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 - >>> 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, - bernoullicomputes- B_n^-(i.e. it used the convention that- B_1is -1/2). The relation given above is for- B_n^+, so the sign of 0.5 does not match the output of- bernoulli(4).