2019
Том 71
№ 11

# Some properties of biorthogonal polynomials and their application to Padé approximations

Holub A. P.

Abstract

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 $$\tilde f(z) = \sum\limits_{m = 0}^M {\alpha _m } \frac{{f(z) - T_{m - 1} [f;z]}}{{z^m }},$$ 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.

English version (Springer): Ukrainian Mathematical Journal 46 (1994), no. 8, pp 1070-1078.

Citation Example: Holub A. P. Some properties of biorthogonal polynomials and their application to Padé approximations // Ukr. Mat. Zh. - 1994. - 46, № 8. - pp. 977–984.

Full text