Geodesic
Hermitian Approximation of Two Exponents
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 13 (2013) no. 1, pp. 87-91

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We study the asymptotic properties of Hermite–Pade approximants $\{\pi_{n,\,m}^j(z;\,e^{\lambda_j\,\xi})\}_{j=1}^2$ for a system consisting of functions $\{e^{\lambda_1 z},e^{\lambda_2 z}\}$. In particular, we determine asymptotic behavior of differences $e^{\lambda_j\,z}-\pi_{n,\,m}^j(z;\,e^{\lambda_j\,\xi})$ for $j=1,2$ and $n\rightarrow\infty$ for any complex number $z$. The obtained results supplement research of Pade, Perron, D. Braess and A. I. Aptekarev dealing with study of the convergence of joinnt Pade approximants for systems of exponents. 
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     author = {A. P. Starovoitov},
     title = {Hermitian {Approximation} of {Two} {Exponents}},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
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     url = {http://geodesic.mathdoc.fr/item/ISU_2013_13_1_a21/}
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A. P. Starovoitov. Hermitian Approximation of Two Exponents. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 13 (2013) no. 1, pp. 87-91. http://geodesic.mathdoc.fr/item/ISU_2013_13_1_a21/