New biparametric families of apostol-frobenius-euler polynomials of level m
We introduce two biparametric families of Apostol-Frobenius-Euler polynomials of level-mm. We give some algebraic properties, as well as some other identities which connect these polynomial class with the generalized λλ-Stirling type numbers of the second kind, the generalized Apostol--Bernoulli pol...
- Autores:
-
Bedoya, D.
Ortega, M.
Ramírez, W.
Urieles, A.
- 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:11323/8005
- Acceso en línea:
- https://hdl.handle.net/11323/8005
https://doi.org/10.30970/ms.55.1.10-23
https://repositorio.cuc.edu.co/
- Palabra clave:
- Generalized Apostol-type polynomials
Apostol–frobennius–euler polynomials
Apostol-bernoulli polynomials of higher order
Apostol–genocchi polynomials of higher order
Generalized λ -Stirling numbers of second kind
- Rights
- openAccess
- License
- CC0 1.0 Universal
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New biparametric families of apostol-frobenius-euler polynomials of level m |
| title |
New biparametric families of apostol-frobenius-euler polynomials of level m |
| spellingShingle |
New biparametric families of apostol-frobenius-euler polynomials of level m Generalized Apostol-type polynomials Apostol–frobennius–euler polynomials Apostol-bernoulli polynomials of higher order Apostol–genocchi polynomials of higher order Generalized λ -Stirling numbers of second kind |
| title_short |
New biparametric families of apostol-frobenius-euler polynomials of level m |
| title_full |
New biparametric families of apostol-frobenius-euler polynomials of level m |
| title_fullStr |
New biparametric families of apostol-frobenius-euler polynomials of level m |
| title_full_unstemmed |
New biparametric families of apostol-frobenius-euler polynomials of level m |
| title_sort |
New biparametric families of apostol-frobenius-euler polynomials of level m |
| dc.creator.fl_str_mv |
Bedoya, D. Ortega, M. Ramírez, W. Urieles, A. |
| dc.contributor.author.spa.fl_str_mv |
Bedoya, D. Ortega, M. Ramírez, W. Urieles, A. |
| dc.subject.spa.fl_str_mv |
Generalized Apostol-type polynomials Apostol–frobennius–euler polynomials Apostol-bernoulli polynomials of higher order Apostol–genocchi polynomials of higher order Generalized λ -Stirling numbers of second kind |
| topic |
Generalized Apostol-type polynomials Apostol–frobennius–euler polynomials Apostol-bernoulli polynomials of higher order Apostol–genocchi polynomials of higher order Generalized λ -Stirling numbers of second kind |
| description |
We introduce two biparametric families of Apostol-Frobenius-Euler polynomials of level-mm. We give some algebraic properties, as well as some other identities which connect these polynomial class with the generalized λλ-Stirling type numbers of the second kind, the generalized Apostol--Bernoulli polynomials, the generalized Apostol--Genocchi polynomials, the generalized Apostol--Euler polynomials and Jacobi polynomials. Finally, we will show the differential properties of this new family of polynomials. |
| publishDate |
2021 |
| dc.date.accessioned.none.fl_str_mv |
2021-03-12T21:34:06Z |
| dc.date.available.none.fl_str_mv |
2021-03-12T21:34:06Z |
| dc.date.issued.none.fl_str_mv |
2021 |
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Artículo de revista |
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http://purl.org/coar/resource_type/c_2df8fbb1 |
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Text |
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acceptedVersion |
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1027-4634 2411-0620 |
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https://hdl.handle.net/11323/8005 |
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https://doi.org/10.30970/ms.55.1.10-23 |
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Corporación Universidad de la Costa |
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REDICUC - Repositorio CUC |
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https://repositorio.cuc.edu.co/ |
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1027-4634 2411-0620 Corporación Universidad de la Costa REDICUC - Repositorio CUC |
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| dc.language.iso.none.fl_str_mv |
eng |
| language |
eng |
| dc.relation.references.spa.fl_str_mv |
