Complex Analysis: Theory and Applications · Problem 7.2.3

Taylor and Laurent Series — Howell & Matthews

Mathematics — Complex Analysis · taylor-series

Problem

Find the Taylor series centered at

a = 1

and state where it converges for ((a))

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

. ((b))

f(z) = \dfrac{1-z}{z-3}

. Hint:

\dfrac{1-z}{z-3} = \left(\tfrac{1}{2}\right)\!\left(\dfrac{z-1}{1-\frac{z-1}{2}}\right) = \left(\tfrac{1}{2}\right)(z-1)\left(\dfrac{1}{1-\frac{z-1}{2}}\right)