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Function List:

C++ API

: [sn, cn, dn, err] = ellipj (u, m)
: [sn, cn, dn, err] = ellipj (u, m, tol)

Compute the Jacobi elliptic functions sn, cn, and dn of complex argument u and real parameter m.

If m is a scalar, the results are the same size as u. If u is a scalar, the results are the same size as m. If u is a column vector and m is a row vector, the results are matrices with length (u) rows and length (m) columns. Otherwise, u and m must conform in size and the results will be the same size as the inputs.

The value of u may be complex. The value of m must be 0 ≤ m ≤ 1.

The optional input tol is currently ignored (MATLAB uses this to allow faster, less accurate approximation).

If requested, err contains the following status information and is the same size as the result.

  1. Normal return.
  2. Error—no computation, algorithm termination condition not met, return NaN.

Reference: Milton Abramowitz and Irene A Stegun, Handbook of Mathematical Functions, Chapter 16 (Sections 16.4, 16.13, and 16.15), Dover, 1965.

See also: ellipke.

Package: octave