University of Vlora - Conference Center, ACA'10, Applications of Computer Algebra

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ANTIQUANTIZATION AND INTEGRAL RELATIONS FOR HEUN EQUATIONS AND SYMMETRIES FOR THE CORRESPONDING PAINLEVE EQUATIONS

Sergey Yuryevich Slavyanov, Alexandr Ya. Kazakov, Filip R. Vukajlovic

Last modified: 2010-03-30

Abstract


Special functions play significant role in Computer
    Algebra packages. Here we can mention all-purpose
    packages like Mathematika or Maple as well as
    specialized packages as SFTools.
    Further development would without doubt be focused
    on more sophisticated Heun functions and closely
    related Painleve transcendents. Partly the
    relationship between Heun equations and Painleve
    equations is presented in the
    package SFTools. However new studies induce revision
    of presentation of these relations. The
    items of these revisions are the following.
    1. Relations between equations belonging to Heun class,
    the corresponding deformed equations with added
    apparent singularity and the corresponding 2x2 systems
    and 3x3 systems of first order equations.
    2. Integral  transforms linking
    different equations belonging to Heun class.
    3. Antiquantization as a tool of derivation
    Painleve-type equations from linear equations.
    4. Derivation  of Okamoto-type symmetries
    for Painleve equations.