Delta amplitude

One of the three fundamental Jacobi elliptic functions. It is denoted by

The delta amplitude is expressed as follows in terms of the Weierstrass sigma-function, the Jacobi theta-functions or a series:

where is the modulus of the delta amplitude, , and , . If one has, respectively,

See also Weierstrass elliptic functions; Elliptic function.

References

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

References

[a1]	H. Bateman (ed.) A. Erdélyi (ed.) et al. (ed.) , Higher transcendental functions , 2. Bessel functions, parabolic cylinder functions, orthogonal polynomials , McGraw-Hill (1953) pp. Chapt. 13