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TMF, 2006, Volume 146, Number 3, Pages 355–364 (Mi tmf2040)  

This article is cited in 11 scientific papers (total in 11 papers)

Integral transformation of solutions for a Fuchsian-class equation corresponding to the Okamoto transformation of the Painlevé VI equation

D. P. Novikov

Omsk State Technical University

Abstract: 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, Heun equation, Euler integral transformation, Schlesinger transformation, Okamoto transformation

DOI: https://doi.org/10.4213/tmf2040

Full text: PDF file (176 kB)
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English version:
Theoretical and Mathematical Physics, 2006, 146:3, 295–303

Bibliographic databases:

Received: 03.03.2005
Revised: 18.08.2005

Citation: D. P. Novikov, “Integral transformation of solutions for a Fuchsian-class equation corresponding to the Okamoto transformation of the Painlevé VI equation”, TMF, 146:3 (2006), 355–364; Theoret. and Math. Phys., 146:3 (2006), 295–303

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. S. Yu. Slavyanov, F. R. Vukailovich, “Isomonodromic deformations and “antiquantization” for the simplest ordinary differential equations”, Theoret. and Math. Phys., 150:1 (2007), 123–131  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. Joshi N, Kitaev AV, Treharne PA, “On the linearization of the Painlevé III-VI equations and reductions of the three-wave resonant system”, Journal of Mathematical Physics, 48:10 (2007), 103512  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    3. Haraoka Y, Filipuk G, “Middle convolution and deformation for Fuchsian systems”, Journal of the London Mathematical Society-Second Series, 76:Part 2 (2007), 438–450  crossref  mathscinet  zmath  isi  scopus  scopus
    4. A. Ya. Kazakov, S. Yu. Slavyanov, “Euler integral symmetries for a deformed Heun equation and symmetries of the Painlevé PVI equation”, Theoret. and Math. Phys., 155:2 (2008), 722–733  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    5. Kouichi Takemura, “Middle Convolution and Heun's Equation”, SIGMA, 5 (2009), 040, 22 pp.  mathnet  crossref  mathscinet  zmath
    6. Filipuk, GV, “A hypergeometric system of the Heun equation and middle convolution”, Journal of Physics A-Mathematical and Theoretical, 42:17 (2009), 175208  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    7. D. P. Novikov, “The $2{\times}2$ matrix Schlesinger system and the Belavin–Polyakov–Zamolodchikov system”, Theoret. and Math. Phys., 161:2 (2009), 1485–1496  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    8. Leroy C. Ishkhanyan A.M., “Expansions of the Solutions of the Confluent Heun Equation in Terms of the Incomplete Beta and the Appell Generalized Hypergeometric Functions”, Integral Transform. Spec. Funct., 26:6 (2015), 451–459  crossref  mathscinet  zmath  isi  scopus  scopus
    9. Nagoya H., “Fractional Calculus of Quantum Painlevé Systems of Type _ ???”, Algebraic and Analytic Aspects of Integrable Systems and Painlev? Equations, Contemporary Mathematics, 651, ed. Dzhamay A. Maruno K. Ormerod C., Amer Mathematical Soc, 2015, 39–64  crossref  mathscinet  zmath  isi
    10. Takemura K., “Integral Transformation of Heun'S Equation and Some Applications”, J. Math. Soc. Jpn., 69:2 (2017), 849–891  crossref  mathscinet  zmath  isi  scopus  scopus
    11. Farrokh Atai, Edwin Langmann, “Series Solutions of the Non-Stationary Heun Equation”, SIGMA, 14 (2018), 011, 32 pp.  mathnet  crossref
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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