Some properties of biorthogonal polynomials and their application to Padé approximations - Holub, A. P. (Ukrains’kyi Matematychnyi Zhurnal, 1994)
Transformations of biorthogonal polynomials under certain transformations of biorthogonalizable sequences are studied. The obtained result is used to construct Padé approximants of orders $[N−1/N],\; N \in ℕ,$ for the functions$$\tilde f(z) = \sum\limits_{m = 0}^M {α _m } \frac{{f(z) - T_{m - 1} [f;z]}}{{z^m }},$$where $f(z)$ is a function with known Padé approximants of the indicated orders, $T_j [f;z]$ are Taylor polynomials of degreej for the function $f(z)$, and $α_{ m, M} = \overline {1,M}$ are constants.