On a limit theorem for some modified operators (Q1912658)

The Voronowskja formula computes the limit of \(n(B_n (f) (x)- f(x))\) as \(n\to \infty\), provided that \(f'' (x)\) exists. Here \(B_n f\) is the Bernstein polynomial. The well-known generalization (assuming the existence of \(f^{(2k)} (x)\)) is called by the author the moment expansion of Bernstein polynomials. In this paper, the author finds the moment expansions for the Bernstein-Kantorovich and for the Szász-Kantorovitch operators. Similar results are also obtained. The method of the proof is probabilistic.