Bernstein polynomial

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Recently the Bernstein polynomials have been defined and studied in many different ways, for example, by q-series, by complex functions, by p-adic Volkenborn integrals, and many algorithms (cf.^[1]
The Bernstein polynomial bases vanish except the first polynomial at , which is equal to 1 and the last polynomial at , which is also equal to 1 over the interval .^[2]
Many properties of the Bézier curves and surfaces come from the properties of the Bernstein polynomials.^[2]
Due to the increasing interest on Bernstein polynomials, the question arises of how to describe their properties in terms of their coefficients when they are given in the Bernstein basis.^[2]
Up to now, and to the best of our Knowledge, many formulae corresponding to those mentioned previously are unknown and are traceless in the literature for Bernstein polynomials.^[2]
Bernstein polynomials can be generalized to k dimensions.^[3]
The Bernstein polynomials of degree form a basis for the power polynomials of degree .^[4]