/ibeta12.png"></span>
        </p>
<p>
          Finally we can sidestep difficult areas, or move to an area with a more
          efficient means of computation, by using the duplication formulae:
        </p>
<p>
          <span class="inlinemediaobject"><img src="../../../../equations/ibeta10.png"></span>
        </p>
<p>
          <span class="inlinemediaobject"><img src="../../../../equations/ibeta11.png"></span>
        </p>
<p>
          The domains of a, b and x for which the various methods are use