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Properties of Analytic Functions

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Part of the book series: Undergraduate Texts in Mathematics ((UTM))

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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Correspondence to Joseph Bak .

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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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