speed for loop in sum

Can the for loop be removed ?

x=linspace(-2,2,100); %some vector
[X,XX]=meshgrid(x,x); %some matrix
a=1/2;%some constant
A0=zeros(size(X));%initialize the sum
A0k = @(k,X,a)(((-1)^k).*((X./a).^(2*k)).*besselj(2*k,X));%series

for l=0:20
    A0 = A0+A0k(l,X,a); %sum of series
end

[Torsten]

What's the problem with the solution I gave ?

[Ole]

I was not able to make it work.

Answer 1

[Torsten]

function main
  x = linspace(-2,2,100); %some vector
  [X,XX] = meshgrid(x,x); %some matrix
  k = 0:20;
  a = 0.5;
  A0 = arrayfun(@(x)sum((-1).^k.*(x/a).^(2*k).*besselj(2*k,x)),X)
end

[Ole]

Thank you!

just as feedback the arrayfun is slower than the loop.

0.096s for the for loop

0.30s for the arrayfun