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Identities on the weighted q-Euler numbers and q-Bernstein polynomials

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Recently, the modified q-Euler and Genocchi numbers and polynomials with weight are introduced in [1, 6, 7, 8]. In this paper, we give some interesting identities on the modified q-Euler numbers and polynomials with weight associated with q-Bernstein polynomials.

Abstract

Recently, the modified q-Euler and Genocchi numbers and polynomials with weight are introduced in [1, 6, 7, 8]. In this paper, we give some interesting identities on the modified q-Euler numbers and polynomials with weight associated with q-Bernstein polynomials.

참고문헌 (12)

  1. Abdelmejid Bayad, "Modular properties of elliptic Bernoulli and Euler functions", Advanced Studies in Contemporary Mathematics, 20(3), pp.389~401 (2010), 장전수학회
  2. Dan Ding, "Some identities related to the Apostol-Euler and Apostol-Bernoulli polynomials", Advanced Studies in Contemporary Mathematics, 20(1), pp.7~21 (2010), 장전수학회
  3. T. Kim, "On the multiple q-Genocchi and Euler numbers", Russ. J. Math. Phys, 15, pp.481~486 (2008)
  4. T. Kim, "A Study on the p-Adic q-Integral Representation on Zp Associated with the Weighted q-Bernstein and q-Bernoulli Polynomials", J. Inequal. Appl (2011)
  5. T. Kim, "A note on q-Bernstein polynomials", Russ. J. Math. Phys, 18(2), pp.41~50 (2011)
  6. T. Kim, "A new Approach of q-Euler Numbers and Polynomials", Proceedings of the Jangjeon Math. Soc, 14, pp.7~14 (2011)
  7. T. Kim, "New approach to q-Euler polynomials of higher order", Russ. J. Math. Phys, 17(2), pp.218~225 (2010)
  8. T. Kim, "Some identities on the q-Euler polynomials of higher order and q-Stirling numbers by the fermionic p-adic integral on Zp", Russ. J. Math. Phys, 16, pp.484~491 (2009)
  9. 유천성, "A note on the weighted q-Euler numbers and polynomials", Advanced Studies in Contemporary Mathematics, 21(1), pp.47~54 (2011), 장전수학회
  10. Jozsef Sandor, "On the Euler minimum and maximum functions", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 13(2), pp.197~204 (2010), 장전수학회
  11. J. V. Leyendekkers, "Integer structure analysis of the product of adjacent integers and Euler’s extension of Fermat’s last theorem", Advanced Studies in Contemporary Mathematics, 17(2), pp.221~229 (2008), 장전수학회
  12. J.P.O. Santos, "On a new combinatorial interpretation for a theorem of Euler", Adv. Stud. Contemp. Math, 3, pp.31~38 (2001)

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