Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

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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