scipy.special.euler¶
-
scipy.special.euler(n)[source]¶ Euler numbers E(0), E(1), …, E(n).
The Euler numbers [1] are also known as the secant numbers.
Because
euler(n)returns floating point values, it does not give exact values for large n. The first inexact value is E(22).- Parameters
- nint
The highest index of the Euler number to be returned.
- Returns
- ndarray
The Euler numbers [E(0), E(1), …, E(n)]. The odd Euler numbers, which are all zero, are included.
References
- 1
Sequence A122045, The On-Line Encyclopedia of Integer Sequences, https://oeis.org/A122045
- 2
Zhang, Shanjie and Jin, Jianming. “Computation of Special Functions”, John Wiley and Sons, 1996. https://people.sc.fsu.edu/~jburkardt/f_src/special_functions/special_functions.html
Examples
>>> from scipy.special import euler >>> euler(6) array([ 1., 0., -1., 0., 5., 0., -61.])
>>> euler(13).astype(np.int64) array([ 1, 0, -1, 0, 5, 0, -61, 0, 1385, 0, -50521, 0, 2702765, 0])
>>> euler(22)[-1] # Exact value of E(22) is -69348874393137901. -69348874393137976.0