If f(z) has a pole of order n at z = a, then residue of function f(z) at a is
1
\(\dfrac{1}{(n)!} \left\lbrace \dfrac{d^{n-1}}{dz^{n-1}}\left((z-a)^{n-1}f(z)\right)\right\rbrace_{z=a}\)
2
\(\dfrac{1}{(n-1)!} \left\lbrace \dfrac{d^{n-1}}{dz^{n-1}}\left((z-a)^{n-1}f(z)\right)\right\rbrace_{z=a}\)
3
\(\dfrac{1}{(n)!} \left\lbrace \dfrac{d^{n-1}}{dz^{n-1}}\left((z-a)^{n}f(z)\right)\right\rbrace_{z=a}\)
4
\(\dfrac{1}{(n-1)!} \left\lbrace \dfrac{d^{n-1}}{dz^{n-1}}\left((z-a)^{n}f(z)\right)\right\rbrace_{z=a}\)