1. Casoratian identities for the Wilson and Askey–Wilson polynomials
- Author
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Satoru Odake and Ryu Sasaki
- Subjects
High Energy Physics - Theory ,High Energy Physics::Lattice ,General Mathematics ,Mathematics::Classical Analysis and ODEs ,FOS: Physical sciences ,Askey–Wilson polynomials ,Classical orthogonal polynomials ,symbols.namesake ,Wilson polynomials ,Classical Analysis and ODEs (math.CA) ,FOS: Mathematics ,Mathematical Physics ,Mathematics ,Quantum Physics ,Numerical Analysis ,Nonlinear Sciences - Exactly Solvable and Integrable Systems ,Gegenbauer polynomials ,Applied Mathematics ,Discrete orthogonal polynomials ,Mathematical Physics (math-ph) ,Algebra ,High Energy Physics - Theory (hep-th) ,Mathematics - Classical Analysis and ODEs ,Orthogonal polynomials ,Hahn polynomials ,symbols ,Jacobi polynomials ,Exactly Solvable and Integrable Systems (nlin.SI) ,Quantum Physics (quant-ph) ,Analysis - Abstract
Infinitely many Casoratian identities are derived for the Wilson and Askey-Wilson polynomials in parallel to the Wronskian identities for the Hermite, Laguerre and Jacobi polynomials, which were reported recently by the present authors. These identities form the basis of the equivalence between eigenstate adding and deleting Darboux transformations for solvable (discrete) quantum mechanical systems. Similar identities hold for various reduced form polynomials of the Wilson and Askey-Wilson polynomials, e.g. the continuous q-Jacobi, continuous (dual) (q-)Hahn, Meixner-Pollaczek, Al-Salam-Chihara, continuous (big) q-Hermite, etc., 31 pages, 2 figures. Comments and references added. To appear in Journal of Approximation Theory
- Published
- 2015
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