a) Laurent's Theorem predicts the existence of a Laurent series, centered at 0, which converges in the region 3 < |z| for the function f(2) = - 2² + 5z – 6 Calculate this series and then state, with reasons, whether the series can be used to find the residue of f at one of its singularities or not. b) Calculate the residues of f at each of its singularities (you do not need Laurent series for this!).

a) Laurent's Theorem predicts the existence of a Laurent series, centered at 0, which converges in the region 3 < |z| for the function f(2) = - 2² + 5z – 6 Calculate this series and then state, with reasons, whether the series can be used to find the residue of f at one of its singularities or not. b) Calculate the residues of f at each of its singularities (you do not need Laurent series for this!).

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.2: Arithmetic Sequences

Problem 67E

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