Inner products involving q-differences: the little q-Laguerre-Sobolev polynomials

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dc.contributor.author Area, Iván
dc.contributor.author Godoy, Eduardo
dc.contributor.author Marcellán Español, Francisco José
dc.contributor.author Moreno Balcázar, Juan José
dc.date.accessioned 2009-12-17T10:29:58Z
dc.date.available 2009-12-17T10:29:58Z
dc.date.issued 2000-06
dc.identifier.bibliographicCitation Journal of Computational and Applied Mathematics, 2000, vol. 118, n. 1-2, p. 1-22
dc.identifier.issn 0377-0427
dc.identifier.uri http://hdl.handle.net/10016/6141
dc.description 22 pages, no figures.-- MSC codes: Primary 33C25; Secondary 33D45.-- Issue title: "Higher transcendental functions and their applications".
dc.description MR#: MR1765938 (2001d:33018)
dc.description Zbl#: Zbl 0957.33008
dc.description.abstract In this paper, polynomials which are orthogonal with respect to the inner product $$\multline\langle p,r\rangle_S=\sum^\infty_{k=0}p(q^k)r(q^k) {(aq)^k(aq;q)_\infty\over(q;q)_k}\\ +\lambda\sum^\infty_{k=0} (D_qp)(q^k)(D_qr)(q^k){(aq)^k(aq;q)_\infty\over(q;q)_k},\endmultline$$ where $D_q$ is the $q$-difference operator, $\lambda\geq0,\ 0<q<1$ and $0<aq<1$, are studied. For these polynomials, algebraic properties and $q$-difference equations are obtained as well as their relation with the monic little $q$-Laguerre polynomials. Some properties of the zeros of these polynomials are also deduced. Finally, the relative asymptotics $\{Q_n(x)/p_n(x;a )\}_n$ on compact subsets of ${\bf C}\sbs[0,1]$ is given, where $Q_n(x)$ is the $n$th degree monic orthogonal polynomial with respect to the above inner product and $p_n(x;a )$ denotes the monic little $q$-Laguerre polynomial of degree $n$.
dc.description.sponsorship E.G. wishes to acknowledge partial financial support by Dirección General de Enseñanza Superior (DGES) of Spain under Grant PB-96-0952. The research of F.M. was partially supported by DGES of Spain under Grant PB96-0120-C03-01 and INTAS Project 93-0219 Ext. J.J.M.B. also wishes to acknowledge partial financial support by Junta de Andalucía, Grupo de Investigación FQM 0229.
dc.format.mimetype application/pdf
dc.language.iso eng
dc.publisher Elsevier
dc.rights © Elsevier
dc.subject.other Orthogonal polynomials
dc.subject.other Sobolev orthogonal polynomials
dc.subject.other Little q-Laguerre polynomials
dc.title Inner products involving q-differences: the little q-Laguerre-Sobolev polynomials
dc.type article
dc.type.review PeerReviewed
dc.description.status Publicado
dc.relation.publisherversion http://dx.doi.org/10.1016/S0377-0427(00)00278-8
dc.subject.eciencia Matemáticas
dc.identifier.doi 10.1016/S0377-0427(00)00278-8
dc.rights.accessRights openAccess
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