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SIGMA, 2009, Volume 5, 040, 22 pages (Mi sigma386)  

This article is cited in 10 scientific papers (total in 10 papers)

Middle Convolution and Heun's Equation

Kouichi Takemura

Department of Mathematical Sciences, Yokohama City University, 22-2 Seto, Kanazawa-ku, Yokohama 236-0027, Japan

Abstract: Heun's equation naturally appears as special cases of Fuchsian system of differential equations of rank two with four singularities by introducing the space of initial conditions of the sixth Painlevé equation. Middle convolutions of the Fuchsian system are related with an integral transformation of Heun's equation.

Keywords: Heun's equation; the space of initial conditions; the sixth Painlevé equation; middle convolution

DOI: https://doi.org/10.3842/SIGMA.2009.040

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ArXiv: 0810.3112
MSC: 34M35; 33E10; 34M55
Received: November 26, 2008; in final form March 25, 2009; Published online April 3, 2009
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Citation: Kouichi Takemura, “Middle Convolution and Heun's Equation”, SIGMA, 5 (2009), 040, 22 pp.

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Simon N. M. Ruijsenaars, “Hilbert–Schmidt Operators vs. Integrable Systems of Elliptic Calogero–Moser Type. III. The Heun Case”, SIGMA, 5 (2009), 049, 21 pp.  mathnet  crossref  mathscinet  zmath
    2. Filipuk G.V., “Middle convolution and the hypergeometric equation”, J. Phys. A, 43:17 (2010), 175204, 10 pp.  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    3. Takemura K., “Integral transformation and Darboux transformation of Heun's differential equation”, Nonlinear and Modern Mathematical Physics, Proceedings of the First International Workshop, AIP Conference Proceedings, 1212, 2010, 58–65  crossref  mathscinet  zmath  adsnasa  isi  scopus
    4. Takemura K., “Heun's equation, generalized hypergeometric function and exceptional Jacobi polynomial”, Journal of Physics A-Mathematical and Theoretical, 45:8 (2012), 085211  crossref  mathscinet  zmath  adsnasa  isi  scopus
    5. Takemura K., “Integral Transformation of Heun's Equation and Apparent Singularity”, Painleve Equations and Related Topics (2012), Degruyter Proceedings in Mathematics, eds. Bruno A., Batkhin A., Walter de Gruyter & Co, 2012, 257–261  mathscinet  isi
    6. A. Ya. Kazakov, S. Yu. Slavyanov, “Euler integral symmetries for the confluent Heun equation and symmetries of the Painlevé equation PV”, Theoret. and Math. Phys., 179:2 (2014), 543–549  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    7. A. Ya. Kazakov, “Integral symmetry for the confluent Heun equation with added apparent singularity”, J. Math. Sci. (N. Y.), 214:3 (2016), 268–276  mathnet  crossref  mathscinet
    8. Yulia Bibilo, Galina Filipuk, “Non-Schlesinger Isomonodromic Deformations of Fuchsian Systems and Middle Convolution”, SIGMA, 11 (2015), 023, 14 pp.  mathnet  crossref  mathscinet
    9. Bibilo Yu. Filipuk G., “Middle Convolution and Non-Schlesinger Deformations”, Proc. Jpn. Acad. Ser. A-Math. Sci., 91:5 (2015), 66–69  crossref  mathscinet  zmath  isi  scopus
    10. Chen Zh., Kuo T.-J., Lin Ch.-Sh., “Hamiltonian system for the elliptic form of Painlevé VI equation”, J. Math. Pures Appl., 106:3 (2016), 546–581  crossref  mathscinet  zmath  isi  elib  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
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