Geodesic
Approximation by Bernstein Polynomials at the Points of Discontinuity of the Derivatives
Matematičeskie zametki, Tome 85 (2009) no. 4, pp. 622-629

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It is proved that, in the asymptotic formulas for the deviations of Bernstein polynomials from functions at the points of discontinuity of the first kind of the highest even-order derivative, the value of such a derivative can be replaced by the half-sum of its limits on the right and on the left.
Keywords: Bernstein polynomial, Peano derivative, point of discontinuity of the first kind, Stirling's formula, modulus of continuity. 
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     author = {S. A. Telyakovskii},
     title = {Approximation by {Bernstein} {Polynomials} at the {Points} of {Discontinuity} of the {Derivatives}},
     journal = {Matemati\v{c}eskie zametki},
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     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2009_85_4_a11/}
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S. A. Telyakovskii. Approximation by Bernstein Polynomials at the Points of Discontinuity of the Derivatives. Matematičeskie zametki, Tome 85 (2009) no. 4, pp. 622-629. http://geodesic.mathdoc.fr/item/MZM_2009_85_4_a11/