Geodesic
Simplified Expressions of the Multi-Indexed Laguerre and Jacobi Polynomials
Symmetry, integrability and geometry: methods and applications, Tome 13 (2017) Cet article a éte moissonné depuis la source Math-Net.Ru

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The multi-indexed Laguerre and Jacobi polynomials form a complete set of orthogonal polynomials. They satisfy second-order differential equations but not three term recurrence relations, because of the ‘holes’ in their degrees. The multi-indexed Laguerre and Jacobi polynomials have Wronskian expressions originating from multiple Darboux transformations. For the ease of applications, two different forms of simplified expressions of the multi-indexed Laguerre and Jacobi polynomials are derived based on various identities. The parity transformation property of the multi-indexed Jacobi polynomials is derived based on that of the Jacobi polynomial.
Keywords: multi-indexed orthogonal polynomials; Laguerre and Jacobi polynomials; Wronskian formula; determinant formula. 
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Satoru Odake; Ryu Sasaki. Simplified Expressions of the Multi-Indexed Laguerre and Jacobi Polynomials. Symmetry, integrability and geometry: methods and applications, Tome 13 (2017). http://geodesic.mathdoc.fr/item/SIGMA_2017_13_a19/

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