This is documentation for Mathematica 6, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.2)


JacobiDN[u, m]
gives the Jacobi elliptic function dn(u|m).
  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • , where phi=am(u❘m).
  • dn(u❘m) a is doubly periodic function in u with periods 2 K(m) and 4 ⅈ K(1-m), where K is the elliptic integral EllipticK.
  • JacobiDN is a meromorphic function in both arguments.
  • For certain special arguments, JacobiDN automatically evaluates to exact values.
  • JacobiDN can be evaluated to arbitrary numerical precision.
  • JacobiDN automatically threads over lists.
New in 1