8. Let f be an entire function such that |f(z)| < A + B\z|" for all z € C, where A and B arepositive real constants and n is a fixed non-negative integer. Show that f is a polynomial ofdegree at most n.9. Let P(z)= z" + an-12n-1 + ..+ a1z + ao be a polynomial of degree n > 1 with a; # 0 for atleast one i. Prove that there exists a point z* such that 2*| = 1 and |P(z*)| > 1.

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Answered: 8. Let f be an entire function such…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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8. Let f be an entire function such that f(z)| < A + B|z|" for all z E C, where A and B are positive real constants and n is a fixed non-negative integer. Show that f is a polynomial of degree at most n.