SOME IDENTITIES FOR q-BERNOULLI NUMBERS AND POLYNOMIALS ARISING FROM q-BERNSTEIN POLYNOMIALS
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In this paper, we study q-Bernoulli numbers and polynomials which are different from Carlitz q-Bernoulli numbers and polynomials and arising from p-adic invariant integrals on Zp, and investigate some properties of these numbers and polynomials. Then we will consider p-adic invariant integrals on Zp of the q-Bernstein polynomials and show that they can be expressed in terms of the q- Bernoulli numbers. In addition, from such p-adic invariant integrals we will derive some identities for the q-Bernoulli numbers.
Abstract
In this paper, we study q-Bernoulli numbers and polynomials which are different from Carlitz q-Bernoulli numbers and polynomials and arising from p-adic invariant integrals on Zp, and investigate some properties of these numbers and polynomials. Then we will consider p-adic invariant integrals on Zp of the q-Bernstein polynomials and show that they can be expressed in terms of the q- Bernoulli numbers. In addition, from such p-adic invariant integrals we will derive some identities for the q-Bernoulli numbers.
참고문헌 (20)
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