A New Generating Function of (q-) Bernstein Type Polynomials and their Interpolation Function

Details A New Generating Function of (q-) Bernstein Type Polynomials and their Interpolation Function A New Generating Function of (q-) Bernstein Type Polynomials and their Interpolation Function

2010-01-19

arxiv.org/abs/1001.3400v1

Mathematics

Number Theory

Scientific paper

The main object of this paper is to construct a new generating function of the (q-) Bernstein type polynomials. We establish elementary properties of this function. By using this generating function, we derive recurrence relation and derivative of the (q-) Bernstein type polynomials. We also give relations between the (q-) Bernstein type polynomials, Hermite polynomials, Bernoulli polynomials of higher-order and the second kind Stirling numbers. By applying Mellin transformation to this generating function, we define interpolation of the (q-) Bernstein type polynomials. Moreover, we give some applications and questions on approximations of (q-) Bernstein type polynomials, moments of some distributions in Statistics.

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