can anyone help me ? i keep getting this error

Here is the code:

num_roots=5; num_functions=6;
%initial guess for roots (from Wolfram MathWorld)
zeros_guess=[2.4,3.8,5.1,6,7.5,8.7;...
   5.5,7,8.4,9.7,11,12;...
   8.6 10,11.6,13,14,16;...
   11.8,13,15,16,18,19;...
   15,16.4,18,19.4,21,22]; 
%Compute first five roots of first six Bessel functions
%Put in variable bzeros with size(bzeros) = [5, 6]
integrand = @(theta,x,n) cos(x.*sin(theta)-n*theta);
J_n = @(x) integral(@(theta)integrand(theta,x,n),0,pi);
for n=0:num_functions-1
    J_n = @(x) integral(@(theta)integrand(theta,x,n),0,pi);
    for k=1:num_roots
        bzeros(k,n+1)=fzero(J_n,bzeros_guess(k,n+1));
    end
end
%print table
fprintf('k     J0(x)     J1(x)     J2(x)     J3(x)     J4(x)     J5(x)\n')
for k=1:num_roots
    fprintf('%i',k)
    for n=0:num_functions-1
        fprintf('%10.4f',bzeros(k,n+1));
    end
    fprintf('\n');
end

this is the output that keeps popping out:

Undefined function 'bzeros_guess' for input arguments of type 'double'.

Error in solution (line 15)

bzeros(k,n+1)=fzero(J_n,bzeros_guess(k,n+1));

what does this mean and is there a way i can rewrite the white section so that it works ?

[David Hill]

https://www.mathworks.com/matlabcentral/fileexchange/48403-bessel-zero-solver?s_tid=ta_fx_results

Answer 1

[Chunru]

num_roots=5; num_functions=6;
%initial guess for roots (from Wolfram MathWorld)
zeros_guess=[2.4,3.8,5.1,6,7.5,8.7;...
   5.5,7,8.4,9.7,11,12;...
   8.6 10,11.6,13,14,16;...
   11.8,13,15,16,18,19;...
   15,16.4,18,19.4,21,22]; 
%Compute first five roots of first six Bessel functions
%Put in variable bzeros with size(bzeros) = [5, 6]
integrand = @(theta,x,n) cos(x.*sin(theta)-n*theta);
J_n = @(x) integral(@(theta)integrand(theta,x,n),0,pi);
for n=0:num_functions-1
    J_n = @(x) integral(@(theta)integrand(theta,x,n),0,pi);
    for k=1:num_roots
        %bzeros(k,n+1)=fzero(J_n,bzeros_guess(k,n+1));
        bzeros(k,n+1)=fzero(J_n, zeros_guess(k,n+1));   % initial guess at the right hand side
    end
end
%print table
fprintf('k     J0(x)     J1(x)     J2(x)     J3(x)     J4(x)     J5(x)\n')

k     J0(x)     J1(x)     J2(x)     J3(x)     J4(x)     J5(x)

for k=1:num_roots
    fprintf('%i',k)
    for n=0:num_functions-1
        fprintf('%10.4f',bzeros(k,n+1));
    end
    fprintf('\n');
end

1

    2.4048    3.8317    5.1356    6.3802    7.5883    8.7715

2

    5.5201    7.0156    8.4172    9.7610   11.0647   12.3386

3

    8.6537   10.1735   11.6198   13.0152   14.3725   15.7002

4

   11.7915   13.3237   14.7960   16.2235   17.6160   18.9801

5

   14.9309   16.4706   17.9598   19.4094   20.8269   22.2178

[Mohamed]

thank you so much

you are a lifesaver

[Torsten]

The Bessel functions are predefined in MATLAB. If it's not explicitly stated in your assignment, you don't need to evaluate them using the integral representation:

https://de.mathworks.com/help/matlab/ref/besselj.html