Jacobi dc

The $\mathrm{dc}$ function is defined by $$\mathrm{dc}(u)=\dfrac{\mathrm{dn}(u)}{\mathrm{cn}(u)},$$ where $\mathrm{dn}$ is the Jacobi dn function and $\mathrm{cn}$ is the Jacobi cn function.

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  Domain coloring of $\mathrm{dc}$ with $m=0.8$.

References

Special functions by Leon Hall

Jacobi Elliptic Functions

Jacobi $\mathrm{cn}$

Jacobi $\mathrm{cd}$

Jacobi $\mathrm{cs}$

Jacobi $\mathrm{dc}$

Jacobi $\mathrm{dn}$

Jacobi $\mathrm{ds}$

Jacobi $\mathrm{nc}$

Jacobi $\mathrm{nd}$

Jacobi $\mathrm{ns}$

Jacobi $\mathrm{sc}$

Jacobi $\mathrm{sd}$

Jacobi $\mathrm{sn}$