bernoulli — SciPy v1.15.2 Manual (original) (raw)

scipy.special.

scipy.special.bernoulli(n)[source]#

Bernoulli numbers B0..Bn (inclusive).

Parameters:

nint

Indicated the number of terms in the Bernoulli series to generate.

Returns:

ndarray

The Bernoulli numbers [B(0), B(1), ..., B(n)].

References

Examples

import numpy as np from scipy.special import bernoulli, zeta bernoulli(4) array([ 1. , -0.5 , 0.16666667, 0. , -0.03333333])

The Wikipedia article ([2]) points out the relationship between the Bernoulli numbers and the zeta function, B_n^+ = -n * zeta(1 - n)for n > 0:

n = np.arange(1, 5) -n * zeta(1 - n) array([ 0.5 , 0.16666667, -0. , -0.03333333])

Note that, in the notation used in the wikipedia article,bernoulli computes B_n^- (i.e. it used the convention thatB_1 is -1/2). The relation given above is for B_n^+, so the sign of 0.5 does not match the output of bernoulli(4).