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Mat. Zametki, 2017, Volume 102, Issue 2, Pages 302–315 (Mi mz11315)  

This article is cited in 2 scientific papers (total in 2 papers)

Asymptotics of Diagonal Hermite–Padé Polynomials for the Collection of Exponential Functions

A. P. Starovoitov

Gomel State University named after Francisk Skorina

Abstract: The asymptotics of diagonal Hermite–Padé polynomials of the first kind is studied for the system of exponential functions $\{e^{\lambda_pz}\}_{p=0}^k$, where $\lambda_0=0$ and the other $\lambda_p$ are the roots of the equation $\xi^k=1$. The theorems proved in the paper supplement the well-known results due to Borwein, Wielonsky, Stahl, Astaf'eva, and Starovoitov obtained for the case in which $\{\lambda_p\}_{p=0}^k$ are different real numbers.

Keywords: system of exponentials, Hermite–Padé approximants of the first kind, asymptotic equalities, Laplace method, saddle-point method.

Funding Agency Grant Number
Ministry of Education of the Republic of Belarus
This work was supported by the Ministry of Education of the Republic of Belarus under the state program for scientific research in the years 2016–2020.


DOI: https://doi.org/10.4213/mzm11315

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English version:
Mathematical Notes, 2017, 102:2, 277–288

Bibliographic databases:

UDC: 517.538.52+517.538.53
Received: 19.07.2016
Revised: 05.12.2016

Citation: A. P. Starovoitov, “Asymptotics of Diagonal Hermite–Padé Polynomials for the Collection of Exponential Functions”, Mat. Zametki, 102:2 (2017), 302–315; Math. Notes, 102:2 (2017), 277–288

Citation in format AMSBIB
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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. 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
    2. 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
  • Математические заметки Mathematical Notes
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