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# scipy.special.hankel2e

scipy.special.hankel2e(v, z, out=None) = <ufunc 'hankel2e'>

  Exponentially scaled Hankel function of the second kind

  Defined as:

      hankel2e(v, z) = hankel2(v, z) * exp(1j * z)

  Parameters:
    v array_like

      Order (float).

    z array_like

      Argument (float or complex).

    out ndarray, optional

      Optional output array for the function values

  Returns:
    scalar or ndarray

      Values of the exponentially scaled Hankel function of the second kind.

  Notes

  A wrapper for the AMOS [1] routine zbesh, which carries out the computation using the relation,

  \[H^{(2)}_v(z) = -\frac{2}{\imath\pi} \exp(\frac{\imath \pi v}{2}) K_v(z exp(\frac{\imath\pi}{2}))\]

  where \(K_v\) is the modified Bessel function of the second kind. For negative orders, the relation

  \[H^{(2)}_{-v}(z) = H^{(2)}_v(z) \exp(-\imath\pi v)\]

  is used.

  References

  [1]

  Donald E. Amos, “AMOS, A Portable Package for Bessel Functions of a Complex Argument and Nonnegative Order”, http://netlib.org/amos/