scipy.special.hankel1e

scipy.special.hankel1e(v, z, out=None) = <ufunc 'hankel1e'>

Exponentially scaled Hankel function of the first kind

Defined as:

hankel1e(v, z) = hankel1(v, z) * exp(-1j * z)

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 exponentially scaled Hankel function.

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/