ail to converge for values of <code>alpha</code> and <code>beta</code> much less than one.</p>
<p>This is where <code>xc</code> is useful. It is defined, for definite integrals, as a high precision version of the distance from <code>x</code> to the nearest endpoint — <code>a - x</code> or <code>b - x</code> for a lower endpoint <code>a</code> and an upper endpoint <code>b</code>. To make use of this for the beta integral, the integrand can be re-coded:</p>
<div class="sourceCode" id="cb4"><pre class="sour