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<title>GNU Scientific Library &ndash; Reference Manual: QAWC adaptive integration for Cauchy principal values</title>

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<a name="QAWC-adaptive-integration-for-Cauchy-principal-values"></a>
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Next: <a href="QAWS-adaptive-integration-for-singular-functions.html#QAWS-adaptive-integration-for-singular-functions" accesskey="n" rel="next">QAWS adaptive integration for singular functions</a>, Previous: <a href="QAGI-adaptive-integration-on-infinite-intervals.html#QAGI-adaptive-integration-on-infinite-intervals" accesskey="p" rel="previous">QAGI adaptive integration on infinite intervals</a>, Up: <a href="Numerical-Integration.html#Numerical-Integration" accesskey="u" rel="up">Numerical Integration</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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<hr>
<a name="QAWC-adaptive-integration-for-Cauchy-principal-values-1"></a>
<h3 class="section">17.7 QAWC adaptive integration for Cauchy principal values</h3>
<a name="index-QAWC-quadrature-algorithm"></a>
<a name="index-Cauchy-principal-value_002c-by-numerical-quadrature"></a>
<dl>
<dt><a name="index-gsl_005fintegration_005fqawc"></a>Function: <em>int</em> <strong>gsl_integration_qawc</strong> <em>(gsl_function * <var>f</var>, double <var>a</var>, double <var>b</var>, double <var>c</var>, double <var>epsabs</var>, double <var>epsrel</var>, size_t <var>limit</var>, gsl_integration_workspace * <var>workspace</var>, double * <var>result</var>, double * <var>abserr</var>)</em></dt>
<dd>
<p>This function computes the Cauchy principal value of the integral of
<em>f</em> over <em>(a,b)</em>, with a singularity at <var>c</var>,
</p>
<div class="example">
<pre class="example">I = \int_a^b dx f(x) / (x - c)
</pre></div>

<p>The adaptive bisection algorithm of QAG is used, with modifications to
ensure that subdivisions do not occur at the singular point <em>x = c</em>.
When a subinterval contains the point <em>x = c</em> or is close to
it then a special 25-point modified Clenshaw-Curtis rule is used to control
the singularity.  Further away from the
singularity the algorithm uses an ordinary 15-point Gauss-Kronrod
integration rule.
</p>
</dd></dl>




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