Asymptotic expansion of a sequence of divided differences with application to positive linear operators (Q2751656)

The authors announce interesting results concerning complete asymptotic expansions for divided differences of monomials and for a sequence of positive linear operators of probabilistic type. The expansions are given in terms of exponential complete Bell polynomials. Previous results obtained by several authors (in particular, by the second author and the reviewer) are considerably extended. Analogous results for classical sequences of positive linear operators were obtained by the first author, see [J. Approximation Theory 97, No. 1, 181-198 (1999; Zbl 0928.41012)].NEWLINENEWLINEFor the entire collection see [Zbl 0968.00041].