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Properties of the Exceptional (X-l) Laguerre and Jacobi Polynomial
en
exceptional orthogonal polynomials
Gram-Schmidt process
Rodrigues formulas
generating functions
Ho Choon Lin
Odake Satoru
Sasaki Ryu
NATL ACAD SCI UKRAINE, INST MATH
SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS. 7:107 (2011)
SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS
7
2011
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.
Article
1815-0659
http://dx.doi.org/10.3842/SIGMA.2011.107|10.3842/SIGMA.2011.107