Let {a n , n≧0} be a sequence of real numbers. Its generating function is the power series
$$A\left( u \right)=\sum\limits_{n=0}^{\infty }{{{a}_{n}}}{{u}^{n}}$$
provided that it has a nonvanishing radius of convergence. In particular if the a n are probabilities then the radius of convergence is at least equal to one. We shall consider u as a real variable.


Generate Function Limit Theorem Discrete Parameter Independent Increment Tauberian Theorem 
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Copyright information

© Springer-Verlag OHG. Berlin · Göttingen · Heidelberg 1960

Authors and Affiliations

  • Kai Lai Chung
    • 1
  1. 1.Syracuse UniversityUSA

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