The Gamma and Zeta Functions

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

Abstract

We now come to a situation where the natural way to define a function is not through a power series but through an integral depending on a parameter. We shall give a natural condition when we can differentiate under the integral sign, and we can then use Goursat’s theorem to conclude that the holomorphic function so defined is analytic.

Keywords

Entire Function Analytic Continuation Meromorphic Function Zeta Function Gamma Function 
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Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

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

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