This article is cited in 4 scientific papers (total in 4 papers)
On uniform approximation of elliptic functions by Padé approximants
D. V. Khristoforov
Steklov Mathematical Institute, Russian Academy of Sciences
Diagonal Padé approximants of elliptic functions are studied. It is known that the absence of uniform convergence of such approximants is related to them having spurious poles that do not correspond to any singularities of the function being approximated. A sequence of piecewise rational functions is proposed, which is
constructed from two neighbouring Padé approximants and approximates an elliptic function locally uniformly in the Stahl domain. The proof of the convergence of this sequence is based on deriving strong asymptotic formulae for the remainder function and Padé polynomials and on the analysis of the behaviour of a spurious pole.
Bibliography: 23 titles.
Padé approximants, elliptic functions, the Stahl domain, uniform approximations.
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Sbornik: Mathematics, 2009, 200:6, 923–941
MSC: Primary 41A21; Secondary 41A30, 30E10, 33E05
Received: 20.08.2008 and 27.10.2008
D. V. Khristoforov, “On uniform approximation of elliptic functions by Padé approximants”, Mat. Sb., 200:6 (2009), 143–160; Sb. Math., 200:6 (2009), 923–941
Citation in format AMSBIB
\paper On uniform approximation of elliptic functions by Pad\'e approximants
\jour Mat. Sb.
\jour Sb. Math.
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D. V. Khristoforov, “On the Phenomenon of Spurious Interpolation of Elliptic Functions by Diagonal Padé Approximants”, Math. Notes, 87:4 (2010), 564–574
A. I. Aptekarev, V. I. Buslaev, A. Martínez-Finkelshtein, S. P. Suetin, “Padé approximants, continued fractions, and orthogonal polynomials”, Russian Math. Surveys, 66:6 (2011), 1049–1131
A. A. Gonchar, E. A. Rakhmanov, S. P. Suetin, “Padé–Chebyshev approximants of multivalued analytic functions, variation of equilibrium energy, and the $S$-property of stationary compact sets”, Russian Math. Surveys, 66:6 (2011), 1015–1048
Martínez-Finkelshtein A. Rakhmanov E.A. Suetin S.P., “Heine, Hilbert, Padé, Riemann, and Stieltjes: John Nuttall's Work 25 years later”, advances in orthogonal polynomials, special functions, and their applications, Contemp. Math., 578, ed. Arvesu J. Lagomasino G., Amer. Math. Soc., Providence, RI, 2011, 165–193
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