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SIGMA 5 (2009), 076, 22 pages arXiv:0907.3851
https://doi.org/10.3842/SIGMA.2009.076
The Symmetrical Hq-Semiclassical Orthogonal Polynomials of Class One
Abdallah Ghressi a and Lotfi Khériji b
a) Faculté des Sciences de Gabès, Route de Mednine 6029 Gabès, Tunisia
b) Institut Supérieur des Sciences Appliquées
et de Technologies de Gabès, Rue Omar Ibn El-Khattab 6072 Gabès, Tunisia
Received December 12, 2008, in final form July 07, 2009; Published online July 22, 2009
Abstract
We investigate the quadratic decomposition and duality to
classify symmetrical Hq-semiclassical orthogonal
q-polynomials of class one where Hq is the Hahn's operator.
For any canonical situation, the recurrence coefficients, the
q-analog of the distributional equation of Pearson type, the
moments and integral or discrete representations are given.
Key words:
quadratic decomposition of symmetrical orthogonal polynomials; semiclassical form; integral representations; q-difference operator; q-series representations; the q-analog of the distributional equation of Pearson type.
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