Abstract
We proved in [8] that the denominators of Newton–Padé 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–Padé 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–Padé numerators, which implies another formal orthogonality.
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Draux, A. Formal Orthogonal Polynomials and Newton–Padé Approximants. Numerical Algorithms 29, 67–74 (2002). https://doi.org/10.1023/A:1014803805476
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DOI: https://doi.org/10.1023/A:1014803805476