Imported Upstream version 1.72.0

[platform/upstream/boost.git] / libs / math / doc / html / math_toolkit / sf_poly / legendre.html

diff --git a/libs/math/doc/html/math_toolkit/sf_poly/legendre.html b/libs/math/doc/html/math_toolkit/sf_poly/legendre.html
index 77bc0e7..e7cad7f 100644 (file)
--- a/libs/math/doc/html/math_toolkit/sf_poly/legendre.html
+++ b/libs/math/doc/html/math_toolkit/sf_poly/legendre.html
@@ -4,7 +4,7 @@
 <title>Legendre (and Associated) Polynomials</title>
 <link rel="stylesheet" href="../../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.10.0">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.11.0">
 <link rel="up" href="../sf_poly.html" title="Polynomials">
 <link rel="prev" href="../sf_poly.html" title="Polynomials">
 <link rel="next" href="legendre_stieltjes.html" title="Legendre-Stieltjes Polynomials">
@@ -38,17 +38,17 @@
 <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
 <a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">legendre_p</span><span class="special">(</span><span class="keyword">int</span> <span class="identifier">n</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">x</span><span class="special">);</span>
 
-<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Chapter&#160;19.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&gt;</span>
-<a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">legendre_p</span><span class="special">(</span><span class="keyword">int</span> <span class="identifier">n</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Chapter&#160;19.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&amp;);</span>
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Chapter&#160;20.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">legendre_p</span><span class="special">(</span><span class="keyword">int</span> <span class="identifier">n</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Chapter&#160;20.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&amp;);</span>
 
 <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
 <a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">legendre_p_prime</span><span class="special">(</span><span class="keyword">int</span> <span class="identifier">n</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">x</span><span class="special">);</span>
 
-<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Chapter&#160;19.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&gt;</span>
-<a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">legendre_p_prime</span><span class="special">(</span><span class="keyword">int</span> <span class="identifier">n</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Chapter&#160;19.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&amp;);</span>
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Chapter&#160;20.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">legendre_p_prime</span><span class="special">(</span><span class="keyword">int</span> <span class="identifier">n</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Chapter&#160;20.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&amp;);</span>
 
-<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Chapter&#160;19.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&gt;</span>
-<span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">legendre_p_zeros</span><span class="special">(</span><span class="keyword">int</span> <span class="identifier">l</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Chapter&#160;19.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&amp;);</span>
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Chapter&#160;20.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&gt;</span>
+<span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">legendre_p_zeros</span><span class="special">(</span><span class="keyword">int</span> <span class="identifier">l</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Chapter&#160;20.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&amp;);</span>
 
 <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
 <span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">legendre_p_zeros</span><span class="special">(</span><span class="keyword">int</span> <span class="identifier">l</span><span class="special">);</span>
@@ -56,14 +56,14 @@
 <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
 <a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">legendre_p</span><span class="special">(</span><span class="keyword">int</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">m</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">x</span><span class="special">);</span>
 
-<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Chapter&#160;19.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&gt;</span>
-<a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">legendre_p</span><span class="special">(</span><span class="keyword">int</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">m</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Chapter&#160;19.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&amp;);</span>
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Chapter&#160;20.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">legendre_p</span><span class="special">(</span><span class="keyword">int</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">m</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Chapter&#160;20.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&amp;);</span>
 
 <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
 <a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">legendre_q</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">x</span><span class="special">);</span>
 
-<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Chapter&#160;19.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&gt;</span>
-<a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">legendre_q</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Chapter&#160;19.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&amp;);</span>
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Chapter&#160;20.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">legendre_q</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Chapter&#160;20.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&amp;);</span>
 
 <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">&gt;</span>
 <a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">legendre_next</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">l</span><span class="special">,</span> <span class="identifier">T1</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">Pl</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">Plm1</span><span class="special">);</span>
@@ -81,9 +81,9 @@
         type.
       </p>
 <p>
-        The final <a class="link" href="../../policy.html" title="Chapter&#160;19.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a> argument is optional and can
+        The final <a class="link" href="../../policy.html" title="Chapter&#160;20.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a> argument is optional and can
         be used to control the behaviour of the function: how it handles errors,
-        what level of precision to use etc. Refer to the <a class="link" href="../../policy.html" title="Chapter&#160;19.&#160;Policies: Controlling Precision, Error Handling etc">policy
+        what level of precision to use etc. Refer to the <a class="link" href="../../policy.html" title="Chapter&#160;20.&#160;Policies: Controlling Precision, Error Handling etc">policy
         documentation for more details</a>.
       </p>
 <h5>
@@ -93,41 +93,43 @@
 <pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
 <a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">legendre_p</span><span class="special">(</span><span class="keyword">int</span> <span class="identifier">l</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">x</span><span class="special">);</span>
 
