1.2.1 Example 1

\[ r=\frac {4x^{6}-8x^{5}+12x^{4}+4x^{3}+7x^{2}-20x+4}{4x^{4}}\]

There is one pole at \(x=0\,\ \)of order \(4\). And \(O\left ( \infty \right ) =4-6=-2\). Conditions for case 1 are met. Since it has a pole of even order. Also \(O\left ( \infty \right ) \) is even. Case 2 are not satisfied, since there is no pole of order \(2\) and no odd pole of order greater than \(2\) exist. Case 3 is also not met, since the pole is order \(4\) and case 3 will only work if pole is order 1 or 2. Hence \(L=\left [ 1\right ] \)