The $\mathrm{ds}$ function is defined by $$\mathrm{ds}(u)=\dfrac{\mathrm{dn}(u)}{\mathrm{sn}(u)},$$ where $\mathrm{dn}$ is the Jacobi dn function and $\mathrm{sn}$ is the Jacobi sn function.
Special functions by Leon Hall
