Fourier expansion and integral representation generalized Apostol-type Frobenius–Euler polynomials
The main purpose of this paper is to investigate the Fourier series representation of the generalized Apostol-type Frobenius–Euler polynomials, and using the above-mentioned series we find its integral representation. At the same time applying the Fourier series representation of the Apostol Frobeni...
- Autores:
-
Urieles, Alejandro
- Tipo de recurso:
- Fecha de publicación:
- 2020
- Institución:
- Universidad del Atlántico
- Repositorio:
- Repositorio Uniatlantico
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.uniatlantico.edu.co:20.500.12834/894
- Acceso en línea:
- https://hdl.handle.net/20.500.12834/894
- Palabra clave:
- Generalized Apostol Frobenius–Euler polynomials; Hurwitz zeta function; Fourier expansion; Generalized Apostol Frobennius–Euler numbers
- Rights
- openAccess
- License
- http://creativecommons.org/licenses/by-nc/4.0/
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Fourier expansion and integral representation generalized Apostol-type Frobenius–Euler polynomials |
| title |
Fourier expansion and integral representation generalized Apostol-type Frobenius–Euler polynomials |
| spellingShingle |
Fourier expansion and integral representation generalized Apostol-type Frobenius–Euler polynomials Generalized Apostol Frobenius–Euler polynomials; Hurwitz zeta function; Fourier expansion; Generalized Apostol Frobennius–Euler numbers |
| title_short |
Fourier expansion and integral representation generalized Apostol-type Frobenius–Euler polynomials |
| title_full |
Fourier expansion and integral representation generalized Apostol-type Frobenius–Euler polynomials |
| title_fullStr |
Fourier expansion and integral representation generalized Apostol-type Frobenius–Euler polynomials |
| title_full_unstemmed |
Fourier expansion and integral representation generalized Apostol-type Frobenius–Euler polynomials |
| title_sort |
Fourier expansion and integral representation generalized Apostol-type Frobenius–Euler polynomials |
| dc.creator.fl_str_mv |
Urieles, Alejandro |
| dc.contributor.author.none.fl_str_mv |
Urieles, Alejandro |
| dc.contributor.other.none.fl_str_mv |
Ramírez, William Ortega, María José Bedoya, Daniel |
| dc.subject.keywords.spa.fl_str_mv |
Generalized Apostol Frobenius–Euler polynomials; Hurwitz zeta function; Fourier expansion; Generalized Apostol Frobennius–Euler numbers |
| topic |
Generalized Apostol Frobenius–Euler polynomials; Hurwitz zeta function; Fourier expansion; Generalized Apostol Frobennius–Euler numbers |
| description |
The main purpose of this paper is to investigate the Fourier series representation of the generalized Apostol-type Frobenius–Euler polynomials, and using the above-mentioned series we find its integral representation. At the same time applying the Fourier series representation of the Apostol Frobenius–Genocchi and Apostol Genocchi polynomials, we obtain its integral representation. Furthermore, using the Hurwitz–Lerch zeta function we introduce the formula in rational arguments of the generalized Apostol-type Frobenius–Euler polynomials in terms of the Hurwitz zeta function. Finally, we show the representation of rational arguments of the Apostol Frobenius Euler polynomials and the Apostol Frobenius–Genocchi polynomials. |
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2020 |
| dc.date.issued.none.fl_str_mv |
2020-09-29 |
| dc.date.submitted.none.fl_str_mv |
2020-04-16 |
| dc.date.accessioned.none.fl_str_mv |
2022-11-15T20:50:24Z |
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2022-11-15T20:50:24Z |
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Artículo |
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https://hdl.handle.net/20.500.12834/894 |
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10.1186/s13662-020-02988-0 |
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Universidad del Atlántico |
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Repositorio Universidad del Atlántico |
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https://hdl.handle.net/20.500.12834/894 |
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10.1186/s13662-020-02988-0 Universidad del Atlántico Repositorio Universidad del Atlántico |
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eng |
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eng |
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A springerOpern Journal |
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Urieles, Alejandro0391d4c9-f0b6-40f2-9037-d06f46fb798bRamírez, WilliamOrtega, María JoséBedoya, Daniel2022-11-15T20:50:24Z2022-11-15T20:50:24Z2020-09-292020-04-16https://hdl.handle.net/20.500.12834/89410.1186/s13662-020-02988-0Universidad del AtlánticoRepositorio Universidad del AtlánticoThe main purpose of this paper is to investigate the Fourier series representation of the generalized Apostol-type Frobenius–Euler polynomials, and using the above-mentioned series we find its integral representation. At the same time applying the Fourier series representation of the Apostol Frobenius–Genocchi and Apostol Genocchi polynomials, we obtain its integral representation. Furthermore, using the Hurwitz–Lerch zeta function we introduce the formula in rational