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A NOTE ON THE WEIGHTED q-BERNOULLI NUMBERS AND THE WEIGHTED q-BERNSTEIN POLYNOMIALS

Dolgy, D.V.;Kim, T.

  • Received : 2011.09.05
  • Accepted : 2011.09.08
  • Published : 2011.12.25

Abstract

Recently, the modified q-Bernoulli numbers and polynomials with weight ${\alpha}$ are introduced in [3]: In this paper we give some interesting p-adic integral representation on $\mathbb{Z}_p$ of the weighted q-Bernstein polynomials related to the modified q-Bernoulli numbers and polynomials with weight ${\alpha}$. From those integral representation on $\mathbb{Z}_p$ of the weighted q-Bernstein polynomials, we can derive some identities on the modified q-Bernoulli numbers and polynomials with weight ${\alpha}$.

Keywords

higher order q-Bernoulli numbers and polynomials with weight ${\alpha}$;p-adic q-integral

References

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Cited by

  1. On the families of q-Euler polynomials and their applications vol.23, pp.1, 2015, https://doi.org/10.1016/j.joems.2014.03.002