Geodesic
Hermite--Pad\'e approximants of the Mittag-Leffler functions
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Complex analysis, mathematical physics, and applications, Tome 301 (2018), pp. 241-258

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The convergence rate of type II Hermite–Padé approximants for a system of degenerate hypergeometric functions $\{_1F_1(1,\gamma;\lambda_jz)\}_{j=1}^k$ is found in the case when the numbers $\{\lambda_j\}_{j=1}^k$ are the roots of the equation $\lambda^k=1$ or real numbers and $\gamma\in\mathbb C\setminus\{0,-1,-2,\dots\}$. More general statements are obtained for approximants of this type (including nondiagonal ones) in the case of $k=2$. The theorems proved in the paper complement and generalize the results obtained earlier by other authors.
Keywords: Hermite–Padé polynomials, asymptotic equalities, Laplace method, saddle-point method.
Mots-clés : Hermite–Padé approximants 
@article{TM_2018_301_a17,
     author = {A. P. Starovoitov},
     title = {Hermite--Pad\'e approximants of the {Mittag-Leffler} functions},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {241--258},
     publisher = {mathdoc},
     volume = {301},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2018_301_a17/}
}
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A. P. Starovoitov. Hermite--Pad\'e approximants of the Mittag-Leffler functions. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Complex analysis, mathematical physics, and applications, Tome 301 (2018), pp. 241-258. http://geodesic.mathdoc.fr/item/TM_2018_301_a17/