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 SIGMA, 2012, Volume 8, 085, 18 pages (Mi sigma762)

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

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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
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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
\Bibitem{SasTak12} \by Ryu~Sasaki, Kouchi~Takemura \paper Global Solutions of Certain Second-Order Differential Equations with a High Degree of Apparent Singularity \jour SIGMA \yr 2012 \vol 8 \papernumber 085 \totalpages 18 \mathnet{http://mi.mathnet.ru/sigma762} \crossref{https://doi.org/10.3842/SIGMA.2012.085} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3007274} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000312377900001} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84870022721} 

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This publication is cited in the following articles:
1. 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
2. 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
3. Odake S., “Recurrence Relations of the Multi-Indexed Orthogonal Polynomials”, J. Math. Phys., 54:8 (2013), 083506
4. Odake S. Sasaki R., “Extensions of Solvable Potentials with Finitely Many Discrete Eigenstates”, J. Phys. A-Math. Theor., 46:23 (2013), 235205
5. Odake S., “Equivalences of the Multi-Indexed Orthogonal Polynomials”, J. Math. Phys., 55:1 (2014), 013502
6. Takemura K., “Multi-Indexed Jacobi Polynomials and Maya Diagrams”, J. Math. Phys., 55:11 (2014), 113501
7. Odake S., “Recurrence Relations of the Multi-Indexed Orthogonal Polynomials. III”, J. Math. Phys., 57:2 (2016), 023514
8. Bonneux N. Kuijlaars A.B.J., “Exceptional Laguerre Polynomials”, Stud. Appl. Math., 141:4, SI (2018), 547–595
9. 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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