HOME    |    BROWSE    |    SEARCH    |    SUBSCRIPTION   |    SUBMISSION    |    REGISTRATION

Quick Search:
Author: Title/Abstract: Vol./No: Page:
PTP Online Top > Volume 125 (2011) > Number 5
| Next Article >

Prog. Theor. Phys. Vol. 125 No. 5 (2011) pp. 851-870

[ Full Text PDF : FREE ACCESS (196K) ]

The Exceptional (Xℓ) (q)-Racah Polynomials

Satoru Odake1 and Ryu Sasaki2

1Department of Physics, Shinshu University, Matsumoto 390-8621, Japan
2Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan

(Received February 7, 2011)

Abstract:

The exceptional Racah and q-Racah polynomials are constructed. Together with the exceptional Laguerre, Jacobi, Wilson and Askey-Wilson polynomials discovered by the present authors in 2009, they exhaust the generic exceptional orthogonal polynomials of a single variable.

Subject Index : 010, 012, 064
URL : http://ptp.ipap.jp/link?PTP/125/851/
DOI : 10.1143/PTP.125.851

[ Full Text PDF : FREE ACCESS (196K) ] Citation:

References:

  1. S. Odake and R. Sasaki, J. Math. Phys. 49 (2008), 053503, [CrossRef] arXiv:0712.4106[e-print arXiv].
    (The dual q-Meixner polynomial in §5.2.4 and dual q-Charlier polynomial in §5.2.8 should be deleted because the hermiticity of the Hamiltonian is lost for these two cases.)
  2. A. F. Nikiforov, S. K. Suslov and V. B. Uvarov, Classical Orthogonal Polynomials of a Discrete Variable (Springer, Berlin, 1991).
  3. G. E. Andrews, R. Askey and R. Roy, Special Functions, Encyclopedia of mathematics and its applications (Cambridge Univ. Press, 1999).
  4. M. E. H. Ismail, Classical and quantum orthogonal polynomials in one variable, Encyclopedia of mathematics and its applications (Cambridge Univ. Press, 2005).
  5. R. Koekoek and R. F. Swarttouw, math/9602214[e-print arXiv].
  6. S. Odake and R. Sasaki, Phys. Lett. B 682 (2009), 130, [CrossRef] arXiv:0909.3668[e-print arXiv].
  7. D. Gómez-Ullate, N. Kamran and R. Milson, J. Approx. Theory 162 (2010), 987, arXiv:0805.3376[e-print arXiv]; J. Math. Anal. Appl. 359 (2009), 352, arXiv:0807.3939[e-print arXiv]; J. of Phys. A 43 (2010), 434016, [CrossRef] arXiv:1002.2666[e-print arXiv].
  8. C. Quesne, J. of Phys. A 41 (2008), 392001, [CrossRef] arXiv:0807.4087[e-print arXiv].
    B. Bagchi, C. Quesne and R. Roychoudhury, Pramana J. Phys. 73 (2009), 337, arXiv:0812.1488[e-print arXiv].
    C. Quesne, SIGMA 5 (2009), 084, arXiv:0906.2331[e-print arXiv].
  9. S. Odake and R. Sasaki, Phys. Lett. B 679 (2009), 414, [CrossRef] arXiv:0906.0142[e-print arXiv].
  10. S. Odake and R. Sasaki, J. Math. Phys. 51 (2010), 053513, [CrossRef] arXiv:0911.1585[e-print arXiv].
  11. S. Odake and R. Sasaki, Phys. Lett. B 684 (2010), 173, [CrossRef] arXiv:0911.3442[e-print arXiv].
  12. C.-L. Ho, S. Odake and R. Sasaki, arXiv:0912.5447[e-print arXiv].
  13. D. Dutta and P. Roy, J. Math. Phys. 51 (2010), 042101[CrossRef].
  14. R. Sasaki, S. Tsujimoto and A. Zhedanov, J. of Phys. A 43 (2010), 315204, [CrossRef] arXiv:1004.4711[e-print arXiv].
  15. S. Odake and R. Sasaki, J. of Phys. A 43 (2010), 335201, [CrossRef] arXiv:1004.0544[e-print arXiv].
  16. S. Odake and R. Sasaki, J. of Phys. A 44 (2011), 195203, [CrossRef] arXiv:1007.3800[e-print arXiv].
  17. M. M. Crum, Quart. J. Math. Oxford Ser. (2) 6 (1955), 121, physics/9908019[e-print arXiv].
  18. M. G. Krein, Dokl. Acad. Nauk. CCCP 113 (1957), 970.
    V. É. Adler, Theor. Math. Phys. 101 (1994), 1381.
  19. S. Odake and R. Sasaki, Prog. Theor. Phys. 122 (2009), 1067, [PTP] arXiv:0902.2593[e-print arXiv].
  20. L. García-Gutiérrez, S. Odake and R. Sasaki, Prog. Theor. Phys. 124 (2010), 1, [PTP] arXiv:1004.0289[e-print arXiv].
  21. S. Odake and R. Sasaki, arXiv:1101.5468[e-print arXiv].
  22. C. Albanese, M. Christandl, N. Datta and A. Ekert, Phys. Rev. Lett. 93 (2004), 230502, [APS] quant-ph/0405029[e-print arXiv].
    R. Chakrabarti and J. Van der Jeugt, J. of Phys. A 43 (2010), 085302, [CrossRef] arXiv:0912.0837[e-print arXiv].
  23. H. Risken, The Fokker-Planck Equation (2nd ed.), (Springer-Verlag, Berlin, 1996).
  24. R. Sasaki, J. Math. Phys. 50 (2009), 103509, [CrossRef] arXiv:0903.3097[e-print arXiv].
  25. P. R. Parthasarathy and R. B. Lenin, Birth and death processes (BDP) models with applications (American Sciences Press, Inc., Columbus, Ohio, 2004).
  26. S. Karlin and J. L. McGregor, Trans. Amer. Math. Soc. 85 (1957), 489.
  27. S. Odake and R. Sasaki, J. Nonlinear Math. Phys. 12 Suppl. 1 (2005), 507, hep-th/0410102[e-print arXiv]; J. Math. Phys. 46 (2005), 063513, [CrossRef] hep-th/0410109[e-print arXiv].
  28. S. Odake and R. Sasaki, Prog. Theor. Phys. 119 (2008), 663, [PTP] arXiv:0802.1075[e-print arXiv].
  29. S. Odake and R. Sasaki, J. Math. Phys. 51 (2010), 083502, [CrossRef] arXiv:0903.2604[e-print arXiv].
  30. L. E. Gendenshtein, JETP Lett. 38 (1983), 356.

Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 126 No. 1 (2011) pp. 1-34 :
    Dual Christoffel Transformations
    Satoru Odake and Ryu Sasaki
  2. Progress of Theoretical Physics Vol. 126 No. 2 (2011) pp. 185-201 :
    Prepotential Approach to Solvable Rational Potentials and Exceptional Orthogonal Polynomials
    Choon-Lin Ho

[PTP HOME] [BROWSE] [SEARCH] [SUBSCRIPTION] [SUBMISSION] [REGISTRATION]

Copyright © Progress of Theoretical Physics 2013 All rights reserved.