Hankel Functions
Let $x$ be a positive real number and $\nu$ an integer number, this application evaluates the Hankel functions of the first and second kind \[ \begin{array}{lcl} H_\nu^{(1)}(x) &=& J_\nu(x) + iY_\nu(x) \\ H_\nu^{(2)}(x) &=& J_\nu(x) - iY_\nu(x) \\ \end{array} \] and spherical Hankel functions of the first and second kind \[ \begin{array}{lcl} h_\nu^{(1)}(x) &=& \sqrt{\frac{\pi}{2}}\frac{1}{\sqrt{x}}H_{\nu+\frac{1}{2}}^{(1)}(x) \\ h_\nu^{(2)}(x) &=& \sqrt{\frac{\pi}{2}}\frac{1}{\sqrt{x}}H_{\nu+\frac{1}{2}}^{(2)}(x) \end{array} \] where $J_\nu(x)$ is the Bessel function of the first kind, and $Y_\nu(x)$ is the Bessel function of the second kind.