Abstract
In the last two chapters, we studied the connection between everywhere convergent power series and entire functions. We now turn our attention to the more general relationship between power series and analytic functions.According to Theorem 2.9 every power series represents an analytic function inside its circle of convergence. Our first goal is the converse of this theorem: we will show that a function analytic in a disc can be represented there by a power series. We then turn to the question of analytic functions in arbitrary open sets and the local behavior of such functions.
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© 2010 Springer Science+Business Media, LLC
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Bak, J., Newman, D.J. (2010). Properties of Analytic Functions. In: Complex Analysis. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-7288-0_6
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DOI: https://doi.org/10.1007/978-1-4419-7288-0_6
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-7287-3
Online ISBN: 978-1-4419-7288-0
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