scipy.special.hankel1

scipy.special.hankel1(v, z, out=None) = <ufunc 'hankel1'>

Hankel function of the first kind

Parameters

varray_like

Order (float).

zarray_like

Argument (float or complex).

outndarray, optional

Optional output array for the function values

Returns

scalar or ndarray

Values of the Hankel function of the first kind.

See also

hankel1e

ndarray This function with leading exponential behavior stripped off.

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.

References

1

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