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7.2.9 Bernoulli numbers

The Bernoulli polynomial Bn is defined by:

B0=1,   Bn′(x)=nBn−1(x),   
1


0
Bn(x) dx=0 

The nth Bernoulli number is Bn=Bn(0), and is also given by the formula:

  
t
et−1
=
+∞
n=0
B(n)
n!
tn. 

The bernoulli command computes the Bernoulli numbers.

Example

bernoulli(6)
     
1
42
          

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