# Infinite sum with Bessel's function

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mery on 10 Aug 2022
Edited: Torsten on 14 Aug 2022
I have this sum with the Bessel function that I am trying to calculate and plot.
Any help would be greatly appreaciated.
Thank you
##### 2 CommentsShowHide 1 older comment
mery on 10 Aug 2022
Edited: mery on 10 Aug 2022
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)

Torsten on 11 Aug 2022
Edited: Torsten on 11 Aug 2022
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 on 11 Aug 2022
@Torsten This community is great because there are people like you.
Thank you, sir.

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