Geodesic
Integral transformation of solutions for a~Fuchsian-class equation corresponding to the Okamoto transformation of the Painlev\'e~VI equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 146 (2006) no. 3, pp. 355-364

Voir la notice de l'article provenant de la source Math-Net.Ru

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.
Keywords: Painlevé VI equation, Euler integral transformation, Schlesinger transformation
Mots-clés : Heun equation, Okamoto transformation. 
@article{TMF_2006_146_3_a0,
     author = {D. P. Novikov},
     title = {Integral transformation of solutions for {a~Fuchsian-class} equation corresponding to the {Okamoto} transformation of the {Painlev\'e~VI} equation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {355--364},
     publisher = {mathdoc},
     volume = {146},
     number = {3},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2006_146_3_a0/}
}
TY  - JOUR
AU  - D. P. Novikov
TI  - Integral transformation of solutions for a~Fuchsian-class equation corresponding to the Okamoto transformation of the Painlev\'e~VI equation
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2006
SP  - 355
EP  - 364
VL  - 146
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_2006_146_3_a0/
LA  - ru
ID  - TMF_2006_146_3_a0
ER  - 
%0 Journal Article
%A D. P. Novikov
%T Integral transformation of solutions for a~Fuchsian-class equation corresponding to the Okamoto transformation of the Painlev\'e~VI equation
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2006
%P 355-364
%V 146
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_2006_146_3_a0/
%G ru
%F TMF_2006_146_3_a0
D. P. Novikov. Integral transformation of solutions for a~Fuchsian-class equation corresponding to the Okamoto transformation of the Painlev\'e~VI equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 146 (2006) no. 3, pp. 355-364. http://geodesic.mathdoc.fr/item/TMF_2006_146_3_a0/