Abstract
In this lecture, we shall show that, for an analytic function in a given domain, all the derivatives exist and are analytic. This result leads to Cauchy’s integral formula for derivatives. Next, we shall prove Morera’s Theorem, which is a converse of the Cauchy–Goursat Theorem. We shall also establish Cauchy’s inequality for the derivatives, which plays an important role in proving Liouville’s Theorem.
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© 2011 Springer Science+Business Media, LLC
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Agarwal, R.P., Perera, K., Pinelas, S. (2011). Cauchy’s Integral Formula for Derivatives. In: An Introduction to Complex Analysis. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-0195-7_18
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DOI: https://doi.org/10.1007/978-1-4614-0195-7_18
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Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4614-0194-0
Online ISBN: 978-1-4614-0195-7
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