3.2.1.5. HankelH_Asym.m¶
Calculate the Hankel function \(H_m(z)\) using the asymptotic method.
3.2.1.5.1. Syntax¶
H = HankelH_Asym(m, z)
3.2.1.5.2. Output arguments¶
H — \(H_m(z)\).
3.2.1.5.3. Input arguments¶
3.2.1.5.3.1. Mandatory arguments¶
m — order
z — the argument \(z\)
3.2.1.5.3.2. Optional arguments¶
approx_order
\(K\in \mathbb{N}\) — Calculate the Hankel function using the asymptotic expansion given by Eq. (3.2.2), see Eq. (10.17.5) in Olver et al. [5].
(3.2.2)¶\[H_m^{(1)}(z)
\sim
\sqrt{\frac{2}{\pi z}}
\mathrm{e}^{-\mathrm{i}\omega}
\sum_{k=0}^K \mathrm{i}^k
\frac{a_k(m)}{z^k}\]
(3.2.3)¶\[H_m^{(1)}(z)
\sim \sqrt{\frac{2}{\mathrm{i}\pi z}}
\frac{\mathrm{e}^{\mathrm{i}z}}{\mathrm{i}^m}\]
3.2.1.5.4. Dependencies¶
NA