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

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 \(\alpha\).

### 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.) |

PDF
BibTeX
XML
Cite

\textit{H. Y. Lee} et al., Abstr. Appl. Anal. 2011, Article ID 123483, 9 p. (2011; Zbl 1232.11029)

Full Text:
DOI

### 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 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.