Paper: Second structure relation for q-semiclassical polynomials of the Hahn Tableau

Second structure relation for q-semiclassical polynomials of the Hahn Tableau

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 {MR2306798,
AUTHOR = {Costas-Santos, R. S.; Marcellan, F.},
TITLE = {Second structure relation for $q$-semiclassical polynomials of the Hahn Tableau},
JOURNAL = {J. Math. Anal. Appl.},
FJOURNAL = {Journal of Mathematical Analysis and Applications},
VOLUME = {329},
NUMBER={1},
YEAR = {2007},
PAGES = {206--228},
ISSN = {0022-247X},
MRCLASS = {33D45},
MRNUMBER = {MR2306798},
ZBL = {1113.33022},
MRREVIEWER = {Qing-Hu Hou},
DOI = {10.1016/j.jmaa.2006.06.036},
URL = {https://doi.org/10.1016/j.jmaa.2006.06.036},
}