In this paper, we establish an intertwining relation between the two singular lowering operators on polynomials Du and D−kδ, for every linear functional on polynomials u with canonical moment (u)0 = −k, for some integer k ≥ 1, (δ is the Dirac delta at point zero). We also build a Du-Appell polynomial sequence and we obtain the connection coefficients betweena Du-Appell polynomial sequence and the canonical basis. As application, we prove that the singular Laguerre-Hahn polynomial sequence with class zero of Hermite type is Du-Appell with (u)0 = −1. Finally, a new connection formulas between the Hermite polynomials and the singular Laguerre-Hahn polynomial sequence with class zero of Hermite type is obtained.