Efficient way to implement a Summation within an Integral

Hi i'm trying to implement the following equation efficiently, where is the normalized column vector

The following is my implementation

% function for normalize column vector
nc = @(col) col./norm(col);

% implementation of equation in picture
for m=1:size(Cs,2)
            ftemp = [];
            for l = 1:size(Cs,2)
                if l ~= m % calculation of integral for every l neq to m
                    fun1 = @(k)(((nc(Cs(:,m)))-(nc(Cs(:,l)).*exp(1j*k)))./(norm(((nc(Cs(:,m)))-(nc(Cs(:,l)).*exp(1j*k))),v)));
                 
                    fint1 = integral(fun1,0,2*pi,'ArrayValued',true);
                    
                    ftemp = [ftemp,fint1];
                end
            end
            % cal the sum for every mth value
            F(:,m) = sum(ftemp,2);
end

I am a bit worried if the summation under the condition is implemented right, is there a way to cross verify and also a better and more efficient way to do the sum inside integrals ???

Please advice.