maxframe.tensor.special.hankel2e#

maxframe.tensor.special.hankel2e(v, z, out=None)[source]#

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:

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

Return type:

scalar or ndarray

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