Geodesic
Rational approximation of the Mittag-Leffler functions
Problemy fiziki, matematiki i tehniki, no. 1 (2021), pp. 65-68

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It is shown that for $m-1\le n$ the Padé approximants $\{\pi_{n,m}(\cdot;F_\gamma)\}$, which locally deliver the best rational approximations to the Mittag-Leffler functions $F_\gamma$, approximate the $F_\gamma$ as $n\to\infty$ uniformly on the compact set $D=\{z:|z|\le1\}$ at a rate asymptotically equal to the best possible one. In particular, analogues of the well-know results of Braess and Trefethen relating to the approximation of $\exp(z)$ are proved for the Mittag-Leffler functions.
Keywords: Padé approximations, asymptotic equality, Mittag–Leffler functions, rational approximations. 
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     title = {Rational approximation of the {Mittag-Leffler} functions},
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N. V. Ryabchenko; A. P. Starovoitov. Rational approximation of the Mittag-Leffler functions. Problemy fiziki, matematiki i tehniki, no. 1 (2021), pp. 65-68. http://geodesic.mathdoc.fr/item/PFMT_2021_1_a10/