Uniform Asymptotics of the Elliptic Sine

Two cases of degeneration of elliptic functions are well known: degeneration into trigonometric functions and degeneration into hyperbolic functions. Approximations of elliptic functions in a neighborhood of a degeneration are usually examined by means of series in the modulus of the elliptic functi...

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Published inJournal of mathematical sciences (New York, N.Y.) Vol. 258; no. 1; pp. 23 - 36
Main Author Kiselev, O. M.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.10.2021
Springer
Springer Nature B.V
Subjects
Approximation
Asymptotic methods
Asymptotic properties
Degeneration
Elliptic functions
Hyperbolic functions
Independent variables
Mathematics
Mathematics and Statistics
Trigonometric functions
33-02
33E05
asymptotics
series
elliptic function
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ISSN1072-3374
1573-8795
DOI10.1007/s10958-021-05534-9

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Summary:Two cases of degeneration of elliptic functions are well known: degeneration into trigonometric functions and degeneration into hyperbolic functions. Approximations of elliptic functions in a neighborhood of a degeneration are usually examined by means of series in the modulus of the elliptic function. For applications of the theory of elliptic functions in the theory of dynamical systems, uniform approximations with respect to the modulus and the independent variable are important. This review contains methods for constructing uniform asymptotics.
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ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-021-05534-9