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TMF, 1996, Volume 107, Number 3, Pages 388–396 (Mi tmf1164)  

This article is cited in 15 scientific papers (total in 15 papers)

Integral relations for special functions of hypergeometric and Heun class

A. Ya. Kazakov, S. Yu. Slavyanov

Saint-Petersburg State University

Abstract: Ordinary differential equations with polynomial coefficients originate different kinds of integral relations for its solutions: integral representations in terms of simpler functions, integral equations etc. In this paper, a new kind of integral relations for functions of the Heun class are presented. These relations are coupling in ivolution eigensolutions, which are characterized by different behaviour at singularities and often also by different intervals of consideration and equations themselves. The studied relations are arranged in two staircases where each succeeding equation may be obtained with the help of the confluence process.

DOI: https://doi.org/10.4213/tmf1164

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English version:
Theoretical and Mathematical Physics, 1996, 107:3, 733–739

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Received: 19.06.1995

Citation: A. Ya. Kazakov, S. Yu. Slavyanov, “Integral relations for special functions of hypergeometric and Heun class”, TMF, 107:3 (1996), 388–396; Theoret. and Math. Phys., 107:3 (1996), 733–739

Citation in format AMSBIB
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\jour Theoret. and Math. Phys.
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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. N. A. Veshev, “Degeneration of solutions of Heun's equation under fusion of singularities”, Theoret. and Math. Phys., 110:2 (1997), 179–182  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. Ochiai, H, “Non-commutative harmonic oscillators and Fuchsian ordinary differential operators”, Communications in Mathematical Physics, 217:2 (2001), 357  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    3. Tarasov, VF, “The Heun-Schrodinger radial equation with two auxiliary parameters for H-like atoms”, Modern Physics Letters B, 16:25 (2002), 937  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    4. D. P. Novikov, “Integral transformation of solutions for a Fuchsian-class equation corresponding to the Okamoto transformation of the Painlevé VI equation”, Theoret. and Math. Phys., 146:3 (2006), 295–303  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    5. Kouichi Takemura, “Middle Convolution and Heun's Equation”, SIGMA, 5 (2009), 040, 22 pp.  mathnet  crossref  mathscinet  zmath
    6. 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
    7. Takemura K., “Integral transformation and Darboux transformation of Heun's differential equation”, Nonlinear and Modern Mathematical Physics, AIP Conference Proceedings, 1212, 2010, 58–65  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    8. El-Jaick L.J., Figueiredo B.D.B., “Transformations of Heun's equation and its integral relations”, J. Phys. A: Math. Theor., 44:7 (2011), 075204  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    9. Takemura K., “Heun's equation, generalized hypergeometric function and exceptional Jacobi polynomial”, J. Phys. A: Math. Theor., 45:8 (2012), 085211  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    10. 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
    11. 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
    12. Cordero R., Turrubiates F.J., Vera J.C., “On a Phase Space Quantum Description of the Spherical 2-Brane”, Phys. Scr., 89:7 (2014), 075001  crossref  adsnasa  isi  scopus  scopus  scopus
    13. El-Jaick L.J., Figueiredo B.D.B., “Integral Relations For Solutions of the Confluent Heun Equation”, Appl. Math. Comput., 256 (2015), 885–904  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    14. 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  scopus
    15. 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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