Imported Upstream version 1.72.0

[platform/upstream/boost.git] / libs / math / doc / html / math_toolkit / sf_gamma / digamma.html

diff --git a/libs/math/doc/html/math_toolkit/sf_gamma/digamma.html b/libs/math/doc/html/math_toolkit/sf_gamma/digamma.html
index 7be08d7..23369b2 100644 (file)
--- a/libs/math/doc/html/math_toolkit/sf_gamma/digamma.html
+++ b/libs/math/doc/html/math_toolkit/sf_gamma/digamma.html
@@ -4,7 +4,7 @@
 <title>Digamma</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_gamma.html" title="Gamma Functions">
 <link rel="prev" href="lgamma.html" title="Log Gamma">
 <link rel="next" href="trigamma.html" title="Trigamma">
@@ -37,8 +37,8 @@
 <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">digamma</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">z</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">digamma</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">z</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">digamma</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">z</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>
@@ -50,16 +50,18 @@
         Returns the digamma or psi function of <span class="emphasis"><em>x</em></span>. Digamma is
         defined as the logarithmic derivative of the gamma function:
       </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+          <span class="inlinemediaobject"><img src="../../../equations/digamma1.svg"></span>
+
+        </p></blockquote></div>
+<div class="blockquote"><blockquote class="blockquote"><p>
+          <span class="inlinemediaobject"><img src="../../../graphs/digamma.svg" align="middle"></span>
+
+        </p></blockquote></div>
 <p>
-        <span class="inlinemediaobject"><img src="../../../equations/digamma1.svg"></span>
-      </p>
-<p>
-        <span class="inlinemediaobject"><img src="../../../graphs/digamma.svg" align="middle"></span>
-      </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>
 <p>
@@ -77,7 +79,7 @@
         any floating point type that is narrower than the one shown will have <a class="link" href="../relative_error.html#math_toolkit.relative_error.zero_error">effectively zero error</a>.
       </p>
 <div class="table">
-<a name="math_toolkit.sf_gamma.digamma.table_digamma"></a><p class="title"><b>Table&#160;7.4.&#160;Error rates for digamma</b></p>
+<a name="math_toolkit.sf_gamma.digamma.table_digamma"></a><p class="title"><b>Table&#160;8.4.&#160;Error rates for digamma</b></p>
 <div class="table-contents"><table class="table" summary="Error rates for digamma">
 <colgroup>
 <col>
@@ -329,15 +331,18 @@
         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/digamma__double.svg" align="middle"></span>
-      </p>
-<p>
-        <span class="inlinemediaobject"><img src="../../../graphs/digamma__80_bit_long_double.svg" align="middle"></span>
-      </p>
-<p>
-        <span class="inlinemediaobject"><img src="../../../graphs/digamma____float128.svg" align="middle"></span>
-      </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+          <span class="inlinemediaobject"><img src="../../../graphs/digamma__double.svg" align="middle"></span>
+
+        </p></blockquote></div>
+<div class="blockquote"><blockquote class="blockquote"><p>
+          <span class="inlinemediaobject"><img src="../../../graphs/digamma__80_bit_long_double.svg" align="middle"></span>
+
+        </p></blockquote></div>
+<div class="blockquote"><blockquote class="blockquote"><p>
+          <span class="inlinemediaobject"><img src="../../../graphs/digamma____float128.svg" align="middle"></span>
+
+        </p></blockquote></div>
 <h5>
 <a name="math_toolkit.sf_gamma.digamma.h3"></a>
         <span class="phrase"><a name="math_toolkit.sf_gamma.digamma.testing"></a></span><a class="link" href="digamma.html#math_toolkit.sf_gamma.digamma.testing">Testing</a>
@@ -386,9 +391,10 @@
 <p>
         For arguments &gt; BIG the asymptotic expansion:
       </p>
-<p>
-        <span class="inlinemediaobject"><img src="../../../equations/digamma2.svg"></span>
-      </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+          <span class="inlinemediaobject"><img src="../../../equations/digamma2.svg"></span>
+
+        </p></blockquote></div>
 <p>
         can be used. However, this expansion is divergent after a few terms: exactly
         how many terms depends on the size of <span class="emphasis"><em>x</em></span>. Therefore the
@@ -403,12 +409,14 @@
         until x &gt; BIG, and then evaluation via the asymptotic expansion above.
         As special cases integer and half integer arguments are handled via:
       </p>
-<p>
-        <span class="inlinemediaobject"><img src="../../../equations/digamma4.svg"></span>
-      </p>
-<p>
-        <span class="inlinemediaobject"><img src="../../../equations/digamma5.svg"></span>
-      </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+          <span class="inlinemediaobject"><img src="../../../equations/digamma4.svg"></span>
+
+        </p></blockquote></div>
+<div class="blockquote"><blockquote class="blockquote"><p>
+          <span class="inlinemediaobject"><img src="../../../equations/digamma5.svg"></span>
+
+        </p></blockquote></div>
 <p>
         The rational approximation <a class="link" href="../sf_implementation.html#math_toolkit.sf_implementation.rational_approximations_used">devised
         by JM</a> in the range [1,2] is derived as follows.
@@ -418,9 +426,10 @@
         differentiated <a class="link" href="../lanczos.html" title="The Lanczos Approximation">Lanczos approximation</a>,
         the form used is:
       </p>
-<p>
-        <span class="inlinemediaobject"><img src="../../../equations/digamma3.svg"></span>
-      </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+          <span class="inlinemediaobject"><img src="../../../equations/digamma3.svg"></span>
+
+        </p></blockquote></div>
 <p>
         Where P(x) and Q(x) are the polynomials from the rational form of the Lanczos
         sum, and P'(x) and Q'(x) are their first derivatives. The Lanzos part of