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# 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:
    n int

      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