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

>>> importnumpyasnp
>>> fromscipy.specialimport 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
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