New results on the q-generalized Bernoulli polynomials of level m
This paper aims to show new algebraic properties from the q-generalized Bernoulli polynomials B[m−1]n(x;q) of level m, as well as some others identities which connect this polynomial class with the q-generalized Bernoulli polynomials of level m, as well as the q-gamma function, and the q-Stirling nu...
- Autores:
-
Urieles Guerrero, Alejandro
Ortega, María José
Ramírez, William
Vega, Samuel
- Tipo de recurso:
- Article of journal
- Fecha de publicación:
- 2019
- Institución:
- Corporación Universidad de la Costa
- Repositorio:
- REDICUC - Repositorio CUC
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.cuc.edu.co:11323/5799
- Acceso en línea:
- http://hdl.handle.net/11323/5799
https://repositorio.cuc.edu.co/
- Palabra clave:
- q-generalized Bernoulli polynomials
q-gamma function
q-Stirling numbers
q-Bernstein poly-nomials
- Rights
- openAccess
- License
- CC0 1.0 Universal
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New results on the q-generalized Bernoulli polynomials of level m |
| title |
New results on the q-generalized Bernoulli polynomials of level m |
| spellingShingle |
New results on the q-generalized Bernoulli polynomials of level m q-generalized Bernoulli polynomials q-gamma function q-Stirling numbers q-Bernstein poly-nomials |
| title_short |
New results on the q-generalized Bernoulli polynomials of level m |
| title_full |
New results on the q-generalized Bernoulli polynomials of level m |
| title_fullStr |
New results on the q-generalized Bernoulli polynomials of level m |
| title_full_unstemmed |
New results on the q-generalized Bernoulli polynomials of level m |
| title_sort |
New results on the q-generalized Bernoulli polynomials of level m |
| dc.creator.fl_str_mv |
Urieles Guerrero, Alejandro Ortega, María José Ramírez, William Vega, Samuel |
| dc.contributor.author.spa.fl_str_mv |
Urieles Guerrero, Alejandro Ortega, María José Ramírez, William Vega, Samuel |
| dc.subject.spa.fl_str_mv |
q-generalized Bernoulli polynomials q-gamma function q-Stirling numbers q-Bernstein poly-nomials |
| topic |
q-generalized Bernoulli polynomials q-gamma function q-Stirling numbers q-Bernstein poly-nomials |
| description |
This paper aims to show new algebraic properties from the q-generalized Bernoulli polynomials B[m−1]n(x;q) of level m, as well as some others identities which connect this polynomial class with the q-generalized Bernoulli polynomials of level m, as well as the q-gamma function, and the q-Stirling numbers of the second kind and the q-Bernstein polynomials. |
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2019 |
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2019-09-17 |
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2020-01-10T19:08:04Z |
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2020-01-10T19:08:04Z |
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Artículo de revista |
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http://purl.org/coar/resource_type/c_2df8fbb1 |
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0420-1213 2391-4661 |
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http://hdl.handle.net/11323/5799 |
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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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| dc.language.iso.none.fl_str_mv |
eng |
| language |
eng |
| dc.relation.ispartof.spa.fl_str_mv |
https://doi.org/10.1515/dema-2019-0039 |
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[1] Natalini P., Bernardini A., A generalization of the Bernoulli polynomials, J. Appl. Math., 2003, 3, 155–163 [2] Carlitz L., q-Bernoulli numbers and polynomials, Duke Math., 1948, 15, 987–1000 [3] Choi J., Anderson P., Srivastava H. M., Carlitz’s q-Bernoulli and q-Euler numbers and polynomials and a class of q-Hurwitz zeta functions, Appl. Math. Comput., 2009, 215, 1185–1208 [4] Ernst T., q-Bernoulli and q-Euler polynomials, an umbral approach, Int. J. Difference Equ., 2006, 1, 31–80 [5] Hegazi A. S., Mansour M., A note on q-Bernoulli numbers and polynomials, J. Nonlinear Math. Phys., 2006, 13(1), 9–18 [6] Kim D., Kim M.