New generalized apostol-frobenius-euler polynomials and their matrix approach

In this paper, we introduce a new extension of the generalized Apostol-Frobenius-Euler polynomials ℋn[m−1,α](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 generaliz...

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Autores:
Ortega, María José
Ramírez, William
Urieles, Alejandro
Tipo de recurso:
Article of journal
Fecha de publicación:
2021
Institución:
Corporación Universidad de la Costa
Repositorio:
REDICUC - Repositorio CUC
Idioma:
eng
OAI Identifier:
oai:repositorio.cuc.edu.co:11323/8632
Acceso en línea:
https://hdl.handle.net/11323/8632
https://doi.org/10.46793/KGJMAT2103.393O
https://repositorio.cuc.edu.co/
Palabra clave:
Generalized Apostol-type polynomial
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
Attribution-NonCommercial-NoDerivatives 4.0 International
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oai_identifier_str oai:repositorio.cuc.edu.co:11323/8632
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repository_id_str
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 polynomial
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
Ramírez, William
Urieles, Alejandro
dc.contributor.author.spa.fl_str_mv Ortega, María José
Ramírez, William
Urieles, Alejandro
dc.subject.spa.fl_str_mv Generalized Apostol-type polynomial
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 polynomial
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 Apostol-Frobenius-Euler polynomials ℋn[m−1,α](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 Apostol-Frobenius-Euler polynomials matrix ????[m−1,α](x; c,a; λ; u) and the new generalized Apostol-Frobenius-Euler matrix ????[m−1,α](c,a; λ; u), we deduce a product formula for ????[m−1,α](x; c,a; λ; u) and provide some factorizations of the Apostol-Frobenius-Euler polynomial matrix ????[m−1,α](x; c,a; λ; u), which involving the generalized Pascal matrix.
publishDate 2021
dc.date.accessioned.none.fl_str_mv 2021-09-06T14:18:52Z
dc.date.available.none.fl_str_mv 2021-09-06T14:18:52Z
dc.date.issued.none.fl_str_mv 2021
dc.type.spa.fl_str_mv Artículo de revista
dc.type.coar.fl_str_mv http://purl.org/coar/resource_type/c_2df8fbb1
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dc.type.content.spa.fl_str_mv Text
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dc.identifier.uri.spa.fl_str_mv https://hdl.handle.net/11323/8632
dc.identifier.doi.spa.fl_str_mv https://doi.org/10.46793/KGJMAT2103.393O
dc.identifier.instname.spa.fl_str_mv Corporación Universidad de la Costa
dc.identifier.reponame.spa.fl_str_mv REDICUC - Repositorio CUC
dc.identifier.repourl.spa.fl_str_mv https://repositorio.cuc.edu.co/
url https://hdl.handle.net/11323/8632
https://doi.org/10.46793/KGJMAT2103.393O
https://repositorio.cuc.edu.co/
identifier_str_mv Corporación Universidad de la Costa
REDICUC - Repositorio CUC
dc.language.iso.none.fl_str_mv eng
language eng
dc.relation.references.spa.fl_str_mv R. Askey, Orthogonal Polynomials and Special Functions, Regional Conference Series in Applied Mathematics, SIAM. J. W. Arrowsmith Ltd., Bristol, England, 1975.
L. Carlitz, Eulerian numbers and polynomials, Math. Mag. 32 (1959), 247–260.
G. Call and D. J. Velleman, Pascal’s matrices, Amer. Math. Monthly 100 (1993), 372–376.
L. Castilla, W. Ramírez and A. Urieles, An extended generalized q-extensions for the Apostol type polynomials, Abstr. Appl. Anal. 2018 (2018), 1–13.
L. Comtet, Advanced Combinatorics: The Art of Finite and Infinite Expansions, Reidel, Dordrecht, Boston, 1974.
R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics, Addison-Wesley, New York, 1994.
L. Hernández, Y. Quintana and A. Urieles, About extensions of generalized Apostol-type polynomials, Results Math. 68 (2015), 203–225.
B. Kurt and Y. Simsek, On the generalized Apostol-type Frobenius-Euler polynomials, Adv. Difference Equ. 2013 (2013), 1–9.
Q. M. Luo, Extensions of the Genocchi polynomials and its Fourier expansions and integral representations, Osaka J. Math. 48 (2011), 291–309.