1. Araci S., Acikgoz M., Construction of fourier expansion of Apostol Frobenius-Euler polynomials and its applications, Adv. Difference Equ., 2018. 2. Askey R., Orthogonal polynomials and special functions, Regional Conference Series in Applied Mathematics, SIAM. J. W. Arrowsmith Ltd., Bristol 3, England, 1975. 3. Carlitz L., Eulerian numbers and polynomials, Math. Mag., 32 (1959), 247–260. 4. Comtet L., Advanced combinatorics: the art of finite and infinite expansions, Reidel, Dordrecht and Boston, 1974. 5. Graham R.L., Knuth D.E., Patashnik O., Concrete Mathematics, Addison-Wesley Publishing Company, Inc., New York, 1994. 6. Kurt B., Simsek Y., On the generalized Apostol-type Frobenius-Euler polynomials, Adv. Difference Equ., 1 (2013). 7. Masjed-Jamei M., Koepf W., Symbolic computation of some power-trigonometric series, J. Symbolic Comput., 80 (2017), 273–284. 8. Natalini P., Bernardini A., A generalization of the Bernoulli polynomials, J. Appl. Math., 3 (2003), 155–163. 9. Kilar N., Simsek Y., Two parametric kinds of Eulerian-type polynomials associated with Eulers formula, Symmetry, 11 (2019), 1–19. 10. Quintana Y., Ram´irez W., Urieles A., On an operational matrix method based on generalized Bernoulli polynomials of level m, Calcolo, 53 (2018). 11. Quintana Y., Ram´irez W., Urieles G., Generalized Apostol-type polynomial matrix and its algebraic properties, Math. Repor., 2, (2019), №2. 12. Quintana Y., Ram´irez, W., Urieles A., Euler matrices and their algebraic properties revisited, Appl. Math. Inf. Sci., 14, (2020), №4, 583–596. 13. Ram´irez W., Castilla L., Urieles A., An extended generalized q–extensions for the Apostol type polynomials, Abstr. Appl. Anal., 2018, Article ID 2937950, DOI: 10.1155/2018/2937950. 14. Ortega M., Ramirez W., Urieles A., New generalized Apostol–Frobenius-Euler polynomials and their matrix approach, Kragujevac. Journal. of Mathematics, 45 (2021), 393–407. 15. Simsek Y., Generating functions for generalized Stirling type numbers, array type polynomials, Eulerian type polynomials and their application, Fixed point Theory and Applications, 87 (2013). 16. Y. Simsek, q–Analogue of twisted l–series and q–twisted Euler numbers, Journal of Number Theory, 110 (2005), 267–278. 17. Y. Simsek, Generating functions for q–Apostol type Frobenius–Euler numbers and polynomials, Axioms, 1 (2012), 395–403; doi:10.3390/axioms1030395. 18. Y. Simsek, O. Yurekli, V. Kurt, On interpolation functions of the twisted generalized Frobenius–Euler numbers, Advanced Studies in Contemporary Math., 15 (2007), №2, 187–194. 19. Y. Simsek, T. Kim, H.M. Srivastava, q–Bernoulli numbers and polynomials associated with multiple q–zeta functions and basic L–series, Russ. J. Math. Phys., 12 (2005), №2, 241–268. 20. Y. Simsek, T. Kim, D.W. Park, Y.S. Ro, L.C. Jang, S.H. Rim, An explicit formula for the multiple Frobenius-Euler numbers and polynomials, JP J. Algebra Number Theory Appl., 4 (2004), №3, 519–529. 21. Srivastava H.M., Garg M., Choudhary S, A new generalization of the Bernoulli and related polynomials, Russian J. of Math. Phys., 17, (2010), 251–261. 22. Srivastava H.M., Garg M., Choudhary S., Some new families of generalized Euler and Genocchi polynomials, Taiwanese J. Math., 15 (2011), №1, 283–305. 23. Urieles A., Ortega M., Ramirez W., Veg S., New results on the q–generalized Bernoulli polynomials of level m, Demonstratio Mathematica, 52 (2019), 511–522. 24. Urieles A., Ram´irez W., Ortega M.J., et al., Fourier expansion and integral representation generalized Apostol-type Frobenius-Euler polynomials, Adv. Differ. Equ., 534 (2020), https://doi.org/ 10.1186/s13662-020-02988-0. |
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Bedoya, D.Ortega, M.Ramírez, W.Urieles, A.2021-03-12T21:34:06Z2021-03-12T21:34:06Z20211027-46342411-0620https://hdl.handle.net/11323/8005https://doi.org/10.30970/ms.55.1.10-23Corporación Universidad de la CostaREDICUC - Repositorio CUChttps://repositorio.cuc.edu.co/We introduce two biparametric families of Apostol-Frobenius-Euler polynomials of level-mm. We give some algebraic properties, as well as some other identities which connect these polynomial class with the generalized λλ-Stirling type numbers of the second kind, the generalized Apostol--Bernoulli polynomials, the generalized Apostol--Genocchi polynomials, the generalized Apostol--Euler polynomials and Jacobi polynomials. Finally, we will show the differential properties of this new family of polynomials.Bedoya, D.Ortega, M.Ramírez, W.Urieles, A.application/pdfengCorporación Universidad de la CostaCC0 1.0 Universalhttp://creativecommons.org/publicdomain/zero/1.