\[\mathbf{H}_{\frac{3}{2}}\left(z\right)=\left(\frac{z}{2\pi}\right)^{\frac{1}{2%
}}\left(1+\frac{2}{z^{2}}\right)-\left(\frac{2}{\pi z}\right)^{\frac{1}{2}}%
\left(\sin z+\frac{\cos z}{z}\right),\]