Double sum with infinite limit

Hi all,

I need to perform the calculation for the following equation:

alpha_k = (k+1/2)*pi/a and beta_n = (n+1/2)*pi/b are the parameters that are varying. All the other parts of the expression (i, w, eta, a, b) are constants. w varies from 1 to 1000, so F must return a vector with complex values. I'm trying to use symsum but am not being able to find results. Any suggestions would be appreciated. Thanks!

Code:

syms k n i omega eta a b pi

alpha_k = (k+1/2)*pi/a;

beta_n = (n+1/2)*pi/b;

A = 1./((((k+1/2)*pi/a).^2).*(((n+1/2)*pi/b).^2).*...

(((k+1/2)*pi/a).^2 + ((n+1/2)*pi/b).^2 +1i.*omega/eta));

B = (4.*1i.*omega./(eta*(a^2)*b^2));

F = A.*B;

func1 = symsum(F,n,0,inf);

func2 = symsum(func1,k,0,inf);

[Jan]

Please post your current code. It is much easier to fix bugs, than to guess a solution, which might match your needs.

[Bjorn Gustavsson]

Why not just write the summation as two nested loops where you make the summation step-by-step. But first insert the expressions for \alpha_k and \beta_n in your terms and have a look at the explicit form of your terms. Or use meshgrid and generate arrays for k and n of different sizes, then you can simply calculate all the corresponding terms at once and calculate different partial sums - that way you can look at how and if the sum seems to converge...

HTH

[Torsten]

I think you missed the (...)^(-1) of the expression to be summed up.

[Augusto Carvalho de Sousa]

I have just updated with the code.