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Matematychni Studiihttp://www.matstud.org.ua/ojs/index.php/matstud/article/view/70Generalized Apostol-type polynomialsApostol–frobennius–euler polynomialsApostol-bernoulli polynomials of higher orderApostol–genocchi polynomials of higher orderGeneralized λ -Stirling numbers of second kindNew biparametric families of apostol-frobenius-euler polynomials of level mArtículo 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/acceptedVersion1. Araci S., Acikgoz M., Construction of fourier expansion of Apostol Frobenius-Euler polynomials and its applications, Adv. Difference Equ., 2018.2. Askey R., Orthogonal polynomials and special functions, Regional Conference Series in Applied Mathematics, SIAM. J. W. Arrowsmith Ltd., Bristol 3, England, 1975.3. Carlitz L., Eulerian numbers and polynomials, Math. Mag., 32 (1959), 247–260.4. Comtet L., Advanced combinatorics: the art of finite and infinite expansions, Reidel, Dordrecht and Boston, 1974.5. Graham R.L., Knuth D.E., Patashnik O., Concrete Mathematics, Addison-Wesley Publishing Company, Inc., New York, 1994. 6. Kurt B., Simsek Y., On the generalized Apostol-type Frobenius-Euler polynomials, Adv. Difference Equ., 1 (2013).7. Masjed-Jamei M., Koepf W., Symbolic computation of some power-trigonometric series, J. Symbolic Comput., 80 (2017), 273–284.8. Natalini P., Bernardini A., A generalization of the Bernoulli polynomials, J. Appl. Math., 3 (2003), 155–163.9. Kilar N., Simsek Y., Two parametric kinds of Eulerian-type polynomials associated with Eulers formula, Symmetry, 11 (2019), 1–19.10. Quintana Y., Ram´irez W., Urieles A., On an operational matrix method based on generalized Bernoulli polynomials of level m, Calcolo, 53 (2018).11. Quintana Y., Ram´irez W., Urieles G., Generalized Apostol-type polynomial matrix and its algebraic properties, Math. Repor., 2, (2019), №2.12. Quintana Y., Ram´irez, W., Urieles A., Euler matrices and their algebraic properties revisited, Appl. Math. Inf. Sci., 14, (2020), №4, 583–596.13. Ram´irez W., Castilla L., Urieles A., An extended generalized q–extensions for the Apostol type polynomials, Abstr. Appl. Anal., 2018, Article ID 2937950, DOI: 10.1155/2018/2937950.14. Ortega M., Ramirez W., Urieles A., New generalized Apostol–Frobenius-Euler polynomials and their matrix approach, Kragujevac. Journal. of Mathematics, 45 (2021), 393–407.15. Simsek Y., Generating functions for generalized Stirling type numbers, array type polynomials, Eulerian type polynomials and their application, Fixed point Theory and Applications, 87 (2013).16. Y. Simsek, q–Analogue of twisted l–series and q–twisted Euler numbers, Journal of Number Theory, 110 (2005), 267–278.17. Y. Simsek, Generating functions for q–Apostol type Frobenius–Euler numbers and polynomials, Axioms, 1 (2012), 395–403; doi:10.3390/axioms1030395.18. Y. Simsek, O. Yurekli, V. Kurt, On interpolation functions of the twisted generalized Frobenius–Euler numbers, Advanced Studies in Contemporary Math., 15 (2007), №2, 187–194.19. Y. Simsek, T. Kim, H.M. Srivastava, q–Bernoulli numbers and polynomials associated with multiple q–zeta functions and basic L–series, Russ. J. Math. Phys., 12 (2005), №2, 241–268.20. Y. Simsek, T. Kim, D.W. Park, Y.S. Ro, L.C. Jang, S.H. Rim, An explicit formula for the multiple Frobenius-Euler numbers and polynomials, JP J. Algebra Number Theory Appl., 4 (2004), №3, 519–529.21. Srivastava H.M., Garg M., Choudhary S, A new generalization of the Bernoulli and related polynomials, Russian J. of Math. Phys., 17, (2010), 251–261.22. Srivastava H.M., Garg M., Choudhary S., Some new families of generalized Euler and Genocchi polynomials, Taiwanese J. Math., 15 (2011), №1, 283–305.23. Urieles A., Ortega M., Ramirez W., Veg S., New results on the q–generalized Bernoulli polynomials of level m, Demonstratio Mathematica, 52 (2019), 511–522.24. Urieles A., Ram´irez W., Ortega M.J., et al., Fourier expansion and integral representation generalized Apostol-type Frobenius-Euler polynomials, Adv. Differ. 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