Complex Analysis: Theory and Applications · Problem 7.3.8

Taylor and Laurent Series — Howell & Matthews

Mathematics — Complex Analysis · laurent-series

Problem

Find the Laurent series for

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

that involves powers of

z

and is valid for

|z| > 1

. Hint:

\dfrac{1}{\left(1-\frac{1}{z}\right)^2} = \dfrac{z^2}{(1-z)^2}