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PFMT, 2015, Issue 3(24), Pages 84–89 (Mi pfmt396)  

This article is cited in 1 scientific paper (total in 1 paper)

MATHEMATICS

On localization of the zeroes Hermite–Padé approximants to the exponential functions

A. P. Starovoitov, E. P. Kechko

F. Scorina Gomel State University, Gomel, Belarus

Abstract: 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.

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

Full text: PDF file (441 kB)
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UDC: 517.538.52+517.538.53
Received: 27.05.2015

Citation: A. P. Starovoitov, E. P. Kechko, “On localization of the zeroes Hermite–Padé approximants to the exponential functions”, PFMT, 2015, no. 3(24), 84–89

Citation in format AMSBIB
\Bibitem{StaKec15}
\by A.~P.~Starovoitov, E.~P.~Kechko
\paper On localization of the zeroes Hermite--Pad\'e approximants to the exponential functions
\jour PFMT
\yr 2015
\issue 3(24)
\pages 84--89
\mathnet{http://mi.mathnet.ru/pfmt396}


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    This publication is cited in the following articles:
    1. A. P. Starovoitov, E. P. Kechko, “On Some Properties of Hermite–Padé Approximants to an Exponential System”, Proc. Steklov Inst. Math., 298 (2017), 317–333  mathnet  crossref  crossref  isi  elib
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