Geodesic
Pad\'e approximants of the Mittag-Leffler functions
Sbornik. Mathematics, Tome 198 (2007) no. 7, pp. 1011-1023

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It is shown that for $m\le n$ 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-known results of Braess and Trefethen relating to the approximation of $\exp{z}$ are proved for the Mittag-Leffler functions. Bibliography: 28 titles. 
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     author = {A. P. Starovoitov and N. A. Starovoitova},
     title = {Pad\'e approximants of the {Mittag-Leffler} functions},
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A. P. Starovoitov; N. A. Starovoitova. Pad\'e approximants of the Mittag-Leffler functions. Sbornik. Mathematics, Tome 198 (2007) no. 7, pp. 1011-1023. http://geodesic.mathdoc.fr/item/SM_2007_198_7_a5/