Formal orthogonal polynomials and Newton-Pade' approximants

We proved in [8] that the denominators of Newton-Pade approximants for a formal Newton series are formal orthogonal with respect to linear functionals. The same functional is used along an antidiagonal of the Newton-Pade denominator table. The two linear functionals, corresponding to two adjacent antidiagonals, are linked with a very simple relation. Recurrence relations between denominators are given along an antidiagonal or two adjacent antidiagonals in the normal and non-normal case. The same recurrence relations are also satisfied by the Newton-Pade numerators. which implies another formal orthogonality.