arguments of the generalized Apostol-type Frobenius–Euler polynomials in terms of the Hurwitz zeta function. Finally, we show the representation of rational arguments of the Apostol Frobenius Euler polynomials and the Apostol Frobenius–Genocchi polynomials.application/pdfenghttp://creativecommons.org/licenses/by-nc/4.0/Attribution-NonCommercial 4.0 Internationalinfo:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2A springerOpern JournalFourier expansion and integral representation generalized Apostol-type Frobenius–Euler polynomialsPúblico generalGeneralized Apostol Frobenius–Euler polynomials; Hurwitz zeta function; Fourier expansion; Generalized Apostol Frobennius–Euler numbersinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArtículohttp://purl.org/coar/version/c_970fb48d4fbd8a85http://purl.org/coar/resource_type/c_2df8fbb1BarranquillaMatemáticasSede Norte1. Alkan, M., Simsek, Y.: Generating function for q-Eulerian polynomials and their decomposition and applications. Fixed Point Theory Appl. 2013(72), 1 (2013). https://doi.org/10.1186/1687-1812-2013-722. Araci, S., Acikgoz, M.: Construction of Fourier expansion of Apostol Frobenius–Euler polynomials and its applications. Adv. Differ. Equ. 2018, 67 (2018). https://doi.org/10.1186/s13662-018-1526-x3. Bayad, A.: Fourier expansion for Apostol Bernoulli, Apostol Euler and Apostol Genocchi polynomials. Math. Comput. 80, 2219–2221 (2011). https://doi.org/10.1090/S0025-5718-2011-02476-24. Bayad, A., Kim, T.: Identities for Apostol-type Frobenius–Euler polynomiasl resulting from the study of a nonlinear operator. Russ. J. Math. Phys. 23, 164–171 (2016). https://doi.org/10.1134/S10619208160200235. Cangul, I.N., Cevik, A.S., Simsek, Y.: Generalization of q-Apostol-type Eulerian numbers and polynomials, and their interpolation functions. Adv. Stud. Contemp. Math. 25(2), 211–220 (2015)6. Carlitz, L.: Eulerian numbers and polynomials. Math. Mag. 32, 247–260 (1959). https://doi.org/10.2307/30292257. Conway, J.B.: Functions of One Complex Variables. Springer, Berlin (1978)8. Cristina, B., Roberto, B.: Fourier expansions for higher-order Apostol–Genocchi, Apostol–Bernoulli and Apostol–Euler polynomialsv. Adv. Differ. Equ. 2020, 346 (2020). https://doi.org/10.1186/s13662-020-02802-x9. Follan, G.: Fourier Analysis and Its Applications (1992)10. Kim, T.: An identity of the symmetry for the Frobenius–Euler polynomials associated with the fermionic p-adic invariant q-integrals on Zp. Rocky Mt. J. Math. 41, 239–247 (2011)11. Kucukoglu, I., Simsek, Y.: Identities and relations on the q-Apostol type Frobenius–Euler numbers and polynomials. J. Korean Math. Soc. 56(1), 265–284 (2019). https://doi.org/10.4134/JKMS.j18018512. Kucukoglu, I., Simsek, Y., Srivastava, H.M.: A new family of Lerch-type zeta functions interpolating a certain class of higher-order Apostol-type numbers and Apostol-type polynomials. Quaest. Math. 42 465–478 (2019). https://doi.org/10.2989/16073606.2018.145992513. Kurt, B., Simsek, Y.: On the generalized Apostol-type Frobenius–Euler polynomials. Adv. Differ. Equ. 2013, 1 (2013). https://doi.org/10.1186/1687-1847-2013-114. Luo, Q.: Fourier expansion and integral representations for the Apostol Bernoulli and Apostol Euler polynomials. Math. Comput. 78, 2193–2208 (2009)15. Luo, Q.-M.: Extensions of the Genocchi polynomials and its Fourier expansions and integral representations. Osaka J. Math. 48, 291–309 (2011)16. Quintana, Y., Ramírez, W., Urieles, A.: Euler matrices and their algebraic properties revisited. Appl. Math. Inf. Sci. 14(4), 583–596 (2020). https://doi.org/10.18576/amis/14040717. Ramírez, W., Ortega, M., Urieles, A.: New generalized Apostol Frobenius–Euler polynomials and their matrix approach. Kragujev. J. Math. 45(3), 393–407 (2021)18. Simsek, Y.: Generating functions for generalized Stirling type numbers, array type polynomials, Eulerian type polynomials and their application. Fixed Point Theory Appl. 2013(87), 1 (2013). https://doi.org/10.1186/1687-1812-2013-8719. Srivastava, H.M., Choi, J.: Zeta and q-Zeta Functions and Associated Series and Integrals. Elsevier, Amsterdam (2012)20. Srivastava, H.M., Kurt, B., Simsek, Y.: Some families of Genocchi type polynomials and their interpolation functions. Integral Transforms Spec. Funct. 23(12), 919–938 (2012). https://doi.org/10.1080/10652469.2011.64362721. Yilmaz, S.: Generating functions for q-Apostol type Frobenius–Euler numbers and polynomials. Axioms 1(3), 395–403 (2012). https://doi.org/10.3390/axioms1030395http://purl.org/coar/resource_type/c_6501ORIGINALs13662-020-02988-0.pdfs13662-020-02988-0.pdfapplication/pdf1509460https://repositorio.uniatlantico.edu.co/bitstream/20.500.12834/894/1/s13662-020-02988-0.pdf7bcff39f2a974e7da3115aabdfd2d9dfMD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8914https://repositorio.uniatlantico.edu.co/bitstream/20.500.12834/894/2/license_rdf24013099e9e6abb1575dc6ce0855efd5MD52LICENSElicense.txtlicense.txttext/plain; charset=utf-81306https://repositorio.uniatlantico.edu.co/bitstream/20.500.12834/894/3/license.txt67e239713705720ef0b79c50b2ececcaMD5320.500.12834/894oai:repositorio.uniatlantico.edu.co:20.500.12834/8942022-11-15 15:50:25.472DSpace de la Universidad de Atlánticosysadmin@mail.uniatlantico.edu.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 |