Integrating Bessel Function Including for Each Value of Array-Valued Vector

I'd like to integrate a function which has bessel functions in it for each value of Q.

I've seen that I should use quadv but this will get me a vector of the same length of Q ?

Q = 0:.1:1; z = 0:0.1:20;
h = sin(2*pi*z);
for i = 1:length(Q)
    integ = @(z) besseli(0,z).*h.* (Q(i)) ...
      ./ (h.*(2*besseli(1,z) - h.*besseli(0,z)));
    dP(i) = quad(integ,0,1);
end

Thanks.

Answer 1

[Walter Roberson]

You are using z for two different purposes. In the first line you make z a vector of specific values. In the second line you make h a vector that depends upon those z values. But then in your integ anonymous function, z has become whatever is passed by quad(), which will generally be a vector of variable length. You then try to multiply besseli(0,that vector) by h where h is the vector made up of specific values from the z that had existence outside the function.

Perhaps you need

Q = 0:.1:1; z = 0:0.1:20;
h = @(z) sin(2*pi*z);
for i = 1:length(Q)
    integ = @(z) besseli(0,z).*h(z).* (Q(i)) ...
      ./ (h(z).*(2*besseli(1,z) - h(z).*besseli(0,z)));
    dP(i) = quad(integ,0,1);
end

This will give you warning messages about minimum step size reached and possible singularity -- probably due to the singularity that the function has at approximately 0.43

[Ezz El-din Abdullah]

Thanks. Now, I deleted the vector z and it works fine.