-S., A note on Carlitz q-Bernoulli numbers and polynomials, Adv. Difference Equ., 2012, 2012:44 [7] Quintana Y., Ramírez W., Urieles A., Generalized Apostol-type polynomials matrix and its algebraic properties, Math. Rep., 2019, 21, 249–264 [8] Ryoo C. S., A note on q-Bernoulli numbers and polynomials, Appl. Math. Lett, 2017, 20(5), 524–531 [9] Garg M., Alha S., A new class of q-Apostol-Bernoulli polynomials of order α, Revi. Tecn. URU, 2014, 6, 67–76 [10] Hernandes P., Quintana Y., Urieles A., About extensions of generalized Apostol-type polynomials, Res. Math., 2015, 68, 203–225 [11] KurtB.,AfurthergeneralizationoftheBernoullipolynomialsandonthe2D-Bernoullipolynomials B2n(x, y),Appl.Math.Sci., 2010, 4(47), 2315–2322 [12] KurtB.,SomerelationshipsbetweenthegeneralizedApostol-BernoulliandApostol-Eulerpolynomials,Turk.Jou.Ana.Num. The., 2013, 1(1), 54–58 [13] LuoQ.-M.,GuoB.-N.,QiF.,DebnathL.,GeneralizationsofBernoullinumbersandpolynomials,Int.J.Math.Math.Sci.,2003, 59, 3769–3776 [14] Mahmudov N. I., On a class of q-Bernoulli and q-Euler polynomials, Adv. Difference Equ., 2013, 1, 108–125 [15] Ramírez 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 [16] Tremblay R., Gaboury S., Fugere J., A further generalization of Apostol-Bernoulli polynomials and related polynomials, Hon. Math. Jou., 2012, 34, 311–326 [17] Quintana Y., Ramírez W., Urieles A., On an operational matrix method based on generalized Bernoulli polynomials of level m, Calcolo, 2018, 55, 30 [18] Mahmudov N. I., Eini Keleshteri M., q-extensions for the Apostol type polynomials, J. Appl. Math., 2014, Article ID 868167, http://dx.doi.org/10.1155/2014/868167 [19] Ernst T., The history of q-calculus and a new method, Licentiate Thesis, Dep. Math. Upps. Unive., 2000 [20] Gasper G., Rahman M., Basic Hypergeometric Series, Cambr. Univ. Press, 2004 [21] Kac V., Cheung P., Quantum Calculus, Springer-Verlag New York, 2002 [22] Araci S., Duran U., Acikgoz M., (p, q)-Volkenborn integration, J. Number Theory, 2017, 171, 18–30 [23] Araci S., Duran U., Acikgoz M., Srivastava H. M., A certain (p, q)-derivative operator and associated divided differences, J. Ineq. Appl., 2016, 2016:301, DOI: 10.1186/s13660-016-1240-8 [24] Srivastava H. M., Choi J., Zeta and q-zeta functions and associated series and integrals, Editorial Elsevier, Boston, 2012, DOI: 10.1016/C2010-0-67023-4 [25] Sharma S., Jain R., On some properties of generalized q-Mittag Leffler, Math. Aeterna, 2014, 4(6), 613–619 [26] Ernst T., A comprehensive treatment of q-calculus, Birkhäuser, 2012 [27] Ostrovska S., q-Bernstein polynomials and their iterates, J. Approx. Theory, 2003, 123(2), 232–255 |
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Demonstratio Mathematica |
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Urieles Guerrero, Alejandroe50f99dccf848bb59e550c20b2d53718Ortega, María José254cb1250885d1dedc9b95016d20107bRamírez, William0d4994e7b9a1e21dee69d197bfd0505cVega, Samuel56e682261a147786acbd96ad570dc6a12020-01-10T19:08:04Z2020-01-10T19:08:04Z2019-09-170420-12132391-4661http://hdl.handle.net/11323/5799Corporación Universidad de la CostaREDICUC - Repositorio CUChttps://repositorio.cuc.edu.co/This paper aims to show new algebraic properties from the q-generalized Bernoulli polynomials B[m−1]n(x;q) of level m, as well as some others identities which connect this polynomial class with the q-generalized Bernoulli polynomials of level m, as well as the q-gamma function, and the q-Stirling numbers of the second kind and the q-Bernstein polynomials.engDemonstratio Mathematicahttps://doi.org/10.1515/dema-2019-0039[1] Natalini P., Bernardini A., A generalization of the Bernoulli polynomials, J. Appl. Math., 2003, 3, 155–163[2] Carlitz L., q-Bernoulli numbers and polynomials, Duke Math., 1948, 15, 987–1000[3] Choi J., Anderson P., Srivastava H. M., Carlitz’s q-Bernoulli and q-Euler numbers and polynomials and a class of q-Hurwitz zeta functions, Appl. Math. Comput., 2009, 215, 1185–1208[4] Ernst T., q-Bernoulli and q-Euler polynomials, an umbral approach, Int. J. Difference Equ., 2006, 1, 31–80[5] Hegazi A. S., Mansour M., A note on q-Bernoulli numbers and polynomials, J. Nonlinear Math. Phys., 2006, 13(1), 9–18[6] Kim D., Kim M.