9In applying the Cauchy integral theorem, note that the real part of the singularities for n are given by -1, Re-(1+(μ + v)2)=r0 and by Re((μ + v)2)=r1>0. We can verify that |r1| < |r0|, 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.