Let f(z) be an entire function satisfying|f (21 + z2)|† < |f (21)|* + \f (22)|*for all 21, 22 E C and some integer n > 0. Show that f(2) is a polynomial in zof degree at most n.

As per the question we are given an entire function which satisfies the following inequality :And…

Answered: Let f(z) be an entire function…

Let f(z) be an entire function satisfying |ƒ (²1 +22)| ≤ |ƒ (2₁)| + + + |ƒ (2₂) | = n for all 2₁, 22 € C and some integer n > 0. Show that f(z) is a polynomial in z of degree at most n.

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter3: Functions

Section3.3: Rates Of Change And Behavior Of Graphs

Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...

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Question

Let f(z) be an entire function satisfying
|f (21 + z2)|† < |f (21)|* + \f (22)|*
for all 21, 22 E C and some integer n > 0. Show that f(2) is a polynomial in z
of degree at most n.

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