Second structure relation for q-semiclassical polynomials of the Hahn Tableau
Marcellan, F. and Costas-Santos, R. S. Journal of Mathematical Analysis and Applications 329, no. 1 (2007), 206 — 228Abstract
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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@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}, }