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.

Becauseeuler(n) returns floating point values, it does not giveexact values for largen. 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 SpecialFunctions”, John Wiley and Sons, 1996.https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html

Examples

Try it in your browser!

>>>importnumpyasnp>>>fromscipy.specialimporteuler>>>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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