Let X = {Xt, t≥ 0} be a càdlàg Lévy process, centered, with moments of all orders. There are two families of orthogonal polynomials associated with X. On one hand, the Kailath–Segall formula gives the relationship between the iterated integrals and the variations of order n ofX, and defines a family of polynomials P1(x1), P2(x1, x2), . . . that are orthogonal with respect to the joint law of th...