Complex Analysis: Theory and Applications · Problem 7.3.6

Taylor and Laurent Series — Howell & Matthews

Mathematics — Complex Analysis · laurent-series

Problem

Show that 1−zz−3=−∑n=0∞2n(z−1)n\dfrac{1-z}{z-3} = -\displaystyle\sum_{n=0}^{\infty}\dfrac{2^n}{(z-1)^n} is valid for ∣z−1∣>2|z-1| > 2. Hint: Use the hint for Exercise 3b, Section 7.2.

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