# Spherical Hankel function Calculator

## Calculates the spherical 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
 $\normal Spherical\ Hankel\ functions\ of\\\ the\ 1st\ kind\ h^{(1)}_\nu(x)\ and\ 2nd\ kind\ h^{(2)}_\nu(x)\\[10](1)\ x^2w''+2xw'+(x^2-\nu(\nu+1))w=0\\\hspace{25} w=c_1h^{(1)}_\nu(x)+c_2h^{(2)}_\nu(x)\\[10](2)\ h^{(1)}_\nu(x)={\large\sqrt{\frac{\pi}{2x}}}H^{(1)}_{\nu+\frac{1}{2}}(x)=j_\nu(x)+iy_\nu(x)\\\hspace{25}h^{(2)}_\nu(x)=j_\nu(x)-iy_\nu(x)\\[10](3)\ h'^{(1)}_\nu(x)=h^{(1)}_{\nu-1}(x)-{\large\frac{\nu+1}{x}}h^{(1)}_\nu(x)=-h^{(1)}_{\nu+1}(x)+{\large\frac{\nu}{x}}h^{(1)}_\nu(x)\\\hspace{25}h'^{(2)}_\nu(x)=h^{(2)}_{\nu-1}(x)-{\large\frac{\nu+1}{x}}h^{(2)}_\nu(x)=-h^{(2)}_{\nu+1}(x)+{\large\frac{\nu}{x}}h^{(2)}_\nu(x)\\$

Spherical Hankel function
 [1-2] /2 Disp-Num5103050100200
[1]  2011/05/22 14:49   Male / 30 years old level / A student / Very /
Comment/Request
why this calculation is inaccurate at v=50, x=20 for spherical hankel function
from Keisan
The algorithm has been improved.Thank you for pointing out.
[2]  2009/04/27 14:33   Male / 20 level / A university student / Very /
Purpose of use
project
Comment/Request
very good

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