-S., A note on Carlitz q-Bernoulli numbers and polynomials, Adv. Difference Equ., 2012, 2012:44[7] Quintana Y., Ramírez W., Urieles A., Generalized Apostol-type polynomials matrix and its algebraic properties, Math. Rep., 2019, 21, 249–264[8] Ryoo C. S., A note on q-Bernoulli numbers and polynomials, Appl. Math. Lett, 2017, 20(5), 524–531[9] Garg M., Alha S., A new class of q-Apostol-Bernoulli polynomials of order α, Revi. Tecn. URU, 2014, 6, 67–76[10] Hernandes P., Quintana Y., Urieles A., About extensions of generalized Apostol-type polynomials, Res. Math., 2015, 68, 203–225[11] KurtB.,AfurthergeneralizationoftheBernoullipolynomialsandonthe2D-Bernoullipolynomials B2n(x, y),Appl.Math.Sci., 2010, 4(47), 2315–2322[12] KurtB.,SomerelationshipsbetweenthegeneralizedApostol-BernoulliandApostol-Eulerpolynomials,Turk.Jou.Ana.Num. The., 2013, 1(1), 54–58[13] LuoQ.-M.,GuoB.-N.,QiF.,DebnathL.,GeneralizationsofBernoullinumbersandpolynomials,Int.J.Math.Math.Sci.,2003, 59, 3769–3776[14] Mahmudov N. I., On a class of q-Bernoulli and q-Euler polynomials, Adv. Difference Equ., 2013, 1, 108–125[15] Ramírez 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[16] Tremblay R., Gaboury S., Fugere J., A further generalization of Apostol-Bernoulli polynomials and related polynomials, Hon. Math. Jou., 2012, 34, 311–326[17] Quintana Y., Ramírez W., Urieles A., On an operational matrix method based on generalized Bernoulli polynomials of level m, Calcolo, 2018, 55, 30[18] Mahmudov N. I., Eini Keleshteri M., q-extensions for the Apostol type polynomials, J. Appl. Math., 2014, Article ID 868167, http://dx.doi.org/10.1155/2014/868167[19] Ernst T., The history of q-calculus and a new method, Licentiate Thesis, Dep. Math. Upps. Unive., 2000[20] Gasper G., Rahman M., Basic Hypergeometric Series, Cambr. Univ. Press, 2004[21] Kac V., Cheung P., Quantum Calculus, Springer-Verlag New York, 2002[22] Araci S., Duran U., Acikgoz M., (p, q)-Volkenborn integration, J. Number Theory, 2017, 171, 18–30[23] Araci S., Duran U., Acikgoz M., Srivastava H. M., A certain (p, q)-derivative operator and associated divided differences, J. Ineq. Appl., 2016, 2016:301, DOI: 10.1186/s13660-016-1240-8[24] Srivastava H. M., Choi J., Zeta and q-zeta functions and associated series and integrals, Editorial Elsevier, Boston, 2012, DOI: 10.1016/C2010-0-67023-4[25] Sharma S., Jain R., On some properties of generalized q-Mittag Leffler, Math. Aeterna, 2014, 4(6), 613–619[26] Ernst T., A comprehensive treatment of q-calculus, Birkhäuser, 2012[27] Ostrovska S., q-Bernstein polynomials and their iterates, J. Approx. Theory, 2003, 123(2), 232–255CC0 1.0 Universalhttp://creativecommons.org/publicdomain/zero/1.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2q-generalized Bernoulli polynomialsq-gamma functionq-Stirling numbersq-Bernstein poly-nomialsNew results on the q-generalized Bernoulli 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/acceptedVersionORIGINALNew results on the q-generalized Bernoulli polynomials of level m.pdfNew results on the q-generalized Bernoulli polynomials of level m.pdfapplication/pdf454042https://repositorio.cuc.edu.co/bitstream/11323/5799/1/New%20results%20on%20the%20q-generalized%20Bernoulli%20polynomials%20of%20level%20m.pdf3f6eca7e39365fbe92d9a50561d77d53MD51open accessCC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8701https://repositorio.cuc.edu.co/bitstream/11323/5799/2/license_rdf42fd4ad1e89814f5e4a476b409eb708cMD52open accessLICENSElicense.txtlicense.txttext/plain; charset=utf-81748https://repositorio.cuc.edu.co/bitstream/11323/5799/3/license.txt8a4605be74aa9ea9d79846c1fba20a33MD53open accessTHUMBNAILNew results on the q-generalized Bernoulli polynomials of level m.pdf.jpgNew results on the q-generalized Bernoulli polynomials of level m.pdf.jpgimage/jpeg53824https://repositorio.cuc.edu.co/bitstream/11323/5799/5/New%20results%20on%20the%20q-generalized%20Bernoulli%20polynomials%20of%20level%20m.pdf.jpgdd8c179913fb649801757e152aa778a2MD55open accessTEXTNew results on the q-generalized Bernoulli polynomials of level m.pdf.txtNew results on the q-generalized Bernoulli polynomials of level m.pdf.txttext/plain26286https://repositorio.cuc.edu.co/bitstream/11323/5799/6/New%20results%20on%20the%20q-generalized%20Bernoulli%20polynomials%20of%20level%20m.pdf.txt3cf5ca5f396374a0a3c73c8f7d2ecbfcMD56open access11323/5799oai:repositorio.cuc.edu.co:11323/57992023-12-14 13:10:12.371CC0 1.0 Universal|||http://creativecommons.org/publicdomain/zero/1.0/open accessRepositorio Universidad de La Costabdigital@metabiblioteca.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 |