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.

McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.