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Lee, H. Y.; Jung, N. S.; Ryoo, C. S.

Some identities of the twisted \(q\)-Genocchi numbers and polynomials with weight \(\alpha\) and \(q\)-Bernstein polynomials with weight \(\alpha\). (English) Zbl 1232.11029

Abstr. Appl. Anal. 2011, Article ID 123483, 9 p. (2011).
Summary: Recently mathematicians have studied some interesting relations between \(q\)-Genocchi numbers, \(q\)-Euler numbers, polynomials, Bernstein polynomials, and \(q\)-Bernstein polynomials. In this paper, we give some interesting identities of the twisted \(q\)-Genocchi numbers, polynomials, and \(q\)-Bernstein polynomials with weighted \(\alpha\).

Cited in 1 Document

MSC:

11B68 Bernoulli and Euler numbers and polynomials
11B75 Other combinatorial number theory
11S80 Other analytic theory (analogues of beta and gamma functions, \(p\)-adic integration, etc.)
33D45 Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.)
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\textit{H. Y. Lee} et al., Abstr. Appl. Anal. 2011, Article ID 123483, 9 p. (2011; Zbl 1232.11029)
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References:

[1] T. Kim, “Some identities on the q-Euler polynomials of higher order and q-Stirling numbers by the fermionic p-adic integral on \Bbb Zp,” Russian Journal of Mathematical Physics, vol. 16, no. 4, pp. 484-491, 2009. · Zbl 1192.05011
[2] T. Kim, “Note on the Euler numbers and polynomials,” Advanced Studies in Contemporary Mathematics, vol. 17, no. 2, pp. 131-136, 2008. · Zbl 1171.11011
[3] T. Kim, “q-Volkenborn integration,” Russian Journal of Mathematical Physics, vol. 9, no. 3, pp. 288-299, 2002. · Zbl 1092.11045
[4] T. Kim, J. Choi, and Y.-H. Kim, “Some identities on the q-Bernstein polynomials, q-Stirling numbers and q-Bernoulli numbers,” Advanced Studies in Contemporary Mathematics, vol. 20, no. 3, pp. 335-341, 2010. · Zbl 1262.11020
[5] I. N. Cangul, H. Ozden, and Y. Simsek, “A new approach to q-Genocchi numbers and their interpolation functions,” Nonlinear Analysis, vol. 71, no. 12, pp. e793-e799, 2009. · Zbl 1238.11017
[6] I. N. Cangul, H. Ozden, V. Kurt, and Y. Simsek, “On the higher-order w-q-Genocchi numbers,” Advanced Studies in Contemporary Mathematics, vol. 19, no. 1, pp. 39-57, 2009. · Zbl 1187.05004
[7] T. Kim, L. C. Jang, and H. Yi, “A note on the modified q-Bernstein polynomials,” Discrete Dynamics in Nature and Society, vol. 2010, Article ID 706483, 12 pages, 2010. · Zbl 1198.33005
[8] T. Kim, J. Choi, Y. H. Kim, and C. S. Ryoo, “On the fermionic p-adic integral representation of Bernstein polynomials associated with Euler numbers and polynomials,” Journal of Inequalities and Applications, vol. 2010, Article ID 864247, 12 pages, 2010. · Zbl 1239.11020
[9] H. Y. Lee, “A note on the twisted q-Genocchi numbers and polynomials with weight \alpha ,” Journal Of Applied Mathematics and Informatics. In press. · Zbl 1235.11024
[10] H. Ozden, I. N. Cangul, and Y. Simsek, “Hurwitz type multiple genocchi Zeta function,” in Numerical Analysis and Applied Math, AIP Conference Proceedings, pp. 1148-1781, 2009.
[11] H. Ozden, Y. Simsek, and H. M. Srivastava, “A unified presentation of the generating functions of the generalized Bernoulli, Euler and Genocchi polynomials,” Computers and Mathematics with Applications, vol. 60, no. 10, pp. 2779-2787, 2010. · Zbl 1207.33015
[12] S. H. Rim, J. H. Jin, E. J. Moon, and S. J. Lee, “Some identities on the q-Genocchi polynomials of higher-order and q-Stirling numbers by the fermionic p-adic integral on \Bbb Zp,” International Journal of Mathematics and Mathematical Sciences, vol. 2010, Article ID 860280, 14 pages, 2010. · Zbl 1208.11031
[13] C. S. Ryoo, “Some identities of the twisted q-Euler numbers and polynomials associated with q-Bernstein polynomials,” vol. 14, no. 2, pp. 239-248, 2011. · Zbl 1255.11005
[14] C. S. Ryoo, “Some relations between twisted q-Euler numbers and Bernstein polynomials,” Advanced Studies in Contemporary Mathematics, vol. 21, no. 2, pp. 217-223, 2011. · Zbl 1266.11040
[15] Y. Simsek, V. Kurt, and D. Kim, “New approach to the complete sum of products of the twisted (h,q)-Bernoulli numbers and polynomials,” Journal of Nonlinear Mathematical Physics, vol. 14, no. 1, pp. 44-56, 2007. · Zbl 1163.11015
[16] Y. Simsek and M. Acikgoz, “A new generating function of q-Bernstein-type polynomials and their interpolation function,” Abstract and Applied Analysis, vol. 2010, Article ID 769095, 12 pages, 2010. · Zbl 1185.33013
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