On localization of the zeroes Hermite--Pad\'e approximants to the exponential functions

A. P. Starovoitov ; E. P. Kechko

Problemy fiziki, matematiki i tehniki, no. 3 (2015), pp. 84-89.

Résumé

The upper estimates are determined for modules of the zeros of Hermite polynomials (Hermite–Padé approximation type I) of the exponential system $\{e^{\lambda_pz}\}_{p=0}^k$, where $\{\lambda_p\}_{p=0}^k$ are arbitrary complex numbers. The proven statements complement and gen- eralize known results about the behavior of the zeros of Hermite polynomials for exponential system $\{e^{pz}\}_{p=0}^k$ by E. Saff and R. Varga, H. Stahl, F. Wielonsky.

Détail

Keywords: exponential system, Hermite polynomials, Hermite–Padé approximation, zeros of Padé approximation.

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