# Generalized Delta coherent pairs

## Repositorio e-Archivo

 dc.contributor.author Kwon, Kil H. dc.contributor.author Lee, J. H. dc.contributor.author Marcellán Español, Francisco José dc.date.accessioned 2009-12-07T09:55:29Z dc.date.available 2009-12-07T09:55:29Z dc.date.issued 2004 dc.identifier.bibliographicCitation Journal of the Korean Mathematical Society, 2004, vol. 41, n. 6, p. 977-994 dc.identifier.issn 0304 - 9914 dc.identifier.uri http://hdl.handle.net/10016/5970 dc.description 18 pages, no figures.-- MSC2000 codes: 42C05, 33C45. dc.description MR#: MR2095548 (2005k:33007) dc.description Zbl#: Zbl 1058.42018 dc.description.abstract 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. dc.description.abstract 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. dc.description.sponsorship The first author (KHK) was partially supported by KOSEF(R01{1999{00001). The second author(JHL) was supported by BK Postdoctoral Program in SNU. The work of the third author (FM) was supported by Dirección General de Enseñanza Superior (DGES) of Spain under grant BFM2000-0206-C04-01. dc.format.mimetype application/pdf dc.language.iso eng dc.publisher Korean Mathematical Society dc.rights © Korean Mathematical Society dc.subject.other Discrete orthogonal polynomials dc.subject.other Delta-coherent pairs dc.title Generalized Delta coherent pairs dc.type article dc.type.review PeerReviewed dc.description.status Publicado dc.relation.publisherversion http://www.mathnet.or.kr/mathnet/kms_content.php?no=366087 dc.subject.eciencia Matemáticas dc.rights.accessRights openAccess
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