On second order q-difference equations satisfied by Al-Salam-Carlitz I-Sobolev type polynomials of higher order
Authors
Lastra Sedano, Alberto; Huertas Cejudo, Edmundo José; Soria Lorente, Anier; Hermoso Ortíz, CarlosIdentifiers
Permanent link (URI): http://hdl.handle.net/10017/45707DOI: 10.3390/math8081300
ISSN: 2227-7390
Publisher
MDPI
Date
2020-08-06Funders
Universidad de Alcalá
Bibliographic citation
Hermoso, C., Huertas, E.J., Lastra, A. & Soria Lorente, A. 2020, “On second order q-difference equations satisfied by Al-Salam–Carlitz I-Sobolev type polynomials of higher order”, Mathematics, vol. 8, no. 8, 1300.
Keywords
Al-Salam-Carlitz I polynomials
Al-Salam-Carlitz I-Sobolev type polynomials
Second order linear q-difference equations
Structure relations
Recurrence relations
Basic hypergeometric series
Project
info:eu-repo/grantAgreement/UAH//CM-JIN-2019-010
Document type
info:eu-repo/semantics/article
Version
info:eu-repo/semantics/publishedVersion
Publisher's version
https://doi.org/10.3390/math8081300Rights
Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
Access rights
info:eu-repo/semantics/openAccess
Abstract
This contribution deals with the sequence fU(a)n (x; q, j)gn_0 of monic polynomials in x,
orthogonal with respect to a Sobolev-type inner product related to the
Al-Salam-Carlitz I ortogonal polynomials, and involving an arbitrary number j of
q-derivatives
on the two boundaries of the corresponding orthogonality interval, for some
fixed real number q ϵ (0,1). We provide several versions of the corresponding connection formulas, ladder
operators, and several versions of the second order q-difference
equations satisfied by polynomials in this sequence. As a novel contribution to
the literature, we provide certain three term recurrence formula with rational
coefficients satisfied by U(a)n
(x; q, j),
which paves the way to establish an appealing generalization of the so-called J-fractions
to the framework of Sobolev-type orthogonality.
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