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    Title: Properties of the Exceptional (Xl) Laguerre and Jacobi Polynomials
    Authors: Ho, Choon-Lin;Satoru Odake;Ryu Sasaki
    Contributors: 淡江大學物理學系
    Keywords: exceptional orthogonal polynomials;Gram-Schmidt process;Rodrigues formulas;generating functions
    Date: 2011-11
    Issue Date: 2014-02-17 11:41:57 (UTC+8)
    Publisher: Kyiv: Natsional'na Akademiya Nauk Ukrainy * Instytut Matematyky
    Abstract: We present various results on the properties of the four infinite sets of the exceptional Xl polynomials discovered recently by Odake and Sasaki [Phys. Lett. B 679 (2009), 414-417; Phys. Lett. B 684 (2010), 173-176]. These Xl polynomials are global solutions of second order Fuchsian differential equations with l+3 regular singularities and their confluent limits. We derive equivalent but much simpler looking forms of the Xl polynomials. The other subjects discussed in detail are: factorisation of the Fuchsian differential operators, shape invariance, the forward and backward shift operations, invariant polynomial subspaces under the Fuchsian differential operators, the Gram-Schmidt orthonormalisation procedure, three term recurrence relations and the generating functions for the Xl polynomials.
    Relation: Symmetry, Integrability and Geometry: Methods and Applications 7, 107(24pages)
    DOI: 10.3842/SIGMA.2011.107
    Appears in Collections:[物理學系暨研究所] 期刊論文

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