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:

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 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/