jacobi_dn( z , m )

The Jacobi dn function of z and parameter m in SageMath. Defined by

\[ \operatorname{dn}( u | m ) = \sqrt{ 1 - m \operatorname{sn}^2( u | m ) } \]

Note that all Jacobi elliptic functions in SageMath use the parameter rather than the elliptic modulus k, which is related to the parameter by \( m = k^2 \).

Plot on the real axis:

Series expansion about the origin:

Special values:

Related functions:   jacobi_am   jacobi_sn   jacobi_cn

Function category: Jacobi elliptic functions sagemath-docs