Abstract
This chapter is devoted to an important method for constructing holomorphic functions. The tool is convergent power series. It is the basis for the introduction of new non-algebraic holomorphic functions, called elementary transcendental functions. It will turn out that all holomorphic functions are described (at least locally) by this tool. This will be proven in the next chapter.
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© 2007 Springer Science+Business Media, LLC
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Gilman, J.P., Kra, I., Rodríguez, R.E. (2007). Power Series. In: Complex Analysis. Graduate Texts in Mathematics, vol 245. Springer, New York, NY. https://doi.org/10.1007/978-0-387-74715-6_3
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DOI: https://doi.org/10.1007/978-0-387-74715-6_3
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-74714-9
Online ISBN: 978-0-387-74715-6
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