Formal orthogonal polynomials and Newton--Padé approximants (Q5961055)

There is quite a number of papers on the Newton-Padé table of a formal Newton series, covering a.o. the block structure in case of a non-normal table. In previous work the author found a similar block structure for the formal orthogonal polynomial table (orthogonality with respect to a linear functional on the space of polynomials). In the paper under review the table of Newton-Padé denominators of a formal power series is considered and using the functional derived previously [\textit{A. Draux}, Numer. Algorithms 111, No. 1-4, 143-158 (1996; Zbl 0852.42016)] results are derived linking the two linear functionals corresponding to adjacent anti-diagonals. Moreover, three-term recurrence relations between denominators along an anti-diagonal (or two adjacent ones) are derived. Finally, it is shown that the Padé numerators satisfy the same recurrence relation, thereby placing the entire Newton-Padé table within the context of (formally) orthogonal polynomial sequences.