Computer-Assisted Proofs of Some Identities for Bessel Functions of Fractional Order

  • Stefan Gerhold
  • Manuel Kauers
  • Christoph Koutschan
  • Peter Paule
  • Carsten Schneider
  • Burkhard Zimmermann
Part of the Texts & Monographs in Symbolic Computation book series (TEXTSMONOGR)


We employ computer algebra algorithms to prove a collection of identities involving Bessel functions with half-integer orders and other special functions. These identities appear in the famous Handbook of Mathematical Functions, as well as in its successor, the DLMF, but their proofs were lost. We use generating functions and symbolic summation techniques to produce new proofs for them.


Recurrence Equation Computer Algebra Spherical Bessel Function Regular Singular Point Holonomic Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This work has been supported by the Austrian Science Fund (FWF) grants P20347-N18, P24880-N25, Y464-N18, DK W1214 (DK6, DK13) and SFB F50 (F5004-N15, F5006-N15, F5009-N15), and by the EU Network LHCPhenoNet PITN-GA-2010-264564.


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Copyright information

© Springer-Verlag Wien 2013

Authors and Affiliations

  • Stefan Gerhold
    • 2
  • Manuel Kauers
    • 1
  • Christoph Koutschan
    • 3
  • Peter Paule
    • 1
  • Carsten Schneider
    • 1
  • Burkhard Zimmermann
    • 1
  1. 1.Research Institute for Symbolic Computation (RISC)Johannes Kepler University LinzLinzAustria
  2. 2.Financial and Actuarial MathematicsVienna University of TechnologyViennaAustria
  3. 3.Johann Radon Institute for Computational and Applied Mathematics (RICAM)Austrian Academy of Sciences (ÖAW)LinzAustria

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