scipy.special.euler

scipy.special.euler(n)

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