Bernoulli Numbers

Given positive integer k, generate the k-th bernoulli number.

Description

Bernoulli numbers are obtained from the series expansion of the function

z/(exp(z) -1 ) = sum(a(k)*z^k);

Then the k-th Bernoulli number is defined as

B(k) = k! * a(k);

  
These numbers are related to the sum of the p-th powers of consecutive n integers (from 1 to n-1) and define:

S(n,p) = sum((1:n-1).^p)

See http://numbers.computation.free.fr/Constants/Miscellaneous/bernoulli.html#CITEDilcher

• MATLAB release: MATLAB 7.0.1 (R14SP1)