The Concrete Tetrahedron

Symbolic Sums, Recurrence Equations, Generating Functions, Asymptotic Estimates

  • Manuel Kauers
  • Peter Paule

Part of the Texts and Monographs in Symbolic Computation book series (TEXTSMONOGR)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Manuel Kauers, Peter Paule
    Pages 1-16
  3. Manuel Kauers, Peter Paule
    Pages 17-41
  4. Manuel Kauers, Peter Paule
    Pages 43-61
  5. Manuel Kauers, Peter Paule
    Pages 63-86
  6. Manuel Kauers, Peter Paule
    Pages 87-112
  7. Manuel Kauers, Peter Paule
    Pages 113-136
  8. Manuel Kauers, Peter Paule
    Pages 137-164
  9. Back Matter
    Pages 165-203

About this book


The book treats four mathematical concepts which play a fundamental role in many different areas of mathematics: symbolic sums, recurrence (difference) equations, generating functions, and asymptotic estimates.

Their key features, in isolation or in combination, their mastery by paper and pencil or by computer programs, and their applications to problems in pure mathematics or to "real world problems" (e.g. the analysis of algorithms) are studied. The book is intended as an algorithmic supplement to the bestselling "Concrete Mathematics" by Graham, Knuth and Patashnik.


asymptotics formal power series recurrence equations symbolic computation symbolic summation

Authors and affiliations

  • Manuel Kauers
    • 1
  • Peter Paule
    • 1
  1. 1.Research Institute for Symbolic Computation (RISC)Johannes Kepler University LinzLinzAustria

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag/Wien 2011
  • Publisher Name Springer, Vienna
  • eBook Packages Computer Science
  • Print ISBN 978-3-7091-0444-6
  • Online ISBN 978-3-7091-0445-3
  • Series Print ISSN 0943-853X
  • Buy this book on publisher's site