MATLAB: Solve equation with bessel function of first kind

Question

I need to solve in matlab this equation in order to find all the alfak that satisfy this equation:

where:

-Jnp is the bessel function of the first kind and order n*p;

-p=10;

-R3=90*10e-3;

-n is an odd positive integer.

Answer 1

Download this package from FEX: https://www.mathworks.com/matlabcentral/fileexchange/48403-bessel-zero-solver and then run the following code. You will need to specify the number of roots you want

n = 2;
p = 10;
R3 = 90*10e-3;
num_roots = 10;
bessel_z = besselzero(n*p, num_roots);
alpha_k = bessel_z/R3;