<title>Gauss-Legendre quadrature</title>
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</p>
<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">quadrature</span><span class="special">{</span>
-<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Real</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">Points</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../policy.html" title="Chapter 19. Policies: Controlling Precision, Error Handling etc">Policy</a> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">policy</span><span class="special"><></span> <span class="special">></span>
+<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Real</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">Points</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../policy.html" title="Chapter 20. Policies: Controlling Precision, Error Handling etc">Policy</a> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">policy</span><span class="special"><></span> <span class="special">></span>
<span class="keyword">struct</span> <span class="identifier">gauss</span>
<span class="special">{</span>
<span class="keyword">static</span> <span class="keyword">const</span> <span class="identifier">RandomAccessContainer</span><span class="special">&</span> <span class="identifier">abscissa</span><span class="special">();</span>
The Gaussian quadrature routine support both real and complex-valued quadrature.
For example, the Lambert-W function admits the integral representation
</p>
-<p>
- W(z) = 1/2Π ∫<sub>-Π</sub><sup>Π</sup> ((1- v cot(v) )^2 + v^2)/(z + v csc(v)
- exp(-v cot(v))) dv
- </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+ <span class="serif_italic"><span class="emphasis"><em>W(z) = 1/2Π ∫<sub>-Π</sub><sup>Π</sup> ((1-
+ v cot(v) )^2 + v^2)/(z + v csc(v) exp(-v cot(v))) dv</em></span></span>
+ </p></blockquote></div>
<p>
so it can be effectively computed via Gaussian quadrature using the following
code: