Asymptotics of Hermite--Pad\'e approximation of exponential functions with complex multipliers in the exponent

A. P. Starovoitov ; G. N. Kazimirov ; M. V. Sidorzov

Problemy fiziki, matematiki i tehniki, no. 2 (2016), pp. 61-67.

Résumé

Asymptotic properties of the diagonal Hermite–Padé approximants of type I for the system of exponentials $\{e^{\lambda_pz}\}^k_{p=0}$, in which $\lambda_0=0$, while the rest $\lambda_p$ are the roots of the equation $\xi^k=1$ are studied. The theorems complement known results of P. Borwein, F. Wielonsky, H. Stahl, A. V. Astafyeva, A. P. Starovoitov, obtained for the case, where the $\{\lambda_p\}^k_{p=0}$ — different real numbers.

Détail

Keywords: exponential system, asymptotic equality, Laplace's method, saddle point method.
Mots-clés : Hermite–Padé approximants

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