Abstract
The analytic functions we have encountered so far have generally been defined either by power series or as a combination of the elementary polynomial, trigonometric and exponential functions, alongwith their inverse functions. In this chapter, we consider three different ways of representing analytic functions. We begin with infinite products and then take a closer look at functions defined by definite integrals, a topic touched upon earlier in Chapter 7 and in Chapter 12.2. Finally, we define Dirichlet series, which provide a link between analytic functions and number theory.
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Bak, J., Newman, D.J. (2010). Different Forms of Analytic Functions. In: Complex Analysis. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-7288-0_17
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DOI: https://doi.org/10.1007/978-1-4419-7288-0_17
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-7287-3
Online ISBN: 978-1-4419-7288-0
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