The Bernoulli and Euler Numbers
The Bernoulli numbers are given by An alternate convention defines the Bernoulli numbers as . This definition gives Bn = −nζ(1 − n) where for n = 0 and n = 1 the expression −nζ(1 − n) is to be understood as limx → 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
Read more about this topic: Bernoulli Polynomials
Famous quotes containing the word numbers:
“I had but three chairs in my house; one for solitude, two for friendship; three for society. When visitors came in larger and unexpected numbers there was but the third chair for them all, but they generally economized the room by standing up.”
—Henry David Thoreau (1817–1862)