Geodesic
Pad\'e approximants for entire functions with regularly decreasing Taylor coefficients
Sbornik. Mathematics, Tome 193 (2002) no. 9, pp. 1303-1332

Voir la notice de l'article provenant de la source Math-Net.Ru

For a class of entire functions the asymptotic behaviour of the Hadamard determinants $D_{n,m}$ as $0\leqslant m\leqslant m(n)\to\infty$ and $n\to\infty$ is described. This enables one to study the behaviour of parabolic sequences from Padé and Chebyshev tables for many individual entire functions. The central result of the paper is as follows: for some sequences $\{(n,m(n))\}$ in certain classes of entire functions (with regular Taylor coefficients) the Padé approximants $\{\pi_{n,m(n)}\}$, which provide the locally best possible rational approximations, converge to the given function uniformly on the compact set $D=\{z:|z|\leqslant 1\}$ with asymptotically best rate. 
@article{SM_2002_193_9_a2,
     author = {V. N. Rusak and A. P. Starovoitov},
     title = {Pad\'e approximants for entire functions with regularly decreasing {Taylor} coefficients},
     journal = {Sbornik. Mathematics},
     pages = {1303--1332},
     publisher = {mathdoc},
     volume = {193},
     number = {9},
     year = {2002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2002_193_9_a2/}
}
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V. N. Rusak; A. P. Starovoitov. Pad\'e approximants for entire functions with regularly decreasing Taylor coefficients. Sbornik. Mathematics, Tome 193 (2002) no. 9, pp. 1303-1332. http://geodesic.mathdoc.fr/item/SM_2002_193_9_a2/