Asymptotic approximation with Stancu Beta operators

The concern of this paper is a beta type operator \(L_n\) recently introduced by D.D. Stancu. We present the complete asymptotic expansion for \(L_n\) as \(n\) tends to infinity. All coefficients of \(n^{-k} \ (k=1,2, \ldots)\) are calculated explicitly in terms of Stirling numbers of the first and second kind. Moreover, we give an asymptotic expansion for \(L_n\) into a series of reciprocal factorials.