Geodesic
Integral transformation of solutions for a Fuchsian-class equation corresponding to the Okamoto transformation of the Painlevé VI equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 146 (2006) no. 3, pp. 355-364 Cet article a éte moissonné depuis la source Math-Net.Ru

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We show that under the Euler integral transformation with the kernel $(x-z)^{-\alpha}$, some solutions of the Fuchs equations (the original pair for the Painlevé VI equation) pass into solutions of a system of the same form with the parameters changed according to the Okamoto transformation.
Mots-clés : Painlevé VI equation, Heun equation, Okamoto transformation.
Keywords: Euler integral transformation, Schlesinger transformation 
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D. P. Novikov. Integral transformation of solutions for a Fuchsian-class equation corresponding to the Okamoto transformation of the Painlevé VI equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 146 (2006) no. 3, pp. 355-364. http://geodesic.mathdoc.fr/item/TMF_2006_146_3_a0/

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