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http://dx.doi.org/10.4134/JKMS.2004.41.6.977

GENERALIZED Δ-COHERENT PAIRS  

Kwon, K.H. (Division of Applied Mathematic KAIST)
Lee, J.H. (Department of Mathematical Science SNU)
F. Marcellan (Departmento de Matematicas Universidad Carlos III de Madrid Avda)
Publication Information
Journal of the Korean Mathematical Society / v.41, no.6, 2004 , pp. 977-994 More about this Journal
Abstract
A pair of quasi-definite linear functionals {u$_{0}$, u$_1$} is a generalized $\Delta$-coherent pair if monic orthogonal polynomials (equation omitted) relative to u$_{0}$ and u$_1$, respectively, satisfy a relation (equation omitted) where $\sigma$$_{n}$ and T$_{n}$ are arbitrary constants and $\Delta$p = p($\chi$＋1) - p($\chi$) is the difference operator. We show that if {u$_{0}$, u$_1$} is a generalized $\Delta$-coherent pair, then u$_{0}$ and u$_{1}$ must be discrete-semiclassical linear functionals. We also find conditions under which either u$_{0}$ or u$_1$ is discrete-classical.ete-classical.
Keywords
discrete orthogonal polynomials; $\Delta$-coherent pairs;
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