Geodesic
Hermite-Pad\'e approximation of exponential functions
Sbornik. Mathematics, Tome 207 (2016) no. 6, pp. 769-791

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The paper is concerned with diagonal Hermite-Padé polynomials of the first kind for the system of exponentials $\{e^{\lambda_jz}\}_{j=0}^k$ with arbitrary distinct complex parameters $\{\lambda_k\}_{j=0}^k$. An asymptotic formula for the remainder term is established and the location of the zeros is described. For real parameters the asymptotics are found and the extremal properties are described. The theorems obtained supplement the well-known results due to Borwein, Wielonsky, Saff, Varga and Stahl. Bibliography: 43 titles.
Keywords: system of exponentials, Padé polynomials, Hermite-Padé polynomials, asymptotic equalities, the Laplace method, the saddle-point method. 
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     author = {A. V. Astafieva and A. P. Starovoitov},
     title = {Hermite-Pad\'e approximation of exponential functions},
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     number = {6},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2016_207_6_a0/}
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A. V. Astafieva; A. P. Starovoitov. Hermite-Pad\'e approximation of exponential functions. Sbornik. Mathematics, Tome 207 (2016) no. 6, pp. 769-791. http://geodesic.mathdoc.fr/item/SM_2016_207_6_a0/