Complex Analysis pp 37-85 | Cite as

# Power Series

Chapter

## Abstract

So far, we have given only rational functions as examples of holomorphic functions. We shall study other ways of defining such functions. One of the principal ways will be by means of power series. Thus we shall see that the series converges for all

$$1 + z + \frac{{{{z}^{2}}}}{{2!}} + \frac{{{{z}^{3}}}}{{3!}} + \cdots$$

*z*to define a function which is equal to*e*^{ z }. Similarly, we shall extend the values of sin*z*and cos*z*by their usual series to complex valued functions of a complex variable, and we shall see that they have similar properties to the functions of a real variable which you already know.## Keywords

Power Series Constant Term Formal Power Series Power Series Expansion Convergent Series
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Copyright information

© Springer Science+Business Media New York 1999