Orthogonality relations for Al-Salam–Carlitz polynomials of type II

Wolter Groenevelt ^[1]
1. [1] Delft University of Technology
  
  Delft University of Technology
  
  Países Bajos
Localización: Journal of approximation theory, ISSN 0021-9045, Vol. 195, Nº 1 (July 2015), 2015, págs. 89-108
Idioma: inglés
DOI: 10.1016/j.jat.2014.07.006
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Resumen
- By use of a special case of Slater’s qq-beta integral evaluation formula, we determine orthogonality relations for the Al-Salam–Carlitz polynomials of type II with respect to a family of measures supported on a discrete subset of R. From spectral analysis of the corresponding second-order qq-difference operator we obtain an infinite set of functions that complement the Al-Salam–Carlitz II polynomials to an orthogonal basis of the associated L2-space.