
<p><span class="math display">\[
z_k
= \frac{x_k}
       {1 - \sum_{k&#39; = 1}^{k-1} x_{k&#39;}}
.
\]</span></p>
</div>
</div>
<div class="footnotes">
<hr />
<ol start="15">
<li id="fn15"><p>For an alternative derivation of the same transform using hyperspherical coordinates, see <span class="citation">(Betancourt <a href="#ref-Betancourt:2010" role="doc-biblioref">2010</a>)</span>.<a href="simplex-transform-section.html#fnref15" class="footnote-back">↩︎</a></p></li>
</ol>
</div>
            </section