# Spherical Bessel function Calculator

## Calculates the spherical Bessel functions of the first kind jv(x) and the second kind yv(x), and their derivatives j'v(x) and y'v(x).

 order v real number x complex number 6digit10digit14digit18digit22digit26digit30digit34digit38digit42digit46digit50digit
 $\normal Spherical\ Bessel\ function\ of\\\ the\ 1st\ kind\ j_\nu(x)\ and\ 2nd\ kind\ y_\nu(x)\\[10](1)\ x^2w''+2xw'+(x^2-\nu(\nu+1))w=0\\\hspace{25} w=c_1j_\nu(x)+c_2y_\nu(x)\\[10](2)\ j_\nu(x)={\large\sqrt{\frac{\pi}{2x}}}J_{\nu+\frac{1}{2}}(x)\\\hspace{25}y_\nu(x)={\large\sqrt{\frac{\pi}{2x}}}Y_{\nu+\frac{1}{2}}(x)\\[10](3)\ j'_\nu(x)=j_{\nu-1}(x)-{\large\frac{\nu+1}{x}}j_\nu(x)=-j_{\nu+1}(x)+{\large\frac{\nu}{x}}j_\nu(x)\\\hspace{25}y'_\nu(x)=y_{\nu-1}(x)-{\large\frac{\nu+1}{x}}y_\nu(x)=-y_{\nu+1}(x)+{\large\frac{\nu}{x}}y_\nu(x)\\$

Spherical Bessel function
 [1-7] /7 Disp-Num5103050100200
[1]  2014/04/18 13:36   Male / 30 years old level / A teacher / A researcher / Very /
Purpose of use
Cross checking the boost::math::special_functions::cyc_bessel_J_zeros code.
[2]  2014/03/16 18:03   Male / 20 years old level / High-school/ University/ Grad student / Very /
Purpose of use
to help bug hunt in scattering code
[3]  2014/02/20 14:36   Female / 30 years old level / A teacher / A researcher / A little /
Purpose of use
Want to compare with the roots that I derived
Comment/Request
Probably can elaborate more on the type of the bessel function
[4]  2013/12/11 10:47   Male / 50 years old level / A teacher / A researcher / Very /
Purpose of use
[5]  2013/02/03 03:42   Male / 40 years old level / High-school/ University/ Grad student / Very /
Purpose of use
Evaluation for homework assignment
[6]  2009/05/05 07:38   Male / 20 level / A university student / Very /
Purpose of use
For calculating scattering coefficient
Comment/Request
This is a good web site. May I give a suggestion, it is possible to show a code for calculating as well as the derive of formula. That will be brillient.
[7]  2009/02/18 14:02   Male / 20 level / A researcher / Very /
Comment/Request
CLASS !!!

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