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On q-Bernstein and q-Hermite polynomials

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Recently, T. Kim([1,2]) introduced q-Bernstein polynomials which are different q-Bernstein polynomials of Phillips. In this paper, we investigate some identities for the q-Bernstein polynomials which are treated by Kim in previous paper([1]).

Abstract

Recently, T. Kim([1,2]) introduced q-Bernstein polynomials which are different q-Bernstein polynomials of Phillips. In this paper, we investigate some identities for the q-Bernstein polynomials which are treated by Kim in previous paper([1]).

참고문헌 (11)

  1. T. Kim, "A note on q Bernstein polynomials", Russian Journal of Mathematical physics, 18(1) (2011)
  2. T. Kim, "q Bernstein polynomials associated with q Stirling numbers and Carlitz’s q Bernoulli numbers", Abstract and Applied Analysis, pp.11~ (2010)
  3. T. Kim, "A note on the modified q Bernstein polynomials", Discrete Dynamics in Nature and Society, pp.12~ (2010)
  4. J. L. Lopez, "Hermite polynomials in asymptotic representations of generalized Bernoulli, Euler, Bessel and Buchholz polynomials"
  5. G. G. Lorentz, "Bernstein polynomials" (1986), United States of America
  6. L.C. Jang, "A study on the p adic integral representation on Zp associated with Bernstein and Bernoulli polynomials", Advances in Difference Equations, pp.6~ (2010)
  7. Y. Simsek, "New generating function of q Bernstein type polynomials and their interpolation function", Abstract and Applied Analysis, pp.12~ (2010)
  8. S. Bernstein, "D˙emonstration du th˙eor˙eme de Weierstrass, fonde˙e sur le Calcul des probabilities", Commun. Soc. Math, Kharkow, 2(13), pp.1~2 (1912)
  9. T. Kim, "Barnes type multiple q zeta function and q Euler polynomials", Journal of physics A: Math. Theor, 43, pp.11~ (2010)
  10. T. Kim, "Some identities on the q Euler polynomials of higher order and q Stirling numbers by the fermionic p adic integral on Zp", Russian Journal of Mathematical physics, 16, pp.484~491 (2009)
  11. S.H. Rim, "On multiple interpolation functions of the q Genocchi polynomials", J. Inequal. Appl, 13, pp.7~ (2010)

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