The paper aims at approximating functions through a sequence of linear positive operators of continuous type. First we define the Appell polynomials of dimension d \((d\ge 2)\) and with their aid we expand the Szász–Mirakjan operators in the Durrmeyer sense. The investigation of the new class of operators involves the study of convergence by using the universal Bohman–Korovkin theorem and the indication of the error by using modulus of smoothness. The main results are given by the asymptotic expansion of both the operators and their derivatives with the explicit specification of all coefficients in a concise form. In particular, Voronovskaja type theorems are obtained.
