jacobi_cn( z , m )

The Jacobi cn function of z and parameter m in SageMath. Defined as the cosine of the Jacobi amplitude:

\[ \operatorname{cn}( u | m ) = \cos [ \operatorname{am}( u | m ) ] \]

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_dn

Function category: Jacobi elliptic functions sagemath-docs