Geodesic
Hermitian approximation of two exponents
Problemy fiziki, matematiki i tehniki, no. 1 (2012), pp. 97-100

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We study the asymptotic properties of diagonal Pade–Hermite approximants $\{\pi^{j}_{2n,2n}(z;e^{j\xi;})\}^{2}_{j=1}$ for a system consisting of functions $\{e^z,e^{2 z}\}$. In particular, we determine the asymptotic behavior of the differences $e^{jz} - \pi^j_{2n,2n}(z; e^{j\xi})$ for $j =1,2$ and $n \to\infty$ for any complex number $z$. The obtained results supplement research of Pade, Perron, Braess and A.I. Aptekarev dealing with the study of the convergence of joint Pade approximants for systems of exponents.
Keywords: perfect system of functions, asymptotic equality, Hermite integrals.
Mots-clés : joint Pade approximant, Pade–Hermite approximants 
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     title = {Hermitian approximation of two exponents},
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}
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N. V. Rjabchenko; A. P. Starovoitov; G. N. Kazimirov. Hermitian approximation of two exponents. Problemy fiziki, matematiki i tehniki, no. 1 (2012), pp. 97-100. http://geodesic.mathdoc.fr/item/PFMT_2012_1_a17/