§ 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



                 (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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