RT Journal Article
T1 Generalized Delta coherent pairs
A1 Kwon, Kil H.
A1 Lee, J. H.
A1 Marcellán Español, Francisco José
AB A pair of quasi-definite linear functionals ${u_0,u_1}$ is a generalized $Delta$-coherent pair if monic orthogonal polynomials $${P_n(x)}_{n=0} nfty$$ and $${R_n(x)}_{n=0} nfty$$ relative to $u_0$ and $u_1$, respectively, satisfy a relation $$ R_n(x) = frac{1}{n+1}Delta P_{n+1}(x)-frac{sigma_n}{n}Delta P_n(x)- frac{ au_{n-1}}{n-1}Delta P_{n-1}(x), ~~ ngeq 2,$$ where $sigma_n$ and $ au_n$ are arbitrary constants and $Delta p=p(x+1)-p(x)$ is the difference operator.
AB We show that if ${u_0,u_1}$ is a generalized $Delta$-coherent pair, then $u_0$ and $u_1$ must be discrete-semiclassical linearfunctionals. We also find conditions under which either $u_0$ or $u_1$ is discrete-classical.
PB Korean Mathematical Society
SN 0304 - 9914
YR 2004
FD 2004
LK https://hdl.handle.net/10016/5970
UL https://hdl.handle.net/10016/5970
LA eng
NO 18 pages, no figures.-- MSC2000 codes: 42C05, 33C45.
NO MR#: MR2095548 (2005k:33007)
NO Zbl#: Zbl 1058.42018
NO The first author (KHK) was partially supported by KOSEF(R01{1999{00001). The second author(JHL) was supported by BK Postdoctoral Program in SNU. Thework of the third author (FM) was supported by Dirección General de Enseñanza Superior (DGES) of Spain under grant BFM2000-0206-C04-01.
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RD 27 may. 2024