Power Series

Part of the Graduate Texts in Mathematics book series (GTM, volume 245)


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.


Power Series Holomorphic Function Meromorphic Function Stereographic Projection Power Series Expansion 
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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Jane P. Gilman
    • 1
  • Irwin Kra
    • 2
    • 3
  • Rubí E. Rodríguez
    • 4
  1. 1.Department of Mathematics and Computer ScienceRutgers UniversityNewarkUSA
  2. 2.Math for AmericaNew YorkUSA
  3. 3.Department of MathematicsState University of New York at Stony BrookStony BrookUSA
  4. 4.Pontificia Universidad Católica de ChileSantiagoChile

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