The Complete Asymptotic Expansions for the Szász–mirakian-Type Operators

Abstract

This paper is devoted to exploring asymptotic behavior of the Szász–Mirakian-type operators including the Szász–Mirakian operators Sn(f;x) and its two kinds of integral modifications [Formula: see text], [Formula: see text]. For these operators, we obtain the complete asymptotic expansions in the form of [Formula: see text] all coefficients ak (f;x) of n-k (k=1,2,…) are calculated explicitly in terms of the Stirling numbers of the first and second kind.