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Mat. Sb., 1996, Volume 187, Number 2, Pages 141–157 (Mi msb113)  

This article is cited in 3 scientific papers (total in 3 papers)

Asymptotic behaviour of the Hadamard determinants and the behaviour of the rows of the Padé and Chebyshev tables for a sum of exponentials

A. P. Starovoitov, N. A. Starovoitova

Francisk Skorina Gomel State University

Abstract: 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 $n \to \infty$.

DOI: https://doi.org/10.4213/sm113

Full text: PDF file (297 kB)
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English version:
Sbornik: Mathematics, 1996, 187:2, 297–313

Bibliographic databases:

UDC: 517.53
MSC: 30E10, 41A20, 41A21
Received: 30.03.1995

Citation: A. P. Starovoitov, N. A. Starovoitova, “Asymptotic behaviour of the Hadamard determinants and the behaviour of the rows of the Padé and Chebyshev tables for a sum of exponentials”, Mat. Sb., 187:2 (1996), 141–157; Sb. Math., 187:2 (1996), 297–313

Citation in format AMSBIB
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\by A.~P.~Starovoitov, N.~A.~Starovoitova
\paper Asymptotic behaviour of the~Hadamard determinants and the~behaviour of the~rows of the~Pad\'e and Chebyshev tables for a~sum of exponentials
\jour Mat. Sb.
\yr 1996
\vol 187
\issue 2
\pages 141--157
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\transl
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\yr 1996
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\pages 297--313
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  • https://doi.org/10.4213/sm113
  • http://mi.mathnet.ru/eng/msb/v187/i2/p141

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. N. Rusak, A. P. Starovoitov, “Padé approximants for entire functions with regularly decreasing Taylor coefficients”, Sb. Math., 193:9 (2002), 1303–1332  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. A. P. Starovoitov, N. A. Starovoitova, “Padé approximants of the Mittag-Leffler functions”, Sb. Math., 198:7 (2007), 1011–1023  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. A. P. Starovoitov, N. A. Starovoitova, “On the Asymptotics of the Rows of the Padé Table of Analytic Functions with Logarithmic Branch Points”, Math. Notes, 84:3 (2008), 379–388  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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