-<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Chapter&#160;19.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&gt;</span>
-<a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">legendre_p</span><span class="special">(</span><span class="keyword">int</span> <span class="identifier">l</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Chapter&#160;19.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&amp;);</span>
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Chapter&#160;20.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">legendre_p</span><span class="special">(</span><span class="keyword">int</span> <span class="identifier">l</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Chapter&#160;20.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&amp;);</span>
 </pre>
 <p>
         Returns the Legendre Polynomial of the first kind:
       </p>
-<p>
-        <span class="inlinemediaobject"><img src="../../../equations/legendre_0.svg"></span>
-      </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+          <span class="inlinemediaobject"><img src="../../../equations/legendre_0.svg"></span>
+
+        </p></blockquote></div>
 <p>
         Requires -1 &lt;= x &lt;= 1, otherwise returns the result of <a class="link" href="../error_handling.html#math_toolkit.error_handling.domain_error">domain_error</a>.
       </p>
 <p>
         Negative orders are handled via the reflection formula:
       </p>
-<p>
-        P<sub>-l-1</sub>(x) = P<sub>l</sub>(x)
-      </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+          P<sub>-l-1</sub>(x) = P<sub>l</sub>(x)
+        </p></blockquote></div>
 <p>
         The following graph illustrates the behaviour of the first few Legendre Polynomials:
       </p>
-<p>
-        <span class="inlinemediaobject"><img src="../../../graphs/legendre_p.svg" align="middle"></span>
-      </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+          <span class="inlinemediaobject"><img src="../../../graphs/legendre_p.svg" align="middle"></span>
+
+        </p></blockquote></div>
 <pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
 <a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">legendre_p_prime</span><span class="special">(</span><span class="keyword">int</span> <span class="identifier">n</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">x</span><span class="special">);</span>
 
-<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Chapter&#160;19.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&gt;</span>
-<a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">legendre_p_prime</span><span class="special">(</span><span class="keyword">int</span> <span class="identifier">n</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Chapter&#160;19.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&amp;);</span>
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Chapter&#160;20.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">legendre_p_prime</span><span class="special">(</span><span class="keyword">int</span> <span class="identifier">n</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Chapter&#160;20.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&amp;);</span>
 </pre>
 <p>
         Returns the derivatives of the Legendre polynomials.
       </p>
-<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Chapter&#160;19.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&gt;</span>
-<span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">legendre_p_zeros</span><span class="special">(</span><span class="keyword">int</span> <span class="identifier">l</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Chapter&#160;19.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&amp;);</span>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Chapter&#160;20.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&gt;</span>
+<span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">legendre_p_zeros</span><span class="special">(</span><span class="keyword">int</span> <span class="identifier">l</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Chapter&#160;20.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&amp;);</span>
 
 <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
 <span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">legendre_p_zeros</span><span class="special">(</span><span class="keyword">int</span> <span class="identifier">l</span><span class="special">);</span>
@@ -155,15 +157,16 @@
 <pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
 <a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">legendre_p</span><span class="special">(</span><span class="keyword">int</span> <span class="identifier">l</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">m</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">x</span><span class="special">);</span>
 
-<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Chapter&#160;19.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&gt;</span>
-<a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">legendre_p</span><span class="special">(</span><span class="keyword">int</span> <span class="identifier">l</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">m</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Chapter&#160;19.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&amp;);</span>
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Chapter&#160;20.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">legendre_p</span><span class="special">(</span><span class="keyword">int</span> <span class="identifier">l</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">m</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Chapter&#160;20.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&amp;);</span>
 </pre>
 <p>
         Returns the associated Legendre polynomial of the first kind:
       </p>
-<p>
-        <span class="inlinemediaobject"><img src="../../../equations/legendre_1.svg"></span>
-      </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+          <span class="inlinemediaobject"><img src="../../../equations/legendre_1.svg"></span>
+
+        </p></blockquote></div>
 <p>
         Requires -1 &lt;= x &lt;= 1, otherwise returns the result of <a class="link" href="../error_handling.html#math_toolkit.error_handling.domain_error">domain_error</a>.
       </p>
@@ -171,9 +174,10 @@
         Negative values of <span class="emphasis"><em>l</em></span> and <span class="emphasis"><em>m</em></span> are
         handled via the identity relations:
       </p>
-<p>
-        <span class="inlinemediaobject"><img src="../../../equations/legendre_3.svg"></span>
-      </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+          <span class="inlinemediaobject"><img src="../../../equations/legendre_3.svg"></span>
+
+        </p></blockquote></div>
 <div class="caution"><table border="0" summary="Caution">
 <tr>
 <td rowspan="2" align="center" valign="top" width="25"><img alt="[Caution]" src="../../../../../../doc/src/images/caution.png"></td>
@@ -210,16 +214,17 @@
 <pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
 <a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">legendre_q</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">x</span><span class="special">);</span>
 
