3 1. Suppose that f(2) is analytic on the set A = {z :1< |z| < 2}, andlet f(z) = E a6z* be its Laurent expansion on A. Show that if yis any closed path contained in A, then| F(e)2πί- ind, (0) a_1f(z) dz = 2 i ·A–1•

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Answered: 1. Suppose that f(2) is analytic on the…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.2: Properties Of Group Elements

Problem 32E: Prove statement d of Theorem 3.9: If G is abelian, (xy)n=xnyn for all integers n.

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Prove statement d of Theorem 3.9: If G is abelian, (xy)n=xnyn for all integers n.
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1. Suppose that f(2) is analytic on the set A = {z :1< |z| < 2}, and let f(2) = E apzk be its Laurent expansion on A. Show that if y is any closed path contained in A, then | f (2) da 2πί - ind, (0) a_1.