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/f77_src/special_functions/special_functions.html

Examples

>>> import numpy as np
>>> 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