Let f be an entire function, and suppose there exists M > 0 andm e N such that |f(z)| < M|z|m for all z E C. Prove that:(a) f(n) (0) = 0 for all n > m+ 1.0, conclude that f(z) is equal to a(b) By writing f as a power series at zpolynomial of degree m.

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Answered: Let f be an entire function, and…

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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Let f be an entire function, and suppose there exists M > 0 and m eN such that |f(z)| < M|z|m for all z E C. Prove that: (a) f(n) (0) = 0 for all n > m+1. 0, conclude that f(z) is equal to a (b) By writing f as a power series at z = polynomial of degree m.