modulus <span class="emphasis"><em>k</em></span>
        as the parameter.
      </p>
<p>
        In addition the variable <span class="emphasis"><em>u</em></span> is sometimes expressed as
        an amplitude &#966;, in our implementation we always use <span class="emphasis"><em>u</em></span>.
      </p>
<p>
        Finally note that our functions all take the elliptic modulus as the first
        argument - this is for alignment with the Elliptic Integrals.
      </p>
<p>
        There are twenve functio