Power Series

  • Serge Lang
Part of the Graduate Texts in Mathematics book series (GTM, volume 103)


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
$$1 + z + \frac{{{z^2}}}{{2!}} + \frac{{{z^3}}}{{3!}} + ...$$
converges for all 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.


Power Series Formal Power Series Power Series Expansion Convergent Series Convergent Power Series 
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Copyright information

© Springer Science+Business Media New York 1985

Authors and Affiliations

  • Serge Lang
    • 1
  1. 1.Department of MathematicsYale UniversityNew HavenUSA

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