Consistent rational approximations of power series, trigonometric series and series of Chebyshev polynomials
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| Format: | Preprint |
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2025
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| _version_ | 1866913951249334272 |
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| author | Starovoitov, A. P. Kruglikov, I. V. Osnach, T. M. |
| author_facet | Starovoitov, A. P. Kruglikov, I. V. Osnach, T. M. |
| contents | For trigonometric series and series of Chebyshev polynomials, we defined trigonometric Hermite-Padé and Hermite-Jacobi approximations, linear and nonlinear Hermite-Chebyshev approximations. We established criterion of the existence and uniqueness of trigonometric Hermite-Padé 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-Padé approximations. Similar examples were made for linear and nonlinear Hermite-Chebyshev approximations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_15672 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Consistent rational approximations of power series, trigonometric series and series of Chebyshev polynomials Starovoitov, A. P. Kruglikov, I. V. Osnach, T. M. Classical Analysis and ODEs Complex Variables 32E30 G.1.2 For trigonometric series and series of Chebyshev polynomials, we defined trigonometric Hermite-Padé and Hermite-Jacobi approximations, linear and nonlinear Hermite-Chebyshev approximations. We established criterion of the existence and uniqueness of trigonometric Hermite-Padé 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-Padé approximations. Similar examples were made for linear and nonlinear Hermite-Chebyshev approximations. |
| title | Consistent rational approximations of power series, trigonometric series and series of Chebyshev polynomials |
| topic | Classical Analysis and ODEs Complex Variables 32E30 G.1.2 |
| url | https://arxiv.org/abs/2507.15672 |