Geodesic
Asymptotics of Hadamard determinants and the convergence of rows of Padé approximants for sums of exponentials
Sbornik. Mathematics, Tome 41 (1982) no. 4, pp. 427-441 Cet article a éte moissonné depuis la source Math-Net.Ru

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The asymptotics of Hadamard determinants $\Delta_{n,m}$ (of dimension $m\times m$) for arbitrary fixed $m$ and $n\to\infty$ for the function $f(z)=\sum^k_{t=1}e^{\lambda_tz}$ are studied, where $\{\lambda_t\}^k_{t=1}$ are distinct complex numbers with unit modulus. A theorem on the convergence of the $(s\cdot p)$th row of the Padé table for the function $f(z)=\sum^k_{t=1}e^{\lambda_tz}$ ($\{\lambda_t\}^k_{t=1}$ are arbitrary distinct complex numbers) in the topology of $H(\mathbf C)$ holds for arbitrary natural numbers $p$ and $s$ equal to the number of $\lambda_t$ with modulus that is maximal among the $\{\lambda_t\}^k_{t=1}$. Bibliography: 8 titles. 
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     author = {A. I. Aptekarev},
     title = {Asymptotics of {Hadamard} determinants and the convergence of rows of {Pad\'e} approximants for sums of exponentials},
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A. I. Aptekarev. Asymptotics of Hadamard determinants and the convergence of rows of Padé approximants for sums of exponentials. Sbornik. Mathematics, Tome 41 (1982) no. 4, pp. 427-441. http://geodesic.mathdoc.fr/item/SM_1982_41_4_a1/

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