Casoratian identities for the Wilson and Askey–Wilson polynomials

• Satoru Odake ^[1] ; Ryu Sasaki ^[1]
  1. [1] Shinshu University

     Shinshu University

     Japón

     
• Localización: Journal of approximation theory, ISSN 0021-9045, Vol. 193, Nº 1 (May 2015), 2015, págs. 184-209
• Idioma: inglés
• DOI: 10.1016/j.jat.2014.04.009
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• Resumen

  • 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.