Geodesic
On the existence of trigonometric Hermite – Jacobi approximations and non-linear Hermite – Chebyshev approximations
Journal of the Belarusian State University. Mathematics and Informatics, Tome 2 (2023), pp. 6-17

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In this paper, analogues of algebraic Hermite – Padé approximations are defined, being trigonometric Hermite – Padé approximations and Hermite – Jacobi approximations. Examples of functions are represented for which trigonometric Hermite – Jacobi approximations exist but are not the same as trigonometric Hermite – Padé approximations. Similar examples are made for linear and non-linear Hermite – Chebyshev approximations, which are multiple analogues of linear and non-linear Padé – Chebyshev approximations. Each type of examples follows from the well-known representations for the numerator and denominator of fractions, introduced by C. Hermite when proving the transcendence of number $e$.
Keywords: trigonometric series; Fourier sums; trigonometric Padé approximations; Hermite – Padé polynomials; Padé – Chebyshev approximations. 
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A. P. Starovoitov; E. P. Kechko; T. M. Osnath. On the existence of trigonometric Hermite – Jacobi approximations and non-linear Hermite – Chebyshev approximations. Journal of the Belarusian State University. Mathematics and Informatics, Tome 2 (2023), pp. 6-17. http://geodesic.mathdoc.fr/item/BGUMI_2023_2_a0/