On uniform approximation of elliptic functions by Pade approximants

Journal Article · Tue Jun 30 00:00:00 EDT 2009 · Sbornik. Mathematics

DOI:https://doi.org/10.1070/SM2009V200N06ABEH004024; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA)· OSTI ID:21301617

Khristoforov, Denis V ^[1]

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1. Steklov Mathematical Institute, Russian Academy of Sciences, Moscow (Russian Federation)

Diagonal Pade 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 Pade 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 Pade polynomials and on the analysis of the behaviour of a spurious pole. Bibliography: 23 titles.

• OSTI ID: 21301617
• Journal Information: Sbornik. Mathematics, Vol. 200, Issue 6; Other Information: DOI: 10.1070/SM2009v200n06ABEH004024; Country of input: International Atomic Energy Agency (IAEA); ISSN 1064-5616
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
APPROXIMATIONS
ASYMPTOTIC SOLUTIONS
CONVERGENCE
POLYNOMIALS
SINGULARITY