Jacobian elliptic function

Jacobian elliptic function

[jə′kō·bē·ən ə¦lip·tik ′fəŋk·shən]
(mathematics)
For m a real number between 0 and 1, and u a real number, let φ be that number such that the 12 Jacobian elliptic functions of u with parameter m are sn (u | m) = sin φ, cn (u | m) = cos φ, dn (u | m) = (1-m sin2φ)1/2, the reciprocals of these three functions, and the quotients of any two of them.
References in periodicals archive ?
occur in the theory of Jacobian theta functions and their applications to Jacobian elliptic functions.
Here, dn(z; [beta]) and cn(z; [beta]) are the Jacobian elliptic functions for z = [alpha](x - [x.
Reduction of the doubly periodic Weierstrass function p to a set of single periodic Jacobian elliptic functions is based on the following relationship between p and cn, sn with modulus M: