# 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
Verify the results of a computer I downloaded from the net.
[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 !!!

Thank you for your questionnaire.
Sending completion

To improve this 'Spherical Bessel 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 person Others
Useful?
Very Useful A little Not at All
Purpose of use?