NEW GENERALIZED APOSTOL-FROBENIUS-EULER POLYNOMIALS AND THEIR MATRIX APPROACH
In this paper, we introduce a new extension of the generalized ApostolFrobenius-Euler polynomials H [m−1,α] n (x; c, a; λ; u). We give some algebraic and differential properties, as well as, relationships between this polynomials class with other polynomials and numbers. We also, introduce the gener...
- Autores:
-
ORTEGA, MARÍA JOSÉ
- Tipo de recurso:
- Fecha de publicación:
- 2018
- Institución:
- Universidad del Atlántico
- Repositorio:
- Repositorio Uniatlantico
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.uniatlantico.edu.co:20.500.12834/890
- Acceso en línea:
- https://hdl.handle.net/20.500.12834/890
- Palabra clave:
- . Generalized Apostol-type polynomials, Apostol-Frobennius-Euler polynomials, Apostol-Bernoulli polynomials of higher order, Apostol-Genocchi polynomials of higher order, Stirling numbers of second kind, generalized Pascal matrix
- Rights
- openAccess
- License
- http://creativecommons.org/licenses/by-nc/4.0/
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| dc.title.spa.fl_str_mv |
NEW GENERALIZED APOSTOL-FROBENIUS-EULER POLYNOMIALS AND THEIR MATRIX APPROACH |
| title |
NEW GENERALIZED APOSTOL-FROBENIUS-EULER POLYNOMIALS AND THEIR MATRIX APPROACH |
| spellingShingle |
NEW GENERALIZED APOSTOL-FROBENIUS-EULER POLYNOMIALS AND THEIR MATRIX APPROACH . Generalized Apostol-type polynomials, Apostol-Frobennius-Euler polynomials, Apostol-Bernoulli polynomials of higher order, Apostol-Genocchi polynomials of higher order, Stirling numbers of second kind, generalized Pascal matrix |
| title_short |
NEW GENERALIZED APOSTOL-FROBENIUS-EULER POLYNOMIALS AND THEIR MATRIX APPROACH |
| title_full |
NEW GENERALIZED APOSTOL-FROBENIUS-EULER POLYNOMIALS AND THEIR MATRIX APPROACH |
| title_fullStr |
NEW GENERALIZED APOSTOL-FROBENIUS-EULER POLYNOMIALS AND THEIR MATRIX APPROACH |
| title_full_unstemmed |
NEW GENERALIZED APOSTOL-FROBENIUS-EULER POLYNOMIALS AND THEIR MATRIX APPROACH |
| title_sort |
NEW GENERALIZED APOSTOL-FROBENIUS-EULER POLYNOMIALS AND THEIR MATRIX APPROACH |
| dc.creator.fl_str_mv |
ORTEGA, MARÍA JOSÉ |
| dc.contributor.author.none.fl_str_mv |
ORTEGA, MARÍA JOSÉ |
| dc.contributor.other.none.fl_str_mv |
RAMÍREZ, WILLIAM URIELES, ALEJANDRO |
| dc.subject.keywords.spa.fl_str_mv |
. Generalized Apostol-type polynomials, Apostol-Frobennius-Euler polynomials, Apostol-Bernoulli polynomials of higher order, Apostol-Genocchi polynomials of higher order, Stirling numbers of second kind, generalized Pascal matrix |
| topic |
. Generalized Apostol-type polynomials, Apostol-Frobennius-Euler polynomials, Apostol-Bernoulli polynomials of higher order, Apostol-Genocchi polynomials of higher order, Stirling numbers of second kind, generalized Pascal matrix |
| description |
In this paper, we introduce a new extension of the generalized ApostolFrobenius-Euler polynomials H [m−1,α] n (x; c, a; λ; u). We give some algebraic and differential properties, as well as, relationships between this polynomials class with other polynomials and numbers. We also, introduce the generalized ApostolFrobenius-Euler polynomials matrix U [m−1,α] (x; c, a; λ; u) and the new generalized Apostol-Frobenius-Euler matrix U [m−1,α] (c, a; λ; u), we deduce a product formula for U [m−1,α] (x; c, a; λ; u) and provide some factorizations of the Apostol-Frobenius-Euler polynomial matrix U [m−1,α] (x; c, a; λ; u), which involving the generalized Pascal matrix. |
| publishDate |
2018 |
| dc.date.submitted.none.fl_str_mv |
2018-06-06 |
| dc.date.issued.none.fl_str_mv |
2019-01-25 |
| dc.date.accessioned.none.fl_str_mv |
2022-11-15T20:49:38Z |
| dc.date.available.none.fl_str_mv |
2022-11-15T20:49:38Z |
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http://purl.org/coar/version/c_970fb48d4fbd8a85 |
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http://purl.org/coar/resource_type/c_2df8fbb1 |
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info:eu-repo/semantics/article |
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info:eu-repo/semantics/publishedVersion |
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Artículo |
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publishedVersion |
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https://hdl.handle.net/20.500.12834/890 |
| dc.identifier.doi.none.fl_str_mv |
10.46793/KgJMat2103.393O |
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Universidad del Atlántico |
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Repositorio Universidad del Atlántico |
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https://hdl.handle.net/20.500.12834/890 |
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10.46793/KgJMat2103.393O Universidad del Atlántico Repositorio Universidad del Atlántico |
| dc.language.iso.spa.fl_str_mv |
eng |
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eng |
