**§ 7 ****Bernoulli numbers and Bernoulli polynomials**

1.
Bernoulli number

function expansion

_{}

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

function

_{} (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:

_{} _{}

_{} _{}

_{}

_{}

_{}

_{}

_{}

_{}

_{}

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