Asymptotic expansions for variants of the gamma and Post–Widder operators preserving 1 and xj

Recently, the authors constructed operators acting on a space of functions defined on and preserving 1 and for a given . To this end, they considered suitable modifications of the Post–Widder and gamma operators. They proved convergence results and established the associated Voronovskaja type formulas. In this paper, we give asymptotic expansions for the sequences of these operators.