2019
Том 71
№ 11

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Some properties of biorthogonal polynomials and their application to Padé approximations

Holub A. P.

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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.

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