Bernoulli Polynomials - The Bernoulli and Euler Numbers

The Bernoulli and Euler Numbers

The Bernoulli numbers are given by An alternate convention defines the Bernoulli numbers as . This definition gives B_n = −nζ(1 − n) where for n = 0 and n = 1 the expression −nζ(1 − n) is to be understood as lim_{x → n} −xζ(1 − x). The two conventions differ only for n = 1 since B₁(1) = 1/2 = −B₁(0).

The Euler numbers are given by