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Mat. Sb., 2016, Volume 207, Number 6, Pages 3–26 (Mi msb8470)  

This article is cited in 6 scientific papers (total in 6 papers)

Hermite-Padé approximation of exponential functions

A. V. Astafieva, A. P. Starovoitov

Francisk Skorina Gomel State University, Belarus

Abstract: The paper is concerned with diagonal Hermite-Padé polynomials of the first kind for the system of exponentials $\{e^{\lambda_jz}\}_{j=0}^k$ with arbitrary distinct complex parameters $\{\lambda_k\}_{j=0}^k$. An asymptotic formula for the remainder term is established and the location of the zeros is described. For real parameters the asymptotics are found and the extremal properties are described. The theorems obtained supplement the well-known results due to Borwein, Wielonsky, Saff, Varga and Stahl.
Bibliography: 43 titles.

Keywords: system of exponentials, Padé polynomials, Hermite-Padé polynomials, asymptotic equalities, the Laplace method, the saddle-point method.

Funding Agency Grant Number
Ministry of Education of the Republic of Belarus
This research was carried out with the financial support of the Ministry of Education of the Republic of Belarus under the Federal Programme for Scientific Research for 2011–2015.

Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/sm8470

Full text: PDF file (636 kB)
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English version:
Sbornik: Mathematics, 2016, 207:6, 769–791

Bibliographic databases:

UDC: 517.538.52+517.538.53+517.518.84
MSC: 41A21
Received: 08.01.2015 and 20.03.2016

Citation: A. V. Astafieva, A. P. Starovoitov, “Hermite-Padé approximation of exponential functions”, Mat. Sb., 207:6 (2016), 3–26; Sb. Math., 207:6 (2016), 769–791

Citation in format AMSBIB
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  • https://doi.org/10.4213/sm8470
  • http://mi.mathnet.ru/eng/msb/v207/i6/p3

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. M. V. Sidortsov, N. A. Starovoitova, A. P. Starovoitov, “Ob asimptotike approksimatsii Ermita–Pade vtorogo roda dlya eksponentsialnykh funktsii s kompleksnymi mnozhitelyami v pokazatelyakh eksponent”, PFMT, 2017, no. 1(30), 73–77  mathnet
    2. M. V. Sidortsov, A. A. Drapeza, A. P. Starovoitov, “Approksimatsii Ermita–Pade vyrozhdennykh gipergeometricheskikh funktsii”, PFMT, 2017, no. 2(31), 69–74  mathnet
    3. A. P. Starovoitov, “Asymptotics of Diagonal Hermite–Padé Polynomials for the Collection of Exponential Functions”, Math. Notes, 102:2 (2017), 277–288  mathnet  crossref  crossref  mathscinet  isi  elib
    4. 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
    5. A. P. Starovoitov, M. V. Sidortsov, A. A. Drapeza, “Skorost skhodimosti kvadratichnykh approksimatsii Ermita–Pade vyrozhdennykh gipergeometricheskikh funktsii”, PFMT, 2018, no. 1(34), 71–78  mathnet
    6. A. P. Starovoitov, “Hermite–Padé approximants of the Mittag-Leffler functions”, Proc. Steklov Inst. Math., 301 (2018), 228–244  mathnet  crossref  crossref  isi  elib  elib
  • Математический сборник Sbornik: Mathematics (from 1967)
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