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/