Geodesic
Euler integral symmetries for a~deformed Heun equation and symmetries
Teoretičeskaâ i matematičeskaâ fizika, Tome 155 (2008) no. 2, pp. 252-264

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Euler integral transformations relate solutions of ordinary linear differential equations and generate integral representations of the solutions in a number of cases or relations between solutions of constrained equations (Euler symmetries) in some other cases. These relations lead to the corresponding symmetries of the monodromy matrices. We discuss Euler symmetries in the case of the simplest Fuchsian system that is equivalent to a deformed Heun equation, which is in turn related to the Painlevé PVI equation. The existence of integral symmetries of the deformed Heun equation leads to the corresponding symmetries of the PVI equation.
Mots-clés : Euler transformation, Heun equation
Keywords: Painlevé equation. 
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     author = {A. Ya. Kazakov and S. Yu. Slavyanov},
     title = {Euler integral symmetries for a~deformed {Heun} equation and symmetries},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {252--264},
     publisher = {mathdoc},
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     number = {2},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2008_155_2_a5/}
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A. Ya. Kazakov; S. Yu. Slavyanov. Euler integral symmetries for a~deformed Heun equation and symmetries. Teoretičeskaâ i matematičeskaâ fizika, Tome 155 (2008) no. 2, pp. 252-264. http://geodesic.mathdoc.fr/item/TMF_2008_155_2_a5/