§ 7 Bernoulli numbers and Bernoulli polynomials
1. Bernoulli number
In , the coefficients of , are called Bernoulli numbers, and are sometimes expanded as functions
To define the relationship between Bernoulli numbers and
For a table of numbers see Chapter V §3 , IX .
2. Bernoulli polynomial
(where is the Bernoulli number)
is called a Bernoulli polynomial, which can also be expanded by the generating function
to define .
The Bernoulli polynomial formula is as follows: