An iterative solution instead of the symbolic one can be more productive this case, like this one
x=[0 5 10 15 20 30 45 60 75 90 105 120];
y=[0 3.87 4.62 4.98 5.21 5.40 5.45 5.50 5.51 5.52 5.54 5.53];
plot(x,y,'bo');
hold on
pause(0.1);
beta0=[39,0.002];
% syms n t
% fun=@(beta,t) beta(1)*(1-6/(pi^2)*symsum((1./n.^2).*exp(-beta(2)*(n.^2).*t),n,1,Inf));
% betafit = nlinfit(x,y,fun,beta0);
beta1=beta0;
delta = 1e-8; % desired objective accuracy
R0=Inf; % initial objective function
for K=1:10000
fun=@(beta,t) beta(1)*(1-6/(pi^2)*sum((1./(1:K)'.^2).*exp(-beta(2)*((1:K)'.^2).*t),1));
[betafit,R] = nlinfit(x,y,fun,beta1);
R = sum(R.^2);
if abs(R0-R)<delta
break;
end
beta1=betafit;
R0 = R;
end
plot(x,fun(betafit,x),'.-r');
xlabel('x');
ylabel('y');
legend('experiment','model');
title(strcat('\beta=[',num2str(betafit),'];----stopped at--','K=',num2str(K)));
