Abstract
Runge’s Theorem can be used to prove Cauchy’s Theorem. This will require the elements of integration theory described in Chapter 2. Recall that for a rectifiable curve γ: [0,1] → ℂ, we let ‖γ‖ denote its length, i.e. ‖γ‖ = <Inline>1</Inline> |γ′(t)|dt, so that
where ‖f‖ = sup{| f(z) |: z ∈ γ}. The reader is reminded that γ^ denotes the “physical curve”, that is the image of γ.
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© 1984 Springer-Verlag New York Inc.
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Luecking, D.H., Rubel, L.A. (1984). The Cauchy Theorem. In: Complex Analysis. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8295-9_11
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DOI: https://doi.org/10.1007/978-1-4613-8295-9_11
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-90993-6
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