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

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

Abstract

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.

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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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