Bessel function summation from 1 to infinity

Hi all I am using matlab for the first time doing more complex equations I am at a lost of how to get the correct syntax for the following equation, in the image.

where alpha is just a number and a_k is the kth zero of Bessel function J_0.

So far I have

 a_k = 1:1000;   
 J = besselj(a_k,alpha);
 J1 = besselj(1,a_k);
 J_final = J/J1;

I am pretty sure even this is wrong, but I have no clue where to go from here. Any help would be tremendous.

Answer 1

[Torsten]

   a_k = array of the first n zeros of J_0  
   J = besselj(1,a_k*alpha);
   J1 = besselj(1,a_k);
   summe = sum(J./J1);

But where do you get a_k from ?

Best wishes

Torsten.

[DragonLady]

Many thanks Torsten. a_k is just from the equation I was given in the picture, in actual fact it is supposed to sigma subscript k.