Antiquantization and the corresponding symmetries
Teoretičeskaâ i matematičeskaâ fizika, Tome 185 (2015) no. 1, pp. 186-191

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We review results on relations between the Heun and Painlevé equations and also their symmetries. Basically, these results are scattered throughout our previous papers and those of collaborators.
Mots-clés : antiquantization, Heun equation, Painlevé equation
Keywords: symmetry, deformed Heun equation, Fuchsian system, integral transform.
S. Yu. Slavyanov. Antiquantization and the corresponding symmetries. Teoretičeskaâ i matematičeskaâ fizika, Tome 185 (2015) no. 1, pp. 186-191. http://geodesic.mathdoc.fr/item/TMF_2015_185_1_a16/
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[1] E. Schrödinger, Ann. der Phys., 384:4 (1926), 361–376 ; 384:4 (1926), 489–527 ; 385:13 (1926), 437–490 ; 386:18, 109–139 | DOI | DOI | Zbl | DOI | Zbl | DOI

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

[3] R. Fuchs, Math. Ann., 63:3 (1907), 301–321 | DOI | MR | Zbl

[4] A. A. Bolibrukh, Obratnye zadachi monodromii v analiticheskoi teorii differentsialnykh uravnenii, MTsNMO, M., 2009

[5] V. A. Fock, Z. Phys., 98:3–4 (1935), 145–154 | DOI | Zbl

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

[7] A. Ya. Kazakov, S. Yu. Slavyanov, TMF, 155:2 (2008), 252–264 | DOI | DOI | MR | Zbl

[8] S. Yu. Slavyanov, TMF, 182:2 (2015), 223–230 | DOI | DOI | MR | Zbl

[9] S. Yu. Slavyanov, F. R. Vukailovich, TMF, 150:1 (2007), 143–151 | DOI | DOI | MR | Zbl

[10] A. Ya. Kazakov, S. Yu. Slavyanov, Zap. nauchn. sem. POMI, 432 (2015), 162–176 | Zbl

[11] 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

[12] K. Iwasaki, H. Kimura, S. Shimomura, M. Yosida, From Gauss to Painlevé. A Modern Theory of Special Functions, Aspects of Mathematics, 16, Vieweg Sohn, Braunschweig, 1991 | DOI | MR

[13] A. Myullyari, S. Yu. Slavyanov, TMF, 166:2 (2011), 261–265 | DOI | DOI