Question

Find the Laurent series for f(z) in the following regions:
\[f(z)=\frac{1}{z^2-1}\]
a) 0 < |z-1| < 2
b) 2 < |z-1| < ∞
c) 0 < |z| < 1

Answer 1

u help me I help u!

Answer 2

In 0<|z|<1, there is absolutely nothing going on, so have at it.

\(\dfrac{-1}{1-z^{2}} = -(1 + z^{2} + z^{4} + ...)\)