MATLAB: Need help programming a few tricky calculations!!

Question

Can somebody show me how to write a program to calculate a program that you input and N and the output is:

thank you

edit: in regualer text rather than attempt to write latex:

f(n) = [ ( (-1)^(n-1)*t^(2-2n) ) / ( 1-t^(-4) ) ] sum_k=0^{n-1} t^-4nk product_{i=0}^k (1-t^(4i-4n))

Answer 1

Here is one way to do the function, assuming you are looking for a numerical output, and that you pass it t as well as n:

n = ... % choose your number
t = ... % ditto
output = fn(n,t);
function f = fn(n,t)
         c = (-1)^(n-1)*t^(2-2*n)/(1-t^-4);
         S = 0;
         for k = 0:n-1
             tm = t^(-4*n*k);
             P = 1;
             for i = 0:k
                 P = P*(1-t^(4*i-4*n));
             end
             S = S + tm*P;
         end
         f = c*S;     
end