# Bessel function (zeros) Calculator

## Calculates the positive zeros of the Bessel functions Jv(x) and Yv(x).

 order v v≦200 ordinal number s of zeros(s=1,2,..) 6digit10digit14digit18digit22digit26digit30digit34digit38digit42digit46digit50digit
 $\normal Bessel\ functions\ of\\\ the\ 1st\ kind\ J_\nu(x)\ and\ 2nd\ kind\ Y_\nu(x)\\[10](1)\ x^2y''+xy'+(x^2-\nu^2)y=0\\\hspace{25} y=c_1J_\nu(x)+c_2Y_\nu(x)\\[10](2)\ J_\nu(x)={\large\sum_{\small k=0}^{\small\infty}\frac{(-1)^k}{k!\Gamma(k+\nu+1)}(\frac{x}{2})^{\nu+2k}}\\\hspace{30} Y_\nu(x)={\large\frac{J_\nu(x)cos(\nu\pi)-J_{-\nu}(x)}{sin(\nu\pi)}}\\(3)\ {\large e^{\frac{x}{2}(t-{\large\frac{1}{t}})}}={\large\sum_{\small n=-\infty}^{\small\infty}}J_n(x)t^n,\hspace{20} n=integer\\$

Bessel function (zeros)
 [1-10] /12 Disp-Num5103050100200
[1]  2019/02/10 04:57   Male / 20 years old level / High-school/ University/ Grad student / Useful /
Purpose of use
To find an approximation for the 14th order roots to aid in coding assignment for MATLAB
[2]  2018/11/04 22:11   Female / Under 20 years old / High-school/ University/ Grad student / Useful /
Purpose of use
Check actual value against a value obtained by iterations on a programme.
[3]  2018/03/08 20:57   Male / 50 years old level / An engineer / Useful /
Purpose of use
dce
[4]  2017/10/20 13:22   Male / 60 years old level or over / A retired people / Very /
Purpose of use
check my Matlab calculation for tutor class
[5]  2016/09/16 22:48   Male / 20 years old level / High-school/ University/ Grad student / Very /
Purpose of use
Checking precision and bounds of routine that calculates roots of J
[6]  2016/03/15 19:19   Male / 50 years old level / An engineer / Very /
Purpose of use
Design for in-house induction heating system for forging
Comment/Request
A smart Android phone
[7]  2016/02/07 16:37   - / 20 years old level / High-school/ University/ Grad student / Very /
Purpose of use
Finding the zeros of bessel function
Comment/Request
I want a help on my project to find the workings on how to determine the zeros of bessel
[8]  2015/10/14 02:22   Female / 30 years old level / A teacher / A researcher / Useful /
Purpose of use
finding zeros of bessels function
[9]  2015/04/29 08:22   Male / Under 20 years old / A teacher / A researcher / Very /
Purpose of use
Researching discontinuities involving the evaluation of bessel functions
[10]  2015/04/10 08:32   Male / 60 years old level or over / An engineer / Very /
Purpose of use
Solve a specific form of the diffusion equation

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