`scipy.special._basic:bernoulli`

source: /scipy/special/_basic.py:1807

Signature

def bernoulli(n)

Summary

Bernoulli numbers B0..Bn (inclusive).

Parameters

n : int: Indicated the number of terms in the Bernoulli series to generate.

Returns

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

Examples

import numpy as np
from scipy.special import bernoulli, zeta

✓

bernoulli(4)

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array([ 1.   , -0.5  ,  0.167,  0.   , -0.033])

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)

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array([ 0.5  ,  0.167, -0.   , -0.033])

Note that, in the notation used in the wikipedia article, `bernoulli` computes ``B_n^-`` (i.e. it used the convention that ``B_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)``.

Aliases

scipy.special.bernoulli