Albanian Journal of Mathematics (ISNN: 1930-1235), Vol 4, No 4 (2010)

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Relations between Heun equations and Painleve equations

Alexander Yakov Kazakov, Sergey Yu. Slavyanov, Filip R. Vukalovic


The article is focused on the following items:
1. Relations between Heun equation,
the corresponding deformed equation with added
apparent singularity and the corresponding 2x2 systems
and 3x3 systems of first order equations.
2. Integral transforms linking
deformed Heun equations.
3. Antiquantization as a tool of derivation
Painleve equation from linear 2x2 system of equations.
4. Derivation of Okamoto-type symmetries
for Painleve equation.

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