This is a complex analysis question. Let {fn} be a sequence of analytic functions on Ω such that fn →f normally on Ω. If fn(z) does not equal 0 for allz ∈ Ω and all n ∈ N,show that either a) f is identically zero, or b) f(z) does not equal 0 for all z ∈ Ω

This is a complex analysis question. Let {fn} be a sequence of analytic functions on Ω such that fn →f normally on Ω. If fn(z) does not equal 0 for allz ∈ Ω and all n ∈ N,show that either a) f is identically zero, or b) f(z) does not equal 0 for all z ∈ Ω

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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This is a complex analysis question.

Let {fn} be a sequence of analytic functions on Ω such that fn →f normally on Ω. If fn(z) does not equal 0 for allz ∈ Ω and all n ∈ N,show that either

a) f is identically zero, or

b) f(z) does not equal 0 for all z ∈ Ω.

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