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arXiv · 2507.15672

Consistent rational approximations of power series, trigonometric series and series of Chebyshev polynomials

A. P. Starovoitov·I. V. Kruglikov·T. M. Osnach
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Abstract

For trigonometric series and series of Chebyshev polynomials, we defined trigonometric Hermite-Pad\'e and Hermite-Jacobi approximations, linear and nonlinear Hermite-Chebyshev approximations. We established criterion of the existence and uniqueness of trigonometric Hermite-Pad\'e polynomials, associated with an arbitrary set of $k$ trigonometric series, and we found explicit form of these polynomials. Similar results were obtained for linear Hermite-Chebyshev approximations. We made examples of systems of functions for which trigonometrical Hermite-Jacobi approximations are existed but aren't the same as trigonometric Hermite-Pad\'e approximations. Similar examples were made for linear and nonlinear Hermite-Chebyshev approximations.

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A. P. Starovoitov, I. V. Kruglikov, T. M. Osnach. 2025-07-21. Consistent rational approximations of power series, trigonometric series and series of Chebyshev polynomials. https://arxiv.org/abs/2507.15672

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