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

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Teoreticheskaya i Matematicheskaya Fizika, 1996, Volume 107, Number 3, Pages 388–396
DOI: https://doi.org/10.4213/tmf1164 (Mi tmf1164)

This article is cited in 21 scientific papers (total in 21 papers)

Integral relations for special functions of hypergeometric and Heun class

A. Ya. Kazakov, S. Yu. Slavyanov

Saint-Petersburg State University

Full-text PDF (211 kB) Citations (21)

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

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.

Received: 19.06.1995

English version:
Theoretical and Mathematical Physics, 1996, Volume 107, Issue 3, Pages 733–739
DOI: https://doi.org/10.1007/BF02070381

Bibliographic databases:

Language: Russian

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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Linking options:

https://www.mathnet.ru/eng/tmf1164

https://doi.org/10.4213/tmf1164

https://www.mathnet.ru/eng/tmf/v107/i3/p388

This publication is cited in the following 21 articles:

Kouichi Takemura, “Kernel Function, $q$-Integral Transformation and $q$-Heun Equations”, SIGMA, 20 (2024), 083, 22 pp.
A. Ya. Kazakov, “Euler Integral Symmetries and the Asymptotics of the Monodromy for the Heun Equation”, J Math Sci, 277:4 (2023), 598
Kouichi Takemura, 2021 Days on Diffraction (DD), 2021, 152
A. Ya. Kazakov, “Integralnaya simmetriya Eilera i asimptotika monodromii dlya uravnenii Goina”, Matematicheskie voprosy teorii rasprostraneniya voln. 50, Posvyaschaetsya devyanostoletiyu Vasiliya Mikhailovicha BABIChA, Zap. nauchn. sem. POMI, 493, POMI, SPb., 2020, 186–199
da Costa R.T., “Mode Stability For the Teukolsky Equation on Extremal and Subextremal Kerr Spacetimes”, Commun. Math. Phys., 378:1 (2020), 705–781
Farrokh Atai, Edwin Langmann, “Series Solutions of the Non-Stationary Heun Equation”, SIGMA, 14 (2018), 011, 32 pp.
Takemura K., “Integral Transformation of Heun'S Equation and Some Applications”, J. Math. Soc. Jpn., 69:2 (2017), 849–891
El-Jaick L.J., Figueiredo B.D.B., “Integral Relations For Solutions of the Confluent Heun Equation”, Appl. Math. Comput., 256 (2015), 885–904
A. Ya. Kazakov, “Integral symmetry for the confluent Heun equation with added apparent singularity”, J. Math. Sci. (N. Y.), 214:3 (2016), 268–276
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
Takemura K., “Heun's equation, generalized hypergeometric function and exceptional Jacobi polynomial”, J. Phys. A: Math. Theor., 45:8 (2012), 085211
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
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
Takemura K., “Integral transformation and Darboux transformation of Heun's differential equation”, Nonlinear and Modern Mathematical Physics, AIP Conference Proceedings, 1212, 2010, 58–65
Kouichi Takemura, “Middle Convolution and Heun's Equation”, SIGMA, 5 (2009), 040, 22 pp.
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.
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
Tarasov, VF, “The Heun-Schrodinger radial equation with two auxiliary parameters for H-like atoms”, Modern Physics Letters B, 16:25 (2002), 937
Ochiai, H, “Non-commutative harmonic oscillators and Fuchsian ordinary differential operators”, Communications in Mathematical Physics, 217:2 (2001), 357
A. Ya. Kazakov, “Integral symmetries, integral invariants, and monodromy matrices for ordinary differential equations”, Theoret. and Math. Phys., 116:3 (1998), 991–1000

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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