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<a name="Integrands-with-weight-functions"></a>
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<p>
Next: <a href="Integrands-with-singular-weight-functions.html#Integrands-with-singular-weight-functions" accesskey="n" rel="next">Integrands with singular weight functions</a>, Previous: <a href="Integrands-without-weight-functions.html#Integrands-without-weight-functions" accesskey="p" rel="previous">Integrands without weight functions</a>, Up: <a href="Numerical-Integration-Introduction.html#Numerical-Integration-Introduction" accesskey="u" rel="up">Numerical Integration Introduction</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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<hr>
<a name="Integrands-with-weight-functions-1"></a>
<h4 class="subsection">17.1.2 Integrands with weight functions</h4>
<a name="index-Clenshaw_002dCurtis-quadrature"></a>
<a name="index-Modified-Clenshaw_002dCurtis-quadrature"></a>
<p>For integrands with weight functions the algorithms use Clenshaw-Curtis
quadrature rules.  
</p>
<p>A Clenshaw-Curtis rule begins with an <em>n</em>-th order Chebyshev
polynomial approximation to the integrand.  This polynomial can be
integrated exactly to give an approximation to the integral of the
original function.  The Chebyshev expansion can be extended to higher
orders to improve the approximation and provide an estimate of the
error.
</p>



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