How to calculate a sum using only the odds index ?

Question

Sleh Eddine Brika 2016-11-8

评论： Walter Roberson 2016-11-8

I need to calculate this sum. I am using symsum but I don't know how to specify the odds index only.

Answer 1

Walter Roberson 2016-11-8

syms P a D M N
Pi = sym('pi');
w_max = 4*P*a^2/(Pi^4 * D) * symsum( symsum( 1/((M*2-1)^2+(N*2-1)^2)^2, N, 1, inf), M, 1, inf)

However, this is only able to eliminate one level of the symsum. The other is difficult to eliminate to a closed form.

Sleh Eddine Brika 2016-11-8

编辑：Sleh Eddine Brika 2016-11-8

Thanks for your answer, you have to add the vpa command as shown here

 w_max = vpa(symsum( symsum( 1/((M*2-1).^2+(N*2-1).^2).^2, N, 1, inf), M, 1, inf))

Thanks but I tried it, and it seems there is something wrong I didn't get the right result.

Walter Roberson 2016-11-8

The approximately 0.2825068 that shows up for the above line agrees with my calculations from another package.

Notice that you neglected 4*P*a^2/(Pi^4 * D)