5.1.2.7 Example 7

\[ r=\frac {1}{x^{2}}\]

One pole at \(x=0\) of order 2. And \(O\left ( \infty \right ) =2-0=2\). Case 1 is satisfied. Also case 2 since pole is even order. Also case 3 is satisfied. Hence all three cases are satisfied. \(L=[1,2,4,6,12]\)