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

Dolgy, D.V.;Kim, T.

• Accepted : 2011.09.08
• Published : 2011.12.25
• 23 4

#### 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