Residue at a pole of order n
= Residue at a pole of order n
If
$$
f(z)=\frac{g(z)}{(z-a)^n}
$$
with $g$ holomorphic at $a$, then
$$
\operatorname{Res}(f,a)
=\frac{g^{(n-1)}(a)}{(n-1)!}.
$$
= Residue at a pole of order n
If
$$
f(z)=\frac{g(z)}{(z-a)^n}
$$
with $g$ holomorphic at $a$, then
$$
\operatorname{Res}(f,a)
=\frac{g^{(n-1)}(a)}{(n-1)!}.
$$