^{9}In applying the Cauchy integral theorem, note that the real part of the singularities for n are given by -1,
Re-(1+(μ + v)∕2)=r_{0} and by Re((μ + v)∕2)=r_{1}>0. We can verify that |r_{1}| < |r_{0}|, so that as contour in the
Cauchy integral we have chosen the circle centered at the origin with radius R <min[1, Re((μ + v)∕2)]. The
numerical computation of the Cauchy integral is obtained trough the Lyness algorithm that reduces the
computation of the integral along a closed path in the complex plane to the computation of a real integral over
[-π,π] by the trapezoidal rule.