Extensions, Contours, Elementary Functions

John Mac Sheridan Nerney
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John Mac Sheridan Nerney: Mathematics

Chapter Chapter 6 in An Introduction to Analytic Functions, 2020, pp 35-40 from Springer

Abstract: Abstract If f is an analytic function with domain R, the following are equivalent: 1. There is a set S ⊆ ℂ $$S\subseteq \mathbb C$$ such that R contains a limit-point of S, and for all z ∈ S, f(z) = 0. 2. There is w ∈ ℂ $$w\in \mathbb C$$ such that for all k ∈ ℕ $$k\in \mathbb N$$ , f (k)(w) = 0. 3. There is w ∈ R and a positive number r such that for all z ∈ D r(w), f(z) = 0. 4. For all z ∈ R, f(z) = 0.

Date: 2020
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DOI: 10.1007/978-3-030-42085-7_7

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