Discussion:
Q: The following function f has an isolated singularity at z=0. Its nature: it is a pole; find the singular part.
f(z)=(z^2+1)/(z(z-1))
Use this equation and definition:
Equation: f(z)= A_m/(z-a)^m +?+ A_1/((z-a) )+g_1 (z) (*)
Where g_1 is analytic in B(a;R) and A_m≠0.
Definition: if f has a pole of order m at z=0 and satisfies (*) then A_m (z-a)^(-m)+?+A_1 (z-a)^(-1) is called the singular part of f at z-a.