Asymptotic behaviour of the~Hadamard determinants and the~behaviour of the~rows of the~Pad\'e and Chebyshev tables for a~sum of exponentials

A. P. Starovoitov ; N. A. Starovoitova

Sbornik. Mathematics, Tome 187 (1996) no. 2, pp. 297-313

Résumé

For function $f(z)=\sum _{j=1}^k e^{\lambda _j z}$ asymptotic equalities for the Hadamard determinants constructed from its Taylor coefficients are established. Using them, the asymptotics of the deviations from $f(z)$ of its Padé approximations $\Pi _{n,m}(z)$ and of the corresponding rational functions of best uniform approximation $r_{n,m}^*(z)=p_n^*(z)=q_m^*(z)$ is found for $m$ fixed as $n \to \infty$.