Question

whats the order of this function pole at z=-1
h(z)=3/(1-cos((z+1)^2)) and g(z)= (z+1)/)(z^3+1)^4)

Answer 1

Hint, but not a proof
\[
h(z) = \frac{3}{(z+1)^2}+1+\frac{1}{5}
(z+1)^2+\frac{2}{63} (z+1)^4+O\left((z+1)^5\right)\\
g(z)=\frac{1}{81 (z+1)^3}+\frac{4}{81 (z+1)^2}+\\ \frac{26}{243
(z+1)}+\frac{40}{243}+\frac{145 (z+1)}{729}+\frac{16}{81}
(z+1)^2+O\left((z+1)^3\right)
\]

Answer 2

Read this, you might find it helpful
http://www.physicsforums.com/showthread.php?t=609593