Asymptotics of Diagonal Hermite--Pad\'e Polynomials for the Collection of Exponential Functions

A. P. Starovoitov

Matematičeskie zametki, Tome 102 (2017) no. 2, pp. 302-315.

Résumé

The asymptotics of diagonal Hermite–Padé polynomials of the first kind is studied for the system of exponential functions $\{e^{\lambda_pz}\}_{p=0}^k$, where $\lambda_0=0$ and the other $\lambda_p$ are the roots of the equation $\xi^k=1$. The theorems proved in the paper supplement the well-known results due to Borwein, Wielonsky, Stahl, Astaf'eva, and Starovoitov obtained for the case in which $\{\lambda_p\}_{p=0}^k$ are different real numbers.

Détail

Keywords: system of exponentials, Hermite–Padé approximants of the first kind, asymptotic equalities, Laplace method, saddle-point method.

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