Annals of Combinatorics

, Volume 12, Issue 1, pp 1–16 | Cite as

Non-Holonomicity of Sequences Defined via Elementary Functions

  • Jason P. Bell
  • Stefan Gerhold
  • Martin Klazar
  • Florian Luca


We present a new method for proving non-holonomicity of sequences, which is based on results about the number of zeros of elementary and of analytic functions. Our approach is applicable to sequences that are defined as the values of an elementary function at positive integral arguments. We generalize several recent results, e.g., non-holonomicity of the logarithmic sequence is extended to rational functions involving log n. Moreover, we show that the sequence that arises from evaluating the Riemann zeta function at an increasing integer sequence with bounded gap lengths is not holonomic.


holonomic sequences fewnomials meromorphic functions 

AMS Subject Classification:

11B37 11B83 


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Copyright information

© Birkhaueser 2008

Authors and Affiliations

  • Jason P. Bell
    • 1
  • Stefan Gerhold
    • 2
  • Martin Klazar
    • 3
  • Florian Luca
    • 4
  1. 1.Department of MathematicsSimon Fraser UniversityBurnabyCanada
  2. 2.Christian Doppler Laboratory for Portfolio Risk ManagementVienna University of TechnologyViennaAustria
  3. 3.Department of Applied Mathematics (KAM) and Institute for Theoretic Computer Science (ITI), Faculty of Mathematics and PhysicsCharles UniversityPrahaCzech Republic
  4. 4.Instituto de Matemáticas UNAMMichoaćanMexico

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