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Mat. Zametki, 2008, Volume 84, Issue 3, Pages 409–419 (Mi mz4049)  

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

On the Asymptotics of the Rows of the Padé Table of Analytic Functions with Logarithmic Branch Points

A. P. Starovoitov, N. A. Starovoitova

Francisk Skorina Gomel State University

Abstract: For the functions $f(z)=\sum_{n=0}^\infty z^{l_n}/a_n$, where $l_n$ and $a_n$ are arithmetic progressions and their Padé approximants $\pi_{n,m}(z;f)$, we establish an asymptotics of the decrease of the difference $f(z)-\pi_{n,m}(z;f)$ for the case in which $z\in D=ż:|z|<1\}$, $m$ is fixed, and $n\to\infty$. In particular, we obtain proximate orders of decrease of best uniform rational approximations to the functions $\ln(1-z)$ and $\operatorname{arctan}z$ in the disk $D_q=ż:|z|\le q<1\}$.

Keywords: Padé approximant, Padé table, analytic function, logarithmic branch point, arithmetic progression, Hadamard determinant, Vandermonde determinant

DOI: https://doi.org/10.4213/mzm4049

Full text: PDF file (566 kB)
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English version:
Mathematical Notes, 2008, 84:3, 379–388

Bibliographic databases:

UDC: 517.51, 517.53
Received: 11.05.2007

Citation: A. P. Starovoitov, N. A. Starovoitova, “On the Asymptotics of the Rows of the Padé Table of Analytic Functions with Logarithmic Branch Points”, Mat. Zametki, 84:3 (2008), 409–419; Math. Notes, 84:3 (2008), 379–388

Citation in format AMSBIB
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    This publication is cited in the following articles:
    1. A. P. Starovoitov, Yu. A. Labych, “Ratsionalnaya approksimatsiya funktsii Markova, porozhdennykh borelevskimi merami stepennogo tipa”, PFMT, 2009, no. 1(1), 69–73  mathnet
  • Математические заметки Mathematical Notes
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