Cosine amplitude

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)