I am in the process of computing an integral using the Cauchy residue theorem, and I am having a hard time computing the residue of a pole of high order.
Concretely, how would one compute the residue of the function $f(z)=\frac{(z^6+1)^2}{az^6(z-a)(z-\frac{1}{a})}$ at $z=0$?
Although it is not needed here, $a$ is a complex number with $|a|<1$.
Thanks in advance for any insight.