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Cosine amplitude

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elliptic cosine

One of the three basic Jacobi elliptic functions, denoted by

The cosine amplitude is expressible in terms of the Weierstrass sigma-functions, the Jacobi theta-functions or a power series, as follows:

where is the modulus of the elliptic function, ; , and . For one has, respectively, , .

References

[1] A. Hurwitz, R. Courant, "Vorlesungen über allgemeine Funktionentheorie und elliptische Funktionen" , 2 , Springer (1964) pp. Chapt. 3


Comments

More on the function , e.g. derivatives, evenness, behaviour on the real line, etc. can be found in [a1].

References

[a1] A.I. Markushevich, "Theory of functions of a complex variable" , 3 , Chelsea (1977) (Translated from Russian)
How to Cite This Entry:
Cosine amplitude. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Cosine_amplitude&oldid=46531
This article was adapted from an original article by E.D. Solomentsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article