On second order q-difference equations satisfied by Al-Salam-Carlitz I-Sobolev type polynomials of higher order

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 o...

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Autores: Lastra Sedano, Alberto|||0000-0002-4012-6471, Huertas Cejudo, Edmundo José|||0000-0001-6802-3303, Soria Lorente, Anier, Hermoso Ortíz, Carlos|||0000-0002-5556-1839
Tipo de recurso: artículo
Fecha de publicación:2020
País:España
Institución:Universidad de Alcalá (UAH)
Repositorio:e_Buah Biblioteca Digital Universidad de Alcalá
Idioma:inglés
OAI Identifier:oai:ebuah.uah.es:10017/45707
Acceso en línea:http://hdl.handle.net/10017/45707
https://dx.doi.org/10.3390/math8081300
Access Level:acceso abierto
Palabra clave: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
Matemáticas
Mathematics
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spelling On second order q-difference equations satisfied by Al-Salam-Carlitz I-Sobolev type polynomials of higher orderLastra Sedano, Alberto|||0000-0002-4012-6471Huertas Cejudo, Edmundo José|||0000-0001-6802-3303Soria Lorente, AnierHermoso Ortíz, Carlos|||0000-0002-5556-1839Al-Salam-Carlitz I polynomialsAl-Salam-Carlitz I-Sobolev type polynomialsSecond order linear q-difference equationsStructure relationsRecurrence relationsBasic hypergeometric seriesMatemáticasMathematicsThis 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.Universidad de AlcaláMDPI20202020-08-06journal articlehttp://purl.org/coar/resource_type/c_6501NAhttp://purl.org/coar/version/c_be7fb7dd8ff6fe43info:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10017/45707https://dx.doi.org/10.3390/math8081300reponame:e_Buah Biblioteca Digital Universidad de Alcaláinstname:Universidad de Alcalá (UAH)InglésengUAH Not available CM-JIN-2019-010open accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:ebuah.uah.es:10017/457072026-06-18T11:13:07Z
dc.title.none.fl_str_mv On second order q-difference equations satisfied by Al-Salam-Carlitz I-Sobolev type polynomials of higher order
title On second order q-difference equations satisfied by Al-Salam-Carlitz I-Sobolev type polynomials of higher order
spellingShingle On second order q-difference equations satisfied by Al-Salam-Carlitz I-Sobolev type polynomials of higher order
Lastra Sedano, Alberto|||0000-0002-4012-6471
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
Matemáticas
Mathematics
title_short On second order q-difference equations satisfied by Al-Salam-Carlitz I-Sobolev type polynomials of higher order
title_full On second order q-difference equations satisfied by Al-Salam-Carlitz I-Sobolev type polynomials of higher order
title_fullStr On second order q-difference equations satisfied by Al-Salam-Carlitz I-Sobolev type polynomials of higher order
title_full_unstemmed On second order q-difference equations satisfied by Al-Salam-Carlitz I-Sobolev type polynomials of higher order
title_sort On second order q-difference equations satisfied by Al-Salam-Carlitz I-Sobolev type polynomials of higher order
dc.creator.none.fl_str_mv Lastra Sedano, Alberto|||0000-0002-4012-6471
Huertas Cejudo, Edmundo José|||0000-0001-6802-3303
Soria Lorente, Anier
Hermoso Ortíz, Carlos|||0000-0002-5556-1839
author Lastra Sedano, Alberto|||0000-0002-4012-6471
author_facet Lastra Sedano, Alberto|||0000-0002-4012-6471
Huertas Cejudo, Edmundo José|||0000-0001-6802-3303
Soria Lorente, Anier
Hermoso Ortíz, Carlos|||0000-0002-5556-1839
author_role author
author2 Huertas Cejudo, Edmundo José|||0000-0001-6802-3303
Soria Lorente, Anier
Hermoso Ortíz, Carlos|||0000-0002-5556-1839
author2_role author
author
author
dc.subject.none.fl_str_mv 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
Matemáticas
Mathematics
topic 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
Matemáticas
Mathematics
description 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.
publishDate 2020
dc.date.none.fl_str_mv 2020
2020-08-06
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
NA
http://purl.org/coar/version/c_be7fb7dd8ff6fe43
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv http://hdl.handle.net/10017/45707
https://dx.doi.org/10.3390/math8081300
url http://hdl.handle.net/10017/45707
https://dx.doi.org/10.3390/math8081300
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv UAH Not available CM-JIN-2019-010
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv MDPI
publisher.none.fl_str_mv MDPI
dc.source.none.fl_str_mv reponame:e_Buah Biblioteca Digital Universidad de Alcalá
instname:Universidad de Alcalá (UAH)
instname_str Universidad de Alcalá (UAH)
reponame_str e_Buah Biblioteca Digital Universidad de Alcalá
collection e_Buah Biblioteca Digital Universidad de Alcalá
repository.name.fl_str_mv
repository.mail.fl_str_mv
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