How to graph a function that consists of summations?

I am trying to graph a fucntion C that includes four different summations. What I have so far is:

g=ga;

T=(0.1:0.001:1);

F1 = sum(-(E.^2)*g*exp(-(E-13)./T),E,0,13);

F2 = sum(-g*exp(-(E-13)./T),E,0,13);

F3 = sum(E*g*exp(-(E-13)./T),E,0,13);

F4 = sum((g*exp(-(E-13)./T)),E,0,13);

C = (1/(T^2))*((F1/F2)-(F3/F4)^2)

Where ga is an array and E goes from 0 to 13. T is a value that increases in 0.001 increments from 0.1 to 1.

I am a little lost as to what to do from here to fix my summations so that I no longer get errors and how to plot C. (I also tried to run each summation as a symsum, with syms E).

Any help is appreciated!

Answer 1

[Mathieu NOE]

hello

I tried this code

clc
clearvars

% g=[1;2;3];
g=[1]; % same curves - whatever g value is

% T=(0.1:0.01:1);
T=logspace(-1,0,50); % better rendering IMHO

E = linspace(0,13,130);

for ci = 1:length(g)
    C(ci,:) = computeC(g(ci),T,E);
end

plot(T,C,'-*');
xlabel('T');
ylabel('C');

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function C = computeC(g,T,E)
 
% F1 = sum(-(E.^2)*g*exp(-(E-13)./T),E,0,13);
% F2 = sum(-g*exp(-(E-13)./T),E,0,13);
% F3 = sum(E*g*exp(-(E-13)./T),E,0,13);
% F4 = sum((g*exp(-(E-13)./T)),E,0,13);

    for ci = 1:length(T)
        F1 = sum(-(E.^2).*g.*exp(-(E-13)./T(ci)));
        F2 = sum(-g.*exp(-(E-13)./T(ci)));
        F3 = sum(E.*g.*exp(-(E-13)./T(ci)));
        F4 = sum(g.*exp(-(E-13)./T(ci)));
        C(ci) = (1/(T(ci)^2))*((F1/F2)-(F3/F4)^2);
    end

end
 
 

and finally found out that whatever the value of g , the result in C does not change. Looking again at the equations it's obvious that g appears both at the numerator and denominator each time so it will cancel out when you do F1/F2 and F3/F4

got this plot :

Answer 2

[Walter Roberson]

g = ga(:);
T=(0.1:0.001:1);
E = reshape(0:13, 1, 1, []) ;
F1 = sum(-(E.^2).*g.*exp(-(E-13)./T),3);
F2 = sum(-g.*exp(-(E-13)./T),3);
F3 = sum(E.*g.*exp(-(E-13)./T),3);
F4 = sum((g.*exp(-(E-13)./T)),3);
C = (1./(T.^2)).*((F1./F2)-(F3./F4).^2);

This should be numel(g) by numel(T)

If you are thinking of plotting then

plot(T, C.')

if you want there to be numel(g) different lines.