Some identities of Bernoulli numbers and polynomials associated with Bernstein polynomials.(English)Zbl 1221.11059

The authors introduce the Bernstein polynomials on the ring of $$p$$-adic integers $$\mathbb Z_p$$ and investigate certain properties of the Bernstein polynomials related to the bosonic $$p$$-adic integrals on $$\mathbb Z_p$$.

MSC:

 11B68 Bernoulli and Euler numbers and polynomials 11S80 Other analytic theory (analogues of beta and gamma functions, $$p$$-adic integration, etc.)
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References:

 [1] Acikgoz M, Araci S: A study on the integral of the product of several type Bernstein polynomials.IST Transaction of Applied Mathematics-Modelling and Simulation. In press [2] Acikgoz, M; Araci, S, On the generating function of the Bernstein polynomials, (2010) [3] Simsek, Y; Acikgoz, M, A new generating function of ([inlineequation not available: see fulltext.]-) Bernstein-type polynomials and their interpolation function, No. 2010, 12, (2010) [4] Bernstein, S, Demonstration du theoreme de Weierstrass, fondee sur le calcul des probabilities, Communications of the Kharkov Mathematical Society, 13, 1-2, (1913) [5] Jang, L-C; Kim, W-J; Simsek, Y, A study on the p-adic integral representation on [inlineequation not available: see fulltext.] associated with Bernstein and Bernoulli polynomials, No. 2010, 6, (2010) [6] Kim, T; Jang, L-C; Yi, H, A note on the modified [inlineequation not available: see fulltext.]-Bernstein polynomials, No. 2010, 12, (2010) [7] Phillips, GM, Bernstein polynomials based on the [inlineequation not available: see fulltext.]-integers, Annals of Numerical Mathematics, 4, 511-518, (1997) · Zbl 0881.41008 [8] Kim, T, On a [inlineequation not available: see fulltext.]-analogue of the [inlineequation not available: see fulltext.]-adic log gamma functions and related integrals, Journal of Number Theory, 76, 320-329, (1999) · Zbl 0941.11048 [9] Kim, T; Choi, J; Kim, Y-H, Some identities on the [inlineequation not available: see fulltext.]-Bernstein polynomials, [inlineequation not available: see fulltext.]-Stirling numbers and [inlineequation not available: see fulltext.]-Bernoulli numbers, Advanced Studies in Contemporary Mathematics, 20, 335-341, (2010) · Zbl 1262.11020
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