Imported Upstream version 1.72.0

[platform/upstream/boost.git] / libs / math / doc / html / math_toolkit / ellint / ellint_d.html

diff --git a/libs/math/doc/html/math_toolkit/ellint/ellint_d.html b/libs/math/doc/html/math_toolkit/ellint/ellint_d.html
index a82c773..781cad8 100644 (file)
--- a/libs/math/doc/html/math_toolkit/ellint/ellint_d.html
+++ b/libs/math/doc/html/math_toolkit/ellint/ellint_d.html
@@ -4,7 +4,7 @@
 <title>Elliptic Integral D - Legendre Form</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="../ellint.html" title="Elliptic Integrals">
 <link rel="prev" href="ellint_3.html" title="Elliptic Integrals of the Third Kind - Legendre Form">
 <link rel="next" href="jacobi_zeta.html" title="Jacobi Zeta Function">
@@ -38,14 +38,14 @@
 <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">&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">ellint_d</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">k</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">phi</span><span class="special">);</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> <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">ellint_d</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">k</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">phi</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">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> <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">ellint_d</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">k</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">phi</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">&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">ellint_d</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">k</span><span class="special">);</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> <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">ellint_d</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">k</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">T1</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">ellint_d</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">k</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="special">}}</span> <span class="comment">// namespaces</span>
 </pre>
@@ -66,31 +66,32 @@
 <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">&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">ellint_d</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">k</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">phi</span><span class="special">);</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> <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">ellint_3</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">k</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">phi</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">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> <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">ellint_3</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">k</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">phi</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 incomplete elliptic integral:
       </p>
-<p>
-        <span class="inlinemediaobject"><img src="../../../equations/ellint_d.svg"></span>
-      </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+          <span class="inlinemediaobject"><img src="../../../equations/ellint_d.svg"></span>
+
+        </p></blockquote></div>
 <p>
         Requires <span class="emphasis"><em>k<sup>2</sup>sin<sup>2</sup>(phi) &lt; 1</em></span>, otherwise returns the result
         of <a class="link" href="../error_handling.html#math_toolkit.error_handling.domain_error">domain_error</a>
         (outside this range the result would be complex).
       </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>
 <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">&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">ellint_d</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">k</span><span class="special">);</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> <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">ellint_d</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">k</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">T1</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">ellint_d</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">k</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 complete elliptic integral <span class="emphasis"><em>D(k) = D(&#960;/2, k)</em></span>
@@ -101,9 +102,9 @@
         (outside this range the result would be complex).
       </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>
@@ -118,7 +119,7 @@ is very large, in which case the usual trigonometric function argument-reduction
         issues apply.
       </p>
 <div class="table">
-<a name="math_toolkit.ellint.ellint_d.table_ellint_d_complete_"></a><p class="title"><b>Table&#160;7.66.&#160;Error rates for ellint_d (complete)</b></p>
+<a name="math_toolkit.ellint.ellint_d.table_ellint_d_complete_"></a><p class="title"><b>Table&#160;8.66.&#160;Error rates for ellint_d (complete)</b></p>
 <div class="table-contents"><table class="table" summary="Error rates for ellint_d (complete)">
 <colgroup>
 <col>
@@ -210,7 +211,7 @@ is very large, in which case the usual trigonometric function argument-reduction
 </table></div>
 </div>
 <br class="table-break"><div class="table">
-<a name="math_toolkit.ellint.ellint_d.table_ellint_d"></a><p class="title"><b>Table&#160;7.67.&#160;Error rates for ellint_d</b></p>
+<a name="math_toolkit.ellint.ellint_d.table_ellint_d"></a><p class="title"><b>Table&#160;8.67.&#160;Error rates for ellint_d</b></p>
 <div class="table-contents"><table class="table" summary="Error rates for ellint_d">
 <colgroup>
 <col>
@@ -309,24 +310,27 @@ is very large, in which case the usual trigonometric function argument-reduction
         precision, and GCC-7.1/Ubuntu for <code class="computeroutput"><span class="keyword">long</span>
         <span class="keyword">double</span></code> and <code class="computeroutput"><span class="identifier">__float128</span></code>.
       </p>
-<p>
-        <span class="inlinemediaobject"><img src="../../../graphs/elliptic_integral_d__double.svg" align="middle"></span>
-      </p>
-<p>
-        <span class="inlinemediaobject"><img src="../../../graphs/elliptic_integral_d__80_bit_long_double.svg" align="middle"></span>
-      </p>
-<p>
-        <span class="inlinemediaobject"><img src="../../../graphs/elliptic_integral_d____float128.svg" align="middle"></span>
-      </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+          <span class="inlinemediaobject"><img src="../../../graphs/elliptic_integral_d__double.svg" align="middle"></span>
+
+        </p></blockquote></div>
+<div class="blockquote"><blockquote class="blockquote"><p>
+          <span class="inlinemediaobject"><img src="../../../graphs/elliptic_integral_d__80_bit_long_double.svg" align="middle"></span>
+
+        </p></blockquote></div>
+<div class="blockquote"><blockquote class="blockquote"><p>
+          <span class="inlinemediaobject"><img src="../../../graphs/elliptic_integral_d____float128.svg" align="middle"></span>
+
+        </p></blockquote></div>
 <h5>
 <a name="math_toolkit.ellint.ellint_d.h3"></a>
         <span class="phrase"><a name="math_toolkit.ellint.ellint_d.testing"></a></span><a class="link" href="ellint_d.html#math_toolkit.ellint.ellint_d.testing">Testing</a>
       </h5>
 <p>
         The tests use a mixture of spot test values calculated using values calculated
-        at wolframalpha.com, and random test data generated using MPFR at 1000-bit
-        precision and a deliberately naive implementation in terms of the Legendre
-        integrals.
+        at <a href="http://www.wolframalpha.com/" target="_top">Wolfram Alpha</a>, and random
+        test data generated using MPFR at 1000-bit precision and a deliberately naive
+        implementation in terms of the Legendre integrals.
       </p>
 <h5>
 <a name="math_toolkit.ellint.ellint_d.h4"></a>
@@ -336,26 +340,27 @@ is very large, in which case the usual trigonometric function argument-reduction
         The implementation for D(&#966;, k) first performs argument reduction using the
         relations:
       </p>
-<p>
-        <span class="emphasis"><em>D(-&#966;, k) = -D(&#966;, k)</em></span>
-      </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+          <span class="serif_italic"><span class="emphasis"><em>D(-&#966;, k) = -D(&#966;, k)</em></span></span>
+        </p></blockquote></div>
 <p>
         and
       </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+          <span class="serif_italic"><span class="emphasis"><em>D(n&#960;+&#966;, k) = 2nD(k) + D(&#966;, k)</em></span></span>
+        </p></blockquote></div>
 <p>
-        <span class="emphasis"><em>D(n&#960;+&#966;, k) = 2nD(k) + D(&#966;, k)</em></span>
-      </p>
-<p>
-        to move &#966; &#160; to the range [0, &#960;/2].
+        to move &#966; to the range [0, &#960;/2].
       </p>
 <p>
         The functions are then implemented in terms of Carlson's integral R<sub>D</sub>
 using
         the relation:
       </p>
-<p>
-        <span class="inlinemediaobject"><img src="../../../equations/ellint_d.svg"></span>
-      </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+          <span class="inlinemediaobject"><img src="../../../equations/ellint_d.svg"></span>
+
+        </p></blockquote></div>
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>