Suppose f(z) is an analytic function with domain C (the set of all complex numbers). Supposefurther that in the region {|z| > 100} ƒ satisfies|f(2)| < a + b|z|"where a, b are positive real numbers and n is an integer. Show that f must be a polynomial ofdegree at most n.

Suppose further that in the region {|z| > 100} f satisfies f(Z)<a+ b |z|^n where a ,b are…

Answered: Suppose f(z) is an analytic function…

Suppose f(z) is an analytic function with domain C (the set of all complex numbers). Suppose further that in the region {|z| > 100} ƒ satisfies |f(2)| < a + b|z|"

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter8: Polynomials

Section8.3: Factorization In F [x]

Problem 13E

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Suppose f(z) is an analytic function with domain C (the set of all complex numbers). Suppose
further that in the region {|z| > 100} ƒ satisfies
|f(2)| < a + b|z|"
where a, b are positive real numbers and n is an integer. Show that f must be a polynomial of
degree at most n.

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