-<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Chapter&#160;19.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&gt;</span>
-<a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">legendre_q</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Chapter&#160;19.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&amp;);</span>
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Chapter&#160;20.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">legendre_q</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Chapter&#160;20.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&amp;);</span>
 </pre>
 <p>
         Returns the value of the Legendre polynomial that is the second solution
         to the Legendre differential equation, for example:
       </p>
-<p>
-        <span class="inlinemediaobject"><img src="../../../equations/legendre_2.svg"></span>
-      </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+          <span class="inlinemediaobject"><img src="../../../equations/legendre_2.svg"></span>
+
+        </p></blockquote></div>
 <p>
         Requires -1 &lt;= x &lt;= 1, otherwise <a class="link" href="../error_handling.html#math_toolkit.error_handling.domain_error">domain_error</a>
         is called.
@@ -228,9 +233,10 @@
         The following graph illustrates the first few Legendre functions of the second
         kind:
       </p>
-<p>
-        <span class="inlinemediaobject"><img src="../../../graphs/legendre_q.svg" align="middle"></span>
-      </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+          <span class="inlinemediaobject"><img src="../../../graphs/legendre_q.svg" align="middle"></span>
+
+        </p></blockquote></div>
 <pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">&gt;</span>
 <a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">legendre_next</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">l</span><span class="special">,</span> <span class="identifier">T1</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">Pl</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">Plm1</span><span class="special">);</span>
 </pre>
@@ -241,9 +247,10 @@
         recurrence relation holds for Legendre Polynomials of both the first and
         second kinds.
       </p>
-<p>
-        <span class="inlinemediaobject"><img src="../../../equations/legendre_4.svg"></span>
-      </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+          <span class="inlinemediaobject"><img src="../../../equations/legendre_4.svg"></span>
+
+        </p></blockquote></div>
 <p>
         For example we could produce a vector of the first 10 polynomial values using:
       </p>
@@ -289,9 +296,10 @@
         polynomials, this function can be used to create a sequence of values evaluated
         at the same <span class="emphasis"><em>x</em></span>, and for rising <span class="emphasis"><em>l</em></span>.
       </p>
-<p>
-        <span class="inlinemediaobject"><img src="../../../equations/legendre_5.svg"></span>
-      </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+          <span class="inlinemediaobject"><img src="../../../equations/legendre_5.svg"></span>
+
+        </p></blockquote></div>
 <p>
         For example we could produce a vector of the first m+10 polynomial values
         using:
@@ -346,7 +354,7 @@
         zero error</a>.
       </p>
 <div class="table">
-<a name="math_toolkit.sf_poly.legendre.table_legendre_p"></a><p class="title"><b>Table&#160;7.32.&#160;Error rates for legendre_p</b></p>
+<a name="math_toolkit.sf_poly.legendre.table_legendre_p"></a><p class="title"><b>Table&#160;8.32.&#160;Error rates for legendre_p</b></p>
 <div class="table-contents"><table class="table" summary="Error rates for legendre_p">
 <colgroup>
 <col>
@@ -442,7 +450,7 @@
 </table></div>
 </div>
 <br class="table-break"><div class="table">
-<a name="math_toolkit.sf_poly.legendre.table_legendre_q"></a><p class="title"><b>Table&#160;7.33.&#160;Error rates for legendre_q</b></p>
+<a name="math_toolkit.sf_poly.legendre.table_legendre_q"></a><p class="title"><b>Table&#160;8.33.&#160;Error rates for legendre_q</b></p>
 <div class="table-contents"><table class="table" summary="Error rates for legendre_q">
 <colgroup>
 <col>
@@ -536,7 +544,7 @@
 </table></div>
 </div>
 <br class="table-break"><div class="table">
-<a name="math_toolkit.sf_poly.legendre.table_legendre_p_associated_"></a><p class="title"><b>Table&#160;7.34.&#160;Error rates for legendre_p (associated)</b></p>
+<a name="math_toolkit.sf_poly.legendre.table_legendre_p_associated_"></a><p class="title"><b>Table&#160;8.34.&#160;Error rates for legendre_p (associated)</b></p>
 <div class="table-contents"><table class="table" summary="Error rates for legendre_p (associated)">
 <colgroup>
 <col>