Integration of a function with modified Bessel function of the first kind.

Hi,

I want to create the function mentioned below on matlab:

Where all the variables are defined numbers (k,s=1,p=6,nc=84,..), W`k is a complex vector and Iν(z) is the modified Bessel function of the first kind.

The integral is function of z.

I'm trying to get the intergral values(not considering the log factor in this case).

f = @(z) ((exp(-s.*z.*((p.*nc)+Sigma2^-2)))./((norm(avg_ww(kk,:)).*sqrt(p.*nc.*z)).^(nc-1))).*besseli(nc-1,2.*s.*(norm(avg_ww(kk,:)).*sqrt(p.*nc.*z))).*besseli(0,2.*s.*(1./Sigma2).*sqrt(z.*abs(Uh)^2));
upper_limit = linspace(0.1,40); % upper limit of the integral (randomly chosen)
xval = arrayfun(@(uplim) integral(f, 0, uplim, 'ArrayValued',true), upper_limit);

Can you please advise if my integration is correct? because it doesn't feel like it

[David Goodmanson]

Hi Anthony,

Youd had better go back and check your parentheses placements, because right now I_0(...) is part ot the argument of the I_(nc-1) bessel function. That may not be the only bad one, I don't know.

[Anthony Koussaifi]

Hi David,

Thank you for this remarque, kindly note that I fixed it in my code and the original post.

I will try to run a few test, and come back with a feedback

Thank you again!