Paper: q-Classical orthogonal polynomial: A general difference calculus approach

q-Classical orthogonal polynomial: A general difference calculus approach

Abstract

q-Classical orthogonal polynomials of the q-Hahn tableau are characterized from their orthogonality condition and by a first and a second structure relation. Unfortunately, for the q-semiclassical orthogonal polynomials (a generalization of the classical ones) we find only in the literature the first structure relation.

In this paper, a second structure relation is deduced. In particular, by means of a general finite-type relation between a q-semiclassical polynomial sequence and the sequence of its q-differences such a structure relation is obtained.

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BibTeX

@article {MR2653053,
AUTHOR={Costas-Santos, R. S. and Marcellan, F.},
TITLE={{$q$}-classical orthogonal polynomials: a general difference calculus approach},
JOURNAL={Acta Appl. Math.},
FJOURNAL={Acta Applicandae Mathematicae},
VOLUME={111},
YEAR={2010},
NUMBER={1},
PAGES={107--128},
ISSN={0167-8019},
MRCLASS={33C45 (33D45 39A13 42C05)},
MRNUMBER={2653053},
ZBL={1204.33011},
MRREVIEWER={Thomas Stoll},
DOI={10.1007/s10440-009-9536-z},
URL={https://doi.org/10.1007/s10440-009-9536-z},
}