Infinite sum with Bessel's function

I have this sum with the Bessel function that I am trying to calculate and plot.

Any help would be greatly appreaciated.

Thank you

[Torsten]

Where is the error and what is the error message ?

By the way: It's nonsense to determine the roots again and again with every call of "findLr".

Determine them only once at the beginning of your program.

[mery]

the error is

Error using ==> findLr

Too many input arguments.

Error in ==> findLp at 5

Lp(i)= findLr(rr1,K,n,sstep);

Error in ==> tset at 4

findLp(K,n,sstep)

Answer 1

[Torsten]

n = 60;
sstep = 1;
a_k = J0ROOTS(n,sstep);
r = (0:0.01:1).';
t = 0:0.1:1;
S = zeros(numel(r),numel(t));
for i = 1:numel(t)
  S(:,i) = sum(2*besselj(0,a_k.*r)./(a_k.^2.*besselj(1,a_k)).*exp(-a_k.*t(i)),2);
end
plot(r,S)

function x=J0ROOTS(n,sstep)
if nargin==0 
    n=20;
    sstep=1;
elseif nargin==1
    sstep=1;
end
J0=@(x) besselj(0,x);
k=0; i=0;
while k<n 
    i1=i+sstep;
    if J0(i)*J0(i1)<0 
        k=k+1;
        x(k)=fzero(J0,[i i1]);
    end
    i=i1;
end
end

[mery]

@Torsten, Thank you very much.

in my problem, I have 0<=t<inf how can I add this condition?

[Torsten]

in my problem, I have 0<=t<inf how can I add this condition?

Incorporated.

[mery]

@Torsten This community is great because there are people like you.

Thank you, sir.

[Andrew Omame]

I am having issue running this code on my MATLAB R2014a version.

The error messgae I get is:

Error using .*

Matrix dimensions

must agree.

Please can anyone help on what to do to resolve this.

[Torsten]

n = 60;
sstep = 1;
a_k = J0ROOTS(n,sstep);
r = (0:0.01:1).';
t = 0:0.1:1;
S = zeros(numel(r),numel(t));
for i = 1:numel(t)
  for k = 1:numel(r)
    for l = 1:n
      S(k,i) = S(k,i) + 2*besselj(0,a_k(l)*r(k))/(a_k(l)^2*besselj(1,a_k(l)))*exp(-a_k(l)*t(i));
    end
  end
end
plot(r,S)

function x=J0ROOTS(n,sstep)
if nargin==0 
    n=20;
    sstep=1;
elseif nargin==1
    sstep=1;
end
J0=@(x) besselj(0,x);
k=0; i=0;
while k<n 
    i1=i+sstep;
    if J0(i)*J0(i1)<0 
        k=k+1;
        x(k)=fzero(J0,[i i1]);
    end
    i=i1;
end
end

[Andrew]

This has now worked on my MATLAB R2014a version. Thank you very much