Q. M. Luo and H. M. Srivastava, Some relationships between the Apostol-Bernoulli and Apostol-Euler polynomials, Comput. Math. Appl. 51 (2006), 631–642.
P. Natalini and A. Bernardini, A generalization of the Bernoulli polynomials, J. Appl. Math. 3 (2003), 155–163.
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.
Y. Quintana, W. Ramírez and A. Urieles, Generalized Apostol-type polynomial matrix and its algebraic properties. Math. Repor. 21(2) (2019).
Z. Zhang and J. Wang, Bernoulli matrix and its algebraic properties, Discrete Appl. Math. 154 (2006), 1622–1632.
dc.rights.spa.fl_str_mv Attribution-NonCommercial-NoDerivatives 4.0 International
dc.rights.uri.spa.fl_str_mv http://creativecommons.org/licenses/by-nc-nd/4.0/
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dc.source.spa.fl_str_mv Kragujevac Journal of Mathematics
institution Corporación Universidad de la Costa
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spelling Ortega, María JoséRamírez, WilliamUrieles, Alejandro2021-09-06T14:18:52Z2021-09-06T14:18:52Z2021https://hdl.handle.net/11323/8632https://doi.org/10.46793/KGJMAT2103.393OCorporación Universidad de la CostaREDICUC - Repositorio CUChttps://repositorio.cuc.edu.co/In this paper, we introduce a new extension of the generalized Apostol-Frobenius-Euler polynomials ℋn[m−1,α](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 Apostol-Frobenius-Euler polynomials matrix ????[m−1,α](x; c,a; λ; u) and the new generalized Apostol-Frobenius-Euler matrix ????[m−1,α](c,a; λ; u), we deduce a product formula for ????[m−1,α](x; c,a; λ; u) and provide some factorizations of the Apostol-Frobenius-Euler polynomial matrix ????[m−1,α](x; c,a; λ; u), which involving the generalized Pascal matrix.Ortega, María JoséRamírez, WilliamUrieles, Alejandroapplication/pdfengAttribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Kragujevac Journal of Mathematicshttps://imi.pmf.kg.ac.rs/kjm/en/index.php?page=10.46793/KgJMat2103.393OGeneralized Apostol-type polynomialApostol-Frobennius-Euler polynomialsApostol-Bernoulli polynomials of higher orderApostol-Genocchi polynomials of higher orderStirling numbers of second kindgeneralized Pascal matrixNew generalized apostol-frobenius-euler polynomials and their matrix approachArtículo 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/acceptedVersionR. Askey, Orthogonal Polynomials and Special Functions, Regional Conference Series in Applied Mathematics, SIAM. J. W. Arrowsmith Ltd., Bristol, England, 1975.L. Carlitz, Eulerian numbers and polynomials, Math. Mag. 32 (1959), 247–260.G. Call and D. J. Velleman, Pascal’s matrices, Amer. Math. Monthly 100 (1993), 372–376.L. Castilla, W. Ramírez and A. Urieles, An extended generalized q-extensions for the Apostol type polynomials, Abstr. Appl. Anal. 2018 (2018), 1–13.L. Comtet, Advanced Combinatorics: The Art of Finite and Infinite Expansions, Reidel, Dordrecht, Boston, 1974.R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics, Addison-Wesley, New York, 1994.L. Hernández, Y. Quintana and A. Urieles, About extensions of generalized Apostol-type polynomials, Results Math. 68 (2015), 203–225.B. Kurt and Y. Simsek, On the generalized Apostol-type Frobenius-Euler polynomials, Adv. Difference Equ. 2013 (2013), 1–9.Q. M. Luo, Extensions of the Genocchi polynomials and its Fourier expansions and integral representations, Osaka J. Math. 48 (2011), 291–309.Q. M. Luo and H. M. Srivastava, Some relationships between the Apostol-Bernoulli and Apostol-Euler polynomials, Comput. Math. Appl. 51 (2006), 631–642.P. Natalini and A. Bernardini, A generalization of the Bernoulli polynomials, J. Appl. Math. 3 (2003), 155–163.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.Y. Quintana, W. Ramírez and A. Urieles, Generalized Apostol-type polynomial matrix and its algebraic properties. Math. Repor. 21(2) (2019).Z. Zhang and J. Wang, Bernoulli matrix and its algebraic properties, Discrete Appl. 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