`scipy.special._basic:bernoulli`

source: build-install/usr/lib/python3.14/site-packages/scipy/special/_basic.py:2108

Signature

def bernoulli(n)

Summary

Bernoulli numbers B_0 through B_n (inclusive).

Parameters

n : int: Index of the last Bernoulli number to return. Non-integer values are cast to integers. Must be non-negative.

Returns

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

Examples

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

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bernoulli(4)

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

The Wikipedia article ([1]_) 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)

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-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