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SIGMA, 2012, Volume 8, 085, 18 pages
(Mi sigma762)
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This article is cited in 9 scientific papers (total in 9 papers)
Global Solutions of Certain Second-Order Differential Equations with a High Degree of Apparent Singularity
Ryu Sasakia, Kouchi Takemurab
a Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan
b Department of Mathematics, Faculty of Science and Technology, Chuo University,
1-13-27 Kasuga, Bunkyo-ku Tokyo 112-8551, Japan
Abstract:
Infinitely many explicit solutions of certain second-order differential equations with an apparent singularity of characteristic exponent $-2$ are constructed by adjusting the parameter of the multi-indexed Laguerre polynomials.
Keywords:
multi-indexed orthogonal polynomials; solvable systems; Fuchsian differential equations; Heun's equation; apparent singularities; high characteristic exponents.
DOI:
https://doi.org/10.3842/SIGMA.2012.085
 Full text:
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http://emis.mi.ras.ru/.../085
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ArXiv:
1207.5302
MSC: 33C45; 33C47
Received: July 24, 2012; in final form November 7, 2012; Published online November 15, 2012
Language:
Citation:
Ryu Sasaki, Kouchi Takemura, “Global Solutions of Certain Second-Order Differential Equations with a High Degree of Apparent Singularity”, SIGMA, 8 (2012), 085, 18 pp.
Citation in format AMSBIB
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\paper Global Solutions of Certain Second-Order Differential Equations with a High Degree of Apparent Singularity
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\yr 2012
\vol 8
\papernumber 085
\totalpages 18
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http://mi.mathnet.ru/eng/sigma762 http://mi.mathnet.ru/eng/sigma/v8/p85
Citing articles on Google Scholar:
Russian citations,
English citations
Related articles on Google Scholar:
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This publication is cited in the following articles:
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Marquette I. Quesne C., “Two-Step Rational Extensions of the Harmonic Oscillator: Exceptional Orthogonal Polynomials and Ladder Operators”, J. Phys. A-Math. Theor., 46:15 (2013), 155201
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Ho C.-L. Sasaki R. Takemura K., “Confluence of Apparent Singularities in Multi-Indexed Orthogonal Polynomials: the Jacobi Case”, J. Phys. A-Math. Theor., 46:11 (2013), 115205
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Odake S., “Recurrence Relations of the Multi-Indexed Orthogonal Polynomials”, J. Math. Phys., 54:8 (2013), 083506
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Odake S. Sasaki R., “Extensions of Solvable Potentials with Finitely Many Discrete Eigenstates”, J. Phys. A-Math. Theor., 46:23 (2013), 235205
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Odake S., “Equivalences of the Multi-Indexed Orthogonal Polynomials”, J. Math. Phys., 55:1 (2014), 013502
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Takemura K., “Multi-Indexed Jacobi Polynomials and Maya Diagrams”, J. Math. Phys., 55:11 (2014), 113501
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Odake S., “Recurrence Relations of the Multi-Indexed Orthogonal Polynomials. III”, J. Math. Phys., 57:2 (2016), 023514
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Bonneux N. Kuijlaars A.B.J., “Exceptional Laguerre Polynomials”, Stud. Appl. Math., 141:4, SI (2018), 547–595
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Angeles Garcia-Ferrero M., Gomez-Ullate D., Milson R., “A Bochner Type Characterization Theorem For Exceptional Orthogonal Polynomials”, J. Math. Anal. Appl., 472:1 (2019), 584–626
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