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Mathematics. Mechanics. Informatics

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Tikhonov I. V., Sherstyukov V. B., Petrosova M. A. Bernstein Polynomials for a Standard Module Function on the Symmetric Interval. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2016, vol. 16, iss. 4, pp. 425-435. DOI: 10.18500/1816-9791-2016-16-4-425-435, EDN: XHPYIH

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Bernstein Polynomials for a Standard Module Function on the Symmetric Interval

Tikhonov Ivan Vladimirovich, Lomonosov Moscow State University
Sherstyukov Vladimir Borisovich, National Research Nuclear University MEPhI
Petrosova Margarita Arsenovna, Moscow Pedagogical State University

Bernstein polynomials are studied on a symmetric interval. Basic relations connected with Bernstein polynomials for a standard module function are received. By the Templ’s formula we establish recurrence relations from which the Popoviciu’s expansion is derived. Suitable formulas for the first and second derivatives are found. As a result an explicit algebraic form for Bernstein polynomials is obtained. We also notice some corollaries. 

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