Warianty tytułu
Języki publikacji
Abstrakty
This paper aims to show new algebraic properties from the q-generalized Bernoulli polynomials [wzór] 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 numbersof the second kind and the q-Bernstein polynomials.
Czasopismo
Rocznik
Tom
Strony
511--522
Opis fizyczny
Bibliogr. 27 poz.
Twórcy
autor
- Programa de Matemática Universidad del Atlántico, Barranquilla Colombia, alejandrourieles@email.uniatlantico.edu.co
autor
- Departamento de Ciencias Naturales y Exactas Universidad de la Costa,Barranquilla Colombia, mortega22@cuc.edu.co
autor
- Departamento de Ciencias Naturales y Exactas Universidad de la Costa,Barranquilla Colombia, wramirez4@cuc.edu.co
autor
- Departamento de Ciencias Naturales y Exactas Universidad de la Costa,Barranquilla Colombia, svega@cuc.edu.co
Bibliografia
- [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] Kurt B., A further generalization of the Bernoulli polynomials and on the 2D-Bernoulli polynomials B2n(x,y), Appl. Math. Sci., 2010, 4(47), 2315-2322
- [12] Kurt B., Some relationships between the generalized Apostol-Bernoulli and Apostol-Euler polynomials, Turk. Jou. Ana. Num. The., 2013, 1(1), 54-58
- [13] Luo Q.-M., Guo B.-N., Qi F., Debnath L., Generalizations of Bernoulli numbers and polynomials, 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
Uwagi
PL
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
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