§3.6 Summation Formulas: The Complex Case

Example (S. 80)

f[z_] := (z^(-4));
Z[t_] := (1 - I t)/2;
FullSimplify[
        Re[(1/(2  I)) f[Z[t]] Cot[π Z[t]] Z'[t]] // 
          ComplexExpand, {t ∈ Reals}] // TraditionalForm