mars.tensor.special.hankel1#

mars.tensor.special.hankel1(v, z, **kwargs)[source]#

Hankel function of the first kind

Parameters

  • v (array_like) – Order (float).

  • z (array_like) – Argument (float or complex).

Returns

out

Return type

Values of the Hankel function of the first kind.

Notes

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

\[H^{(1)}_v(z) = \frac{2}{\imath\pi} \exp(-\imath \pi v/2) K_v(z \exp(-\imath\pi/2))\]

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

\[H^{(1)}_{-v}(z) = H^{(1)}_v(z) \exp(\imath\pi v)\]

is used.

See also

hankel1e

this function with leading exponential behavior stripped off.

References

1

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