How can I find the order of the pole z=π2 for f(z)=1(2log(z))(1−sin(z))? I know the...
How can I find the order of the pole ? I know the answer should be 2, but I cant
Answer & Explanation
First, note that does not vanish at , so we can ignore it; it does not contribute to the pole. So consider simply . We want to write things in terms of ,
so let , where at the end I have used a simple trig formula. Then we can expand , so
Thus, we can see that the order of the pole is 2.
you have the function
is a zero of order two for h, therefore is a pole for of order two.
Write Observe that g(z) is analytic and non- zero at hence the order of zero of h(z) there determines the order of pole for rational function f(z). suggests h(z) has zero of order 2 at so f(z) has pole of order 2 there.