The Symmetrical $H_{q}$-Semiclassical Orthogonal Polynomials of Class One

Details The Symmetrical $H_{q}$-Semiclassical Orthogonal Polynomials of Class One The Symmetrical $H_{q}$-Semiclassical Orthogonal Polynomials of Class One

2009-07-22

arxiv.org/abs/0907.3851v1

SIGMA 5 (2009), 076, 22 pages

Mathematics

Classical Analysis and ODEs

Scientific paper

10.3842/SIGMA.2009.076

We investigate the quadratic decomposition and duality to classify
symmetrical $H_{q}$-semiclassical orthogonal $q$-polynomials of class one where
$H_{q}$ 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.

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