Abstract
Let T-c := D(x - c)((x - c)D + 2II) be a second-order linear differential operator, where c is an arbitrary complex number, D:=d/dx and II represents the identity on the linear space of polynomials with complex coefficients. The aim of this paper is to describe all of the T-c-classical orthogonal polynomials. Two canonical situations appear: the Laguerre {Ln(2)}n >= 0 and the Jacobi {Pn(alpha-2,2)}(n >= 0).