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New results on the q-generalized Bernoulli polynomials of level m

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Języki publikacji
EN
Abstrakty
EN
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.
Wydawca
Rocznik
Strony
511--522
Opis fizyczny
Bibliogr. 27 poz.
Twórcy
  • Programa de Matemática Universidad del Atlántico, Barranquilla Colombia
  • Departamento de Ciencias Naturales y Exactas Universidad de la Costa,Barranquilla Colombia
  • Departamento de Ciencias Naturales y Exactas Universidad de la Costa,Barranquilla Colombia
autor
  • Departamento de Ciencias Naturales y Exactas Universidad de la Costa,Barranquilla Colombia
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
Identyfikator YADDA
bwmeta1.element.baztech-be157db8-05c4-42bf-9514-34848b415547
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