scipy.special.hankel1e¶
-
scipy.special.hankel1e(v, z) = <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).
- Returns
- outValues 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/