scipy.special.bernoulli#
- 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
- 1
Zhang, Shanjie and Jin, Jianming. “Computation of Special Functions”, John Wiley and Sons, 1996. https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
- 2
“Bernoulli number”, Wikipedia, https://en.wikipedia.org/wiki/Bernoulli_number
Examples
>>> 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)
forn > 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
computesB_n^-
(i.e. it used the convention thatB_1
is -1/2). The relation given above is forB_n^+
, so the sign of 0.5 does not match the output ofbernoulli(4)
.