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<b>QuantLib</b>::<a class="el" href="class_quant_lib_1_1_gaussian_orthogonal_polynomial.html">GaussianOrthogonalPolynomial</a></div>
<h1>GaussianOrthogonalPolynomial Class Reference</h1><!-- doxytag: class="QuantLib::GaussianOrthogonalPolynomial" --><code>#include <ql/Math/gaussianorthogonalpolynomial.hpp></code>
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Inheritance diagram for GaussianOrthogonalPolynomial:<p><center><img src="class_quant_lib_1_1_gaussian_orthogonal_polynomial__inherit__graph.png" border="0" usemap="#_gaussian_orthogonal_polynomial__inherit__map" alt="Inheritance graph"></center>
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orthogonal polynomial for Gaussian quadratures
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References: Gauss quadratures and orthogonal polynomials<p>
G.H. Gloub and J.H. Welsch: Calculation of Gauss quadrature rule. Math. Comput. 23 (1986), 221-230<p>
"Numerical Recipes in C", 2nd edition, Press, Teukolsky, Vetterling, Flannery,<p>
The polynomials are defined by the three-term recurrence relation <p class="formulaDsp">
<img class="formulaDsp" alt="\[ P_{k+1}(x)=(x-\alpha_k) P_k(x) - \beta_k P_{k-1}(x) \]" src="form_97.png">
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and <p class="formulaDsp">
<img class="formulaDsp" alt="\[ \mu_0 = \int{w(x)dx} \]" src="form_98.png">
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<table border="0" cellpadding="0" cellspacing="0">
<tr><td></td></tr>
<tr><td colspan="2"><br><h2>Public Member Functions</h2></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="29542d40134e19c90df7b423ae604b02"></a><!-- doxytag: member="QuantLib::GaussianOrthogonalPolynomial::mu_0" ref="29542d40134e19c90df7b423ae604b02" args="() const=0" -->
virtual Real </td><td class="memItemRight" valign="bottom"><b>mu_0</b> () const=0</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="29e3b856fb9e8ff348c8ced895de0a9f"></a><!-- doxytag: member="QuantLib::GaussianOrthogonalPolynomial::alpha" ref="29e3b856fb9e8ff348c8ced895de0a9f" args="(Size i) const=0" -->
virtual Real </td><td class="memItemRight" valign="bottom"><b>alpha</b> (Size i) const=0</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="3df9e16cb17982f17f22eab7ed3b2ab5"></a><!-- doxytag: member="QuantLib::GaussianOrthogonalPolynomial::beta" ref="3df9e16cb17982f17f22eab7ed3b2ab5" args="(Size i) const=0" -->
virtual Real </td><td class="memItemRight" valign="bottom"><b>beta</b> (Size i) const=0</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="a5c6910604bb766292bf708ae09be1c6"></a><!-- doxytag: member="QuantLib::GaussianOrthogonalPolynomial::w" ref="a5c6910604bb766292bf708ae09be1c6" args="(Real x) const=0" -->
virtual Real </td><td class="memItemRight" valign="bottom"><b>w</b> (Real x) const=0</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="d296be30ef56fed69fd613802e61cd02"></a><!-- doxytag: member="QuantLib::GaussianOrthogonalPolynomial::value" ref="d296be30ef56fed69fd613802e61cd02" args="(Size i, Real x) const" -->
Real </td><td class="memItemRight" valign="bottom"><b>value</b> (Size i, Real x) const</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="b30980be7480836527b7f68d02ee96af"></a><!-- doxytag: member="QuantLib::GaussianOrthogonalPolynomial::weightedValue" ref="b30980be7480836527b7f68d02ee96af" args="(Size i, Real x) const" -->
Real </td><td class="memItemRight" valign="bottom"><b>weightedValue</b> (Size i, Real x) const</td></tr>
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