How can i find a variable that is in the infinite series?

Hello everyone,

I'm trying to learn MATLAB on my own, and I have a problem. I got this equation and i know everything except 'L' in the infinite series. I need to find it, but i couldn't solve it when it is in the infinite series.

Deff=(2.02)*10^(-10);

t=22320;

a=0.1425; % a is equal to ((X-X*)/(X0-X*))*(pi^2)/8

n=1:10000;

Ser = @(L) sum((exp(((pi^2)*(-1)*Deff*t*(2*n-1))./(4*L.^2))/((2*n-1).^2)));

L = fzero(@(L) Ser(L)-a,0)

I wrote this but i couldn't find L. Could someone help me please??

Answer 1

[David Hill]

Deff=(2.02)*10^(-10);
t=22320;
a=0.1425;
n=1:100000;
Ser = @(L) sum(1./(2*n-1).^2.*exp(-(2*n-1).^2*pi^2*Deff*t/4/L^2));
l= fzero(@(L) Ser(L)-a,.0024);

[Burak Akayoglu]

Hello David,thank you for your answer. How did you find 0.0024 value in the fzero function?

[David Hill]

Just needs to be relatively close to the root. Just plugged in a few numbers of L.

[Burak Akayoglu]

thank you very much David