RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



SIGMA:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


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

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: PDF file (409 kB)
Full text: http://emis.mi.ras.ru/.../085
References: PDF file   HTML file

Bibliographic databases:

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
\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}


Linking options:
  • http://mi.mathnet.ru/eng/sigma762
  • http://mi.mathnet.ru/eng/sigma/v8/p85

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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. 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  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    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  crossref  mathscinet  zmath  adsnasa  isi  scopus
    3. Odake S., “Recurrence Relations of the Multi-Indexed Orthogonal Polynomials”, J. Math. Phys., 54:8 (2013), 083506  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    4. Odake S. Sasaki R., “Extensions of Solvable Potentials with Finitely Many Discrete Eigenstates”, J. Phys. A-Math. Theor., 46:23 (2013), 235205  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    5. Odake S., “Equivalences of the Multi-Indexed Orthogonal Polynomials”, J. Math. Phys., 55:1 (2014), 013502  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    6. Takemura K., “Multi-Indexed Jacobi Polynomials and Maya Diagrams”, J. Math. Phys., 55:11 (2014), 113501  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    7. Odake S., “Recurrence Relations of the Multi-Indexed Orthogonal Polynomials. III”, J. Math. Phys., 57:2 (2016), 023514  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    8. Bonneux N. Kuijlaars A.B.J., “Exceptional Laguerre Polynomials”, Stud. Appl. Math., 141:4, SI (2018), 547–595  crossref  mathscinet  zmath  isi  scopus
    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  crossref  mathscinet  isi  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
    Number of views:
    This page:148
    Full text:32
    References:30

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019