A 'missing' family of classical orthogonal polynomials

@article{Vinet2011AF,
  title={A 'missing' family of classical orthogonal polynomials},
  author={L. Vinet and A. Zhedanov},
  journal={Journal of Physics A},
  year={2011},
  volume={44},
  pages={085201}
}
  • L. Vinet, A. Zhedanov
  • Published 2011
  • Mathematics
  • Journal of Physics A
  • We study a family of 'classical' orthogonal polynomials which satisfy (apart from a three-term recurrence relation) an eigenvalue problem with a differential operator of Dunkl type. These polynomials can be obtained from the little q-Jacobi polynomials in the limit q = −1. We also show that these polynomials provide a nontrivial realization of the Askey–Wilson algebra for q = −1. 
    Dunkl shift operators and Bannai-Ito polynomials
    • 79
    • PDF
    J an 2 01 2 Dunkl shift operators and
    • 2012
    A limit $q=-1$ for the big q-Jacobi polynomials
    • 40
    • PDF
    The Universal Askey-Wilson Algebra
    • 82
    • PDF
    The Bannai-Ito polynomials as Racah coefficients of the sl_{-1}(2) algebra
    • 46
    • PDF
    Dual -1 Hahn polynomials: "classical" polynomials beyond the Leonard duality
    • 33
    • PDF
    A Bochner theorem for Dunkl polynomials.
    • 25
    • PDF
    The Bannai–Ito algebra and a superintegrable system with reflections on the two-sphere
    • 36
    • PDF
    FROM slq(2) TO A PARABOSONIC HOPF ALGEBRA
    • 30
    • PDF
    Bispectrality of the Complementary Bannai-Ito Polynomials
    • 28
    • PDF

    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 31 REFERENCES
    Ordinary Differential Equations.
    • 6,054
    • PDF
    Supersymmetry and quantum mechanics
    • 1,856
    • Highly Influential
    • PDF
    Rational spectral transformations and orthogonal polynomials
    • 154
    “Hidden symmetry” of Askey-Wilson polynomials
    • 177