Complex Numbers and Analysis

  • Daniel Alpay


We begin by discussing complex-valued functions of a real variable. This gives us more freedom for exercises in the sequel of the chapter. We discuss series and power series, and introduce the exponential function and the various trigonometric functions. Infinite products are also discussed. At the end of this chapter, we therefore will have a number of examples of functions, some highly non-trivial, which will be shown in subsequent chapters to be instances of analytic functions.


Power Series Complex Number Unit Disk Blaschke Product Power Series Expansion 
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Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Daniel Alpay
    • 1
    • 2
  1. 1.Department of MathematicsBen-Gurion University of the NegevBeer ShevaIsrael
  2. 2.Department of MathematicsChapman UniversityOrangeUSA

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