# Hankel function Calculator

## Calculates the Hankel functions of the first kind Hv(1)(x) and the second kind Hv(2)(x), and their derivatives H'v(1)(x) and H'v(2)(x).

order v
 real number
x
 complex number
 6dgt10dgt14dgt18dgt22dgt26dgt30dgt34dgt38dgt42dgt46dgt50dgt
 $\normal Hankel\ functions\ of\ the\ 1st\ kind\\\hspace{75} H^{(1)}_\nu(x)\ and\ 2nd\ kind\ H^{(2)}_\nu(x)\\[10](1)\ x^2y''+xy'+(x^2-\nu^2)y=0\\\hspace{25} y=c_1H^{(1)}_\nu(x)+c_2H^{(2)}_\nu(x)\\[10](2)\ H^{(1)}_\nu(x)=J_\nu(x)+iY_\nu(x)\\\hspace{25} H^{(2)}_\nu(x)=J_\nu(x)-iY_\nu(x)\\[10](3)\ H'^{(1)}_\nu(x)=H^{(1)}_{\nu-1}(x)-{\large\frac{\nu}{x}}H^{(1)}_\nu(x)=-H^{(1)}_{\nu+1}(x)+{\large\frac{\nu}{x}}H^{(1)}_\nu(x)\\\hspace{25}H'^{(2)}_\nu(x)=H^{(2)}_{\nu-1}(x)-{\large\frac{\nu}{x}}H^{(2)}_\nu(x)=-H^{(2)}_{\nu+1}(x)+{\large\frac{\nu}{x}}H^{(2)}_\nu(x)\\$

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