A numerical method for the evaluation of complex integrals

A numerical method for evaluating the complex integral
I = \frac{1}{2\pij} \oint \frac{B(z)B(z^{-1})}{A(z)A(z^{-1})} \frac{dz}{z}
along the unit circle in a positive direction (where
A
and
B
are polynomials with real coefficients), is presented in this paper. The method developed in this paper is shown to be obtainable as a FORTRAN program as well as a table form. The results achieved represent significant reduction of the computations compared to other existing methods.