# 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 6digit10digit14digit18digit22digit26digit30digit34digit38digit42digit46digit50digit
 $\normal Hankel\ functions\ of\ the\ 1st\ kind\\\hspace{75} H^{(1)}_\nu(x)\ and\ 2nd\ kind\ H^{(2)}_\nu(x)\\[10](1)\ x^2y''+xy'+(x^2-\nu^2)y=0\\\hspace{25} y=c_1H^{(1)}_\nu(x)+c_2H^{(2)}_\nu(x)\\[10](2)\ H^{(1)}_\nu(x)=J_\nu(x)+iY_\nu(x)\\\hspace{25} H^{(2)}_\nu(x)=J_\nu(x)-iY_\nu(x)\\[10](3)\ H'^{(1)}_\nu(x)=H^{(1)}_{\nu-1}(x)-{\large\frac{\nu}{x}}H^{(1)}_\nu(x)=-H^{(1)}_{\nu+1}(x)+{\large\frac{\nu}{x}}H^{(1)}_\nu(x)\\\hspace{25}H'^{(2)}_\nu(x)=H^{(2)}_{\nu-1}(x)-{\large\frac{\nu}{x}}H^{(2)}_\nu(x)=-H^{(2)}_{\nu+1}(x)+{\large\frac{\nu}{x}}H^{(2)}_\nu(x)\\$
Hankel function
 [1-4] /4 Disp-Num5103050100200
[1]  2017/08/29 20:54   Male / 30 years old level / A teacher / A researcher / Very /
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PhD
Comment/Request
please i want the exact equations.

i searched a lot and i find different equations.
[2]  2015/06/05 22:09   Female / 40 years old level / A teacher / A researcher / Not at All /
Comment/Request
request for a calculator for a Bessel function of the third kind and its derivative
[3]  2014/06/11 11:14   Female / 20 years old level / High-school/ University/ Grad student / A little /
Purpose of use
research
[4]  2009/08/11 23:10   Male / 40 level / A specialized student / Very /
Comment/Request
very useful thank you very much

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