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

Sending completion

To improve this 'Hankel function Calculator', please fill in questionnaire.
Male or Female ?
Male Female
Age
Under 20 years old 20 years old level 30 years old level
40 years old level 50 years old level 60 years old level or over
Occupation
Elementary school/ Junior high-school student
High-school/ University/ Grad student A homemaker An office worker / A public employee
Self-employed people An engineer A teacher / A researcher
A retired people Others
Useful?
Very Useful A little Not at All
Purpose of use?