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<p>orthogonal polynomial for Gaussian quadratures
<a href="class_quant_lib_1_1_gaussian_orthogonal_polynomial.html#details">More...</a></p>
<p><code>#include <ql/math/integrals/gaussianorthogonalpolynomial.hpp></code></p>
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<img id="dynsection-0-trigger" src="closed.png" alt="+"/> Inheritance diagram for GaussianOrthogonalPolynomial:</div>
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Public Member Functions</h2></td></tr>
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virtual <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><b>mu_0</b> () const =0</td></tr>
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virtual <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><b>alpha</b> (<a class="el" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77">Size</a> i) const =0</td></tr>
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virtual <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><b>beta</b> (<a class="el" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77">Size</a> i) const =0</td></tr>
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virtual <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><b>w</b> (<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> x) const =0</td></tr>
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<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><b>value</b> (<a class="el" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77">Size</a> i, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> x) const</td></tr>
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<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><b>weightedValue</b> (<a class="el" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77">Size</a> i, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> x) const</td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>orthogonal polynomial for Gaussian quadratures </p>
<p>References: Gauss quadratures and orthogonal polynomials</p>
<p>G.H. Gloub and J.H. Welsch: Calculation of Gauss quadrature rule. Math. Comput. 23 (1986), 221-230</p>
<p>"Numerical Recipes in C", 2nd edition, Press, Teukolsky, Vetterling, Flannery,</p>
<p>The polynomials are defined by the three-term recurrence relation </p><p class="formulaDsp">
\[ P_{k+1}(x)=(x-\alpha_k) P_k(x) - \beta_k P_{k-1}(x) \]
</p>
<p> and </p><p class="formulaDsp">
\[ \mu_0 = \int{w(x)dx} \]
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