Jacobian elliptic function

Jacobian elliptic function [jə′kō·bē·ən ə¦lip·tik ′fəŋk·shən]

(mathematics)

Forma real number between 0 and 1, andua real number, let φ be that number such thatthe 12 Jacobian elliptic functions ofuwith parametermare sn (u|m) = sin φ, cn (u|m) = cos φ, dn (u|m) = (1-msin²φ)^1/2, the reciprocals of these three functions, and the quotients of any two of them.