Bernoulli number

短语

词形变化

Bernoulli numbers 复数 Bernoulli numbers

别名

Bernoulli's number

释义与例句

n.
  1. 1.

    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.

    数学

    1993, Serge Lang, Complex Analysis, Springer, 3rd Edition, page 418, 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!)

词源

Named after Swiss mathematician Jacob Bernoulli (1654–1705), who discovered the numbers independently of and at about the same time as Japanese mathematician Seki Kōwa. The numbers first appeared as coefficients in Bernoulli's formulae for the sum of the first n positive integers, each raised to a given power. The sequence was subsequently found in numerous other contexts.

来源：wiktionary