Abstract
In this paper, we establish an intertwining relation between the two singular lowering operators on polynomials D-u and D-k delta, for every linear functional on polynomials u with canonical moment (u)(0) = -k, for some integer k >= 1, (delta is the Dirac delta at point zero). We also build a D-u-Appell sequence and we obtain the connection coefficients between any D-u-Appell sequence and the canonical basis. As an application, we prove that the singular Laguerre-Hahn polynomial sequence with class zero of Hermite type, denoted by { (S) over cap (n)(x; lambda, rho)}(n >= 0), is D-u- Appell sequence, where (u)0 = -1. This allows us to list some new connection formulas between { (S) over cap (n)(x; lambda, rho)}(n >= 0) and the Hermite polynomial sequence. Finally, we highlight a new derivative operator which makes { (S) over cap (n)(x; lambda, rho)}(n >= 0) an Appell sequence.