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http://creativecommons.org/licenses/by-nc/4.0/ |
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Attribution-NonCommercial 4.0 International |
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info:eu-repo/semantics/openAccess |
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http://creativecommons.org/licenses/by-nc/4.0/ Attribution-NonCommercial 4.0 International http://purl.org/coar/access_right/c_abf2 |
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openAccess |
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Sede Norte |
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Universidad de la costa |
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ORTEGA, MARÍA JOSÉ6260da4a-d027-4383-b6ec-0a094433e42dRAMÍREZ, WILLIAMURIELES, ALEJANDRO2022-11-15T20:49:38Z2022-11-15T20:49:38Z2019-01-252018-06-06https://hdl.handle.net/20.500.12834/89010.46793/KgJMat2103.393OUniversidad del AtlánticoRepositorio Universidad del AtlánticoIn this paper, we introduce a new extension of the generalized ApostolFrobenius-Euler polynomials H [m−1,α] n (x; c, a; λ; u). We give some algebraic and differential properties, as well as, relationships between this polynomials class with other polynomials and numbers. We also, introduce the generalized ApostolFrobenius-Euler polynomials matrix U [m−1,α] (x; c, a; λ; u) and the new generalized Apostol-Frobenius-Euler matrix U [m−1,α] (c, a; λ; u), we deduce a product formula for U [m−1,α] (x; c, a; λ; u) and provide some factorizations of the Apostol-Frobenius-Euler polynomial matrix U [m−1,α] (x; c, a; λ; u), which involving the generalized Pascal matrix.application/pdfenghttp://creativecommons.org/licenses/by-nc/4.0/Attribution-NonCommercial 4.0 Internationalinfo:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Universidad de la costaNEW GENERALIZED APOSTOL-FROBENIUS-EULER POLYNOMIALS AND THEIR MATRIX APPROACHPúblico general. Generalized Apostol-type polynomials, Apostol-Frobennius-Euler polynomials, Apostol-Bernoulli polynomials of higher order, Apostol-Genocchi polynomials of higher order, Stirling numbers of second kind, generalized Pascal matrixinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArtículohttp://purl.org/coar/version/c_970fb48d4fbd8a85http://purl.org/coar/resource_type/c_2df8fbb1BarranquillaSede Norte1] R. Askey, Orthogonal Polynomials and Special Functions, Regional Conference Series in Applied Mathematics, SIAM. J. W. Arrowsmith Ltd., Bristol, England, 1975.[2] L. Carlitz, Eulerian numbers and polynomials, Math. Mag. 32 (1959), 247–260.[3] G. Call and D. J. Velleman, Pascal’s matrices, Amer. Math. Monthly 100 (1993), 372–376.[4] L. Castilla, W. Ramírez and A. Urieles, An extended generalized q-extensions for the Apostol type polynomials, Abstr. Appl. Anal. 2018 (2018), 1–13.[5] L. Comtet, Advanced Combinatorics: The Art of Finite and Infinite Expansions, Reidel, Dordrecht, Boston, 1974.[6] R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics, Addison-Wesley, New York, 1994[7] L. Hernández, Y. Quintana and A. Urieles, About extensions of generalized Apostol-type polynomials, Results Math. 68 (2015), 203–225[8] B. Kurt and Y. Simsek, On the generalized Apostol-type Frobenius-Euler polynomials, Adv. Difference Equ. 2013 (2013), 1–9.[9] Q. M. Luo, Extensions of the Genocchi polynomials and its Fourier expansions and integral representations, Osaka J. Math. 48 (2011), 291–309.[10] Q. M. Luo and H. M. Srivastava, Some relationships between the Apostol-Bernoulli and ApostolEuler polynomials, Comput. Math. Appl. 51 (2006), 631–642.[11] P. Natalini and A. Bernardini, A generalization of the Bernoulli polynomials, J. Appl. Math. 3 (2003), 155–163[12] Y. Quintana, W. Ramírez and A. Urieles, On an operational matrix method based on generalized Bernoulli polynomials of level m, Calcolo 55 (2018), 23–40.13] Y. Quintana, W. Ramírez and A. Urieles, Generalized Apostol-type polynomial matrix and its algebraic properties. Math. Repor. 21(2) (2019).[14] Z. Zhang and J. Wang, Bernoulli matrix and its algebraic properties, Discrete Appl. Math. 154 (2006), 1622–1632.http://purl.org/coar/resource_type/c_6501CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8914https://repositorio.uniatlantico.edu.co/bitstream/20.500.12834/890/2/license_rdf24013099e9e6abb1575dc6ce0855efd5MD52LICENSElicense.txtlicense.txttext/plain; charset=utf-81306https://repositorio.uniatlantico.edu.co/bitstream/20.500.12834/890/3/license.txt67e239713705720ef0b79c50b2ececcaMD53ORIGINALkjm_45_3-6.pdfkjm_45_3-6.pdfapplication/pdf499341https://repositorio.uniatlantico.edu.co/bitstream/20.500.12834/890/1/kjm_45_3-6.pdfbb2a10bdc61507bdafb05f694616b12dMD5120.500.12834/890oai:repositorio.uniatlantico.edu.co:20.500.12834/8902022-11-15 15:49:39.276DSpace de la Universidad de Atlánticosysadmin@mail.uniatlantico.edu.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 |