How to get infinite sum containing double integral expression ?

 fun = @(u,v) (-1)^n.* exp(-(const1)*v).* exp(-(condn1)*u).* v.^(n2+beta1-n-2).* u.^(n1+alpha1+n);
ymax = @(u) u;
Int1 = integral2(fun, 0, inf, 0, ymax);

Here 'const1' 'condn1' 'n1' 'n2' 'alpha1' beta1' are all positive constants.

I want to find summation of Int1 from n = 0 to infinity. I have MatLab 2012a version. Please provide me an appropriate solution for this.

Answer 1

[Roger Stafford]

I think it likely your series is divergent as you have it defined. Take advantage of the fact that the sum of double integrals varying with n, all taken over the same region, is equal to the double integral of the sum of their integrands over that region. Unfortunately that integrand sum appears to be divergent. Excluding all factors except those involving n, the sum of (-u/v)^n from n = 0 to inf is divergent for v < u which, as you have defined 'int1' and 'ymax', holds over the region of integration. If you had (-v/u)^n in your integrand, then it would presumably be convergent, and you could solve your problem with one double integration.