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},
}