Examples
- Consider the rational function:
We recognize in p(x) and q(x) respectively the Chebyshev polynomials of degree 3 and 5. Therefore r(x) has poles, and, i.e. for . We can see on the picture that and . For the pole in zero, we have since the left and right limits are equal (which is because p(x) also has a root in zero). We conclude that since q(x) has only five roots, all in . We cannot use here the Routh–Hurwitz theorem as each complex polynomial with f(iy) = q(y) + ip(y) has a zero on the imaginary line (namely at the origin).
Read more about this topic: Cauchy Index
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