Rational approximations of power series, trigonometric series and series of Chebyshev polynomials - Starovoitov, Alexander P.; Kruglikov, Igor V.; Osnach, Tatyana M. (Journal of the Belarusian State University. Mathematics and Informatics, 2024)
In this paper, we defined trigonometric Hermite – Pade and Hermite – Jacobi approximations as well as linear and nonlinear Hermite – Chebyshev approximations for trigonometric and Chebyshev series. We established the criterion of the existence and uniqueness of trigonometric Hermite – Pade polynomials, associated with an arbitrary set of k trigonometric series, and we found the 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 existed which were not the same as trigonometric Hermite – Pade approximations. Similar examples were represented for linear and nonlinear Hermite – Chebyshev approximations.