How to generate a loop for the problem mentioned in the context

Dear, scholars,

Anybody can help me with writing a decent code for finding the below equation:

I can write the code for the second coefficient of numerator (I mean the following part):

But I can not extend it to the whole equation,

Any ideas?

I attach my code for the second part:

clc
clear all
close all 
 
we = linspace(0,100,101);
gh = [1 3 5]; 
w = [21 39 88];

for i = 1:3
    for j = 1:length(we)
        a(i,j) = gh(i) * we(j);
        C(i,j) = (1/12)+1i*we(j);
        x(i,j) = 12*gh(i);
        s3(i,j) = 1i*gh(i)*we(j);
        s2(i,j) = w(i)^2 - we(j)^2+1i*w(i);
        s1(i,j) = 1i*gh(i)*we(j);
        v2(i,j) = s3(i,j)/s2(i,j)+C(i,j);
        v1(i,j) = s1(i,j)/s2(i,j);
        v(i,j) = abs(v1(i,j)/v2(i,j))
        d = log10(sum(v))
        d1 = sum(v);
        end
end
figure 
plot(we,d,'LineWidth',2)
    grid on 

Answer 1

[Guru Mohanty]

Hi, I understand you are getting issues in calculating sum of the given expression. You can do this using MATLAB Symbolic Toolbox-

1. Create symbolic variables using syms.
2. Build the expression need to be evaluated.
3. Through an iteration substitute all the variables using subs function. It will output an array.
4. Finally, Evaluate the summation of the expression using sum function.

Here is a sample code using random values as input.

n=3;
syms s 3
syms C x a
% Create Random Data
av=rand(1,n);
s1_1v=rand(1,n);
s2_1v=rand(1,n);
s3_1v=rand(1,n);
Cv=rand(1,1);
xv=rand(1,n);
% Set Up The Expression
Var=sum(s(1)/s(2))/(C +sum(s(3)/s(2)));
toSum=(Var*x + a)/s(2);
disp(toSum);
for i=1:n
    % Substitute Values through Iteration
    subSum(i)=subs(toSum,{a , s1_1 , s2_1 , s3_1 , C , x}, ... 
                         {av(i),s1_1v(i),s2_1v(i),s3_1v(i),Cv,xv(i)});
end
OutSum=double(sum(subSum));
disp(OutSum);