Geodesic
Antiquantization of deformed Heun-class equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 186 (2016) no. 1, pp. 142-151 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We consider deformed Heun-class equations, i.e., equations of the Heun class with an added apparent singularity. We prove that each deformed Heun-class equation under antiquantization realizes a transfer from the Heun-class equation to the corresponding Painlevé equation, and we completely list such transfers.
Mots-clés : antiquantization, Heun-class equation, Painlevé equation.
Keywords: deformed Heun-class equation 
@article{TMF_2016_186_1_a8,
     author = {S. Yu. Slavyanov and O. L. Stesik},
     title = {Antiquantization of deformed {Heun-class} equations},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {142--151},
     year = {2016},
     volume = {186},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2016_186_1_a8/}
}
TY  - JOUR
AU  - S. Yu. Slavyanov
AU  - O. L. Stesik
TI  - Antiquantization of deformed Heun-class equations
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2016
SP  - 142
EP  - 151
VL  - 186
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_2016_186_1_a8/
LA  - ru
ID  - TMF_2016_186_1_a8
ER  - 
%0 Journal Article
%A S. Yu. Slavyanov
%A O. L. Stesik
%T Antiquantization of deformed Heun-class equations
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2016
%P 142-151
%V 186
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_2016_186_1_a8/
%G ru
%F TMF_2016_186_1_a8
S. Yu. Slavyanov; O. L. Stesik. Antiquantization of deformed Heun-class equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 186 (2016) no. 1, pp. 142-151. http://geodesic.mathdoc.fr/item/TMF_2016_186_1_a8/

[1] S. Yu. Slavyanov, V. Lai, Spetsialnye funktsii. Edinaya teoriya, osnovannaya na analize osobennostei, Nevskii Dialekt, SPb., 2002 | MR | Zbl

[2] S. Yu. Slavyanov, J. Phys. A: Math. Gen., 29:22 (1996), 7329–7335 | DOI | MR | Zbl

[3] S. Yu. Slavyanov, “Kovalevskaya's dynamics and Schrödinger equations of Heun class”, Operator Methods in Ordinary and Partial Differential Equations (Stockholm, Sweden, June 2000), Operator Theory: Advances and Applications, 132, eds. S. Albeverio, N. Elander, W. N. Everitt, P. Kurasov, Birkhäuser, Basel, 2002, 395–402 | MR | Zbl

[4] S. Yu. Slavyanov, TMF, 123:3 (2000), 395–406 | DOI | DOI | MR | Zbl

[5] A. R. Its, V. Y. Novokshenov, The Isomodromic Deformation Method in the Theory of the Penlevé Equations, Lecture Notes in Mathematics, 1191, Berlin, 1986 | DOI | MR | Zbl