脈で、整数のべき乗の和の公式や特定の冪級数展開に現れる、有理数からなる数列の一要素として定義される数値

When deriving the closed form for sums of powers, Euler used a Bernoulli number to express one of the coefficients in the formula.

べき乗の和の閉形式を導くとき、オイラーは式の係数の一つを表すためにベルヌーイ数を用いた。

意味（1）

(mathematical analysis, number theory) Any one of the rational numbers in a sequence of such that appears in numerous contexts, including formulae for sums of integer powers and certain power series expansions.

The assertion about the value of the zeta function at negative integers then comes immediately from the definition of the Bernoulli numbers in terms of the coefficients of a power series, namely t/(eᵗ-1)=∑ₙ₌₀ ᪲B_n(tⁿ)/(n!)

Bernoulli numbers （ plural ）