Probability, Random Variables, and Random Processes: Theory and Signal Processing Applications

B.25 BERNOULLI NUMBERS

Definition: Bernoulli Numbers The Bernoulli numbers {Bn} are rational numbers specified by the coefficients in the following series:

(B.139)

They include: B0 = 1, B1 = −1/2, B2 = 1/6, B3 = 0, B4 = −1/30, B5 = 0, B6 = 1/42, B7 = 0, B8 = −1/30, B9 = 0, B10 = 5/66, and B20 = −174, 611/330. Note that Bn = 0 if the subscript can be expressed as n = 2m+1 for , that is, for all odd n (except n = 1). The Bernoulli numbers appear in expressions for the central moments of the logistic random variable.