Generating Functions

  • Matthias Beck
  • Ross Geoghegan
Part of the Undergraduate Texts in Mathematics book series (UTM, volume 0)


Assume \((a_n )_{n = 0}^\infty\) is a sequence of real numbers that is not explicitly defined by a formula, for example, a recursive sequence. One can sometimes get useful information about this sequence—identities, formulas, etc.— by embedding it in a generating function: \(A(x): = \sum\limits_{n - 0}^\infty {a_n x^n}.\) We use the convention that the members of the sequence are named by a lowercase letter and the corresponding generating function is named by its uppercase equivalent. We think of this series A(x) as a formal power series, in the sense that questions of convergence are ignored. So operations on formal power series have to be defined from scratch.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Matthias Beck and Ross Geoghegan 2010

Authors and Affiliations

  1. 1.Department of MathematicsSan Francisco State UniversitySan FranciscoUSA
  2. 2.Department of Mathematical SciencesBinghamton University State University of New YorkBinghamtonUSA

Personalised recommendations