Euler matrices and their algebraic properties revisited
This paper addresses the generalized Euler polynomial matrix E (α) (x) and the Euler matrix E . Taking into account some properties of Euler polynomials and numbers, we deduce product formulae for E (α) (x) and define the inverse matrix of E . We establish some explicit expressions for the Euler pol...
- Autores:
-
Quintana, Yamilet
Ramírez, William
Urieles, Alejandro
- Tipo de recurso:
- Article of journal
- Fecha de publicación:
- 2020
- Institución:
- Corporación Universidad de la Costa
- Repositorio:
- REDICUC - Repositorio CUC
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.cuc.edu.co:11323/6387
- Acceso en línea:
- https://hdl.handle.net/11323/6387
https://repositorio.cuc.edu.co/
- Palabra clave:
- Euler polynomials
Euler matrix
Generalized Euler matrix
Generalized Pascal matrix
Fibonacci matrix
Lucas matrix
- Rights
- openAccess
- License
- CC0 1.0 Universal
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| dc.title.spa.fl_str_mv |
Euler matrices and their algebraic properties revisited |
| title |
Euler matrices and their algebraic properties revisited |
| spellingShingle |
Euler matrices and their algebraic properties revisited Euler polynomials Euler matrix Generalized Euler matrix Generalized Pascal matrix Fibonacci matrix Lucas matrix |
| title_short |
Euler matrices and their algebraic properties revisited |
| title_full |
Euler matrices and their algebraic properties revisited |
| title_fullStr |
Euler matrices and their algebraic properties revisited |
| title_full_unstemmed |
Euler matrices and their algebraic properties revisited |
| title_sort |
Euler matrices and their algebraic properties revisited |
| dc.creator.fl_str_mv |
Quintana, Yamilet Ramírez, William Urieles, Alejandro |
| dc.contributor.author.spa.fl_str_mv |
Quintana, Yamilet Ramírez, William Urieles, Alejandro |
| dc.subject.spa.fl_str_mv |
Euler polynomials Euler matrix Generalized Euler matrix Generalized Pascal matrix Fibonacci matrix Lucas matrix |
| topic |
Euler polynomials Euler matrix Generalized Euler matrix Generalized Pascal matrix Fibonacci matrix Lucas matrix |
| description |
This paper addresses the generalized Euler polynomial matrix E (α) (x) and the Euler matrix E . Taking into account some properties of Euler polynomials and numbers, we deduce product formulae for E (α) (x) and define the inverse matrix of E . We establish some explicit expressions for the Euler polynomial matrix E (x), which involves the generalized Pascal, Fibonacci and Lucas matrices, respectively. From these formulae, we get some new interesting identities involving Fibonacci and Lucas numbers. Also, we provide some factorizations of the Euler polynomial matrix in terms of Stirling matrices, as well as a connection between the shifted Euler matrices and Vandermonde matrices. |
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2020 |
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2020-06-19T04:52:18Z |
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2020-06-19T04:52:18Z |
| dc.date.issued.none.fl_str_mv |
2020 |
| dc.type.spa.fl_str_mv |
Artículo de revista |
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http://purl.org/coar/resource_type/c_2df8fbb1 |
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http://purl.org/coar/resource_type/c_6501 |
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http://purl.org/coar/resource_type/c_6501 |
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https://hdl.handle.net/11323/6387 |
| dc.identifier.instname.spa.fl_str_mv |
Corporación Universidad de la Costa |
| dc.identifier.reponame.spa.fl_str_mv |
REDICUC - Repositorio CUC |
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https://repositorio.cuc.edu.co/ |
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https://hdl.handle.net/11323/6387 https://repositorio.cuc.edu.co/ |
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Corporación Universidad de la Costa REDICUC - Repositorio CUC |
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eng |
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eng |
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CC0 1.0 Universal |
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http://creativecommons.org/publicdomain/zero/1.0/ |
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info:eu-repo/semantics/openAccess |
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CC0 1.0 Universal http://creativecommons.org/publicdomain/zero/1.0/ http://purl.org/coar/access_right/c_abf2 |
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openAccess |
| dc.publisher.spa.fl_str_mv |
Applied Mathematics and Information Sciences |
| institution |
Corporación Universidad de la Costa |
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Quintana, YamiletRamírez, WilliamUrieles, Alejandro2020-06-19T04:52:18Z2020-06-19T04:52:18Z2020https://hdl.handle.net/11323/6387Corporación Universidad de la CostaREDICUC - Repositorio CUChttps://repositorio.cuc.edu.co/This paper addresses the generalized Euler polynomial matrix E (α) (x) and the Euler matrix E . Taking into account some properties of Euler polynomials and numbers, we deduce product formulae for E (α) (x) and define the inverse matrix of E . We establish some explicit expressions for the Euler polynomial matrix E (x), which involves the generalized Pascal, Fibonacci and Lucas matrices, respectively. From these formulae, we get some new interesting identities involving Fibonacci and Lucas numbers. Also, we provide some factorizations of the Euler polynomial matrix in terms of Stirling matrices, as well as a connection between the shifted Euler matrices and Vandermonde matrices.Quintana, YamiletRamírez, WilliamUrieles, AlejandroengApplied Mathematics and Information SciencesCC0 1.0 Universalhttp://creativecommons.org/publicdomain/zero/1.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Euler polynomialsEuler matrixGeneralized Euler matrixGeneralized Pascal matrixFibonacci matrixLucas matrixEuler matrices and their algebraic properties revisitedArtículo de revistahttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1Textinfo:eu-repo/semantics/articlehttp://purl.org/redcol/resource_type/ARTinfo:eu-repo/semantics/acceptedVersionPublicationORIGINALEuler Matrices and their Algebraic Properties Revisited.pdfEuler Matrices and their Algebraic Properties Revisited.pdfapplication/pdf428750https://repositorio.cuc.edu.co/bitstreams/c390554a-60da-45d1-9494-ec6c24128474/download17cf5c0cc220963a053d440868bb1f19MD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8701https://repositorio.cuc.edu.co/bitstreams/3009e2c9-ce9c-4546-bf62-dd40f7d2078a/download42fd4ad1e89814f5e4a476b409eb708cMD52LICENSElicense.txtlicense.txttext/plain; charset=utf-81748https://repositorio.cuc.edu.co/bitstreams/da0a32af-61ff-4cdd-83f9-4f94a17cf39d/download8a4605be74aa9ea9d79846c1fba20a33MD53THUMBNAILEuler Matrices and their Algebraic Properties Revisited.pdf.jpgEuler Matrices and their Algebraic Properties Revisited.pdf.jpgimage/jpeg57638https://repositorio.cuc.edu.co/bitstreams/61b3d054-350f-48c5-bbd5-b393c545537f/download2ffc4350a03e53ed341b7e7256dcc56dMD54TEXTEuler Matrices and their Algebraic Properties Revisited.pdf.txtEuler Matrices and their Algebraic Properties Revisited.pdf.txttext/plain47859https://repositorio.cuc.edu.co/bitstreams/b84a8751-d9a1-4928-99ee-27a834e0859b/downloadcd670200ab76c706f7f6e302fa6686c6MD5511323/6387oai:repositorio.cuc.edu.co:11323/63872024-09-17 10:56:43.398http://creativecommons.org/publicdomain/zero/1.0/CC0 1.0 Universalopen.accesshttps://repositorio.cuc.edu.coRepositorio de la Universidad de la Costa CUCrepdigital@cuc.edu.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 |