double integral implementation in matlab

Question

I am in trouble to implement the following double integral. there is a summation inside the integral which make things a bit complicated. The matlab code I did is as follows and always has error like "Matrix dimensions must agree." , any hint to implement it? thanks

n=3;
nn=1:n;
aa=gamma([1:n])
thre=3;
lapha=4;
r=3;
fun1= @(theta, x) (1-sum( lambda *pi *( (x-r).^2+r^2-(x-r).*r.*cos(theta)).^(nn-1)./aa).*exp(-1*lambda *pi*((x-r).^2+r^2-(x-r).*r.*cos(theta)))).*lambda/n*(1-1/2^n).*thre.*r.^alpha.*(x-r).^(1-alpha) ;
answer=integral2( fun1, 0, 2*pi, 0, inf )

The double integral:

Answer 1

Your problem is the way you calculate the sum in the integrated function. The documentation of intergal2 says that the function argument must accept arrays X and Y of the same size and return an array of corresponding values. But this expression inside the function definition:

((x-r).^2 + r^2 - (x-r).*r.*cos(theta)).^(nn-1)./aa

is not working the way you expect, because it's you who decide the size of nn and aa, while it's integral2 that decides the size of the vectors x and theta; no wonder that there are disagreements on it.