Imported Upstream version 1.72.0

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

diff --git a/libs/math/doc/html/math_toolkit/sf_poly/legendre_stieltjes.html b/libs/math/doc/html/math_toolkit/sf_poly/legendre_stieltjes.html
index b15bcd4..0320553 100644 (file)
--- a/libs/math/doc/html/math_toolkit/sf_poly/legendre_stieltjes.html
+++ b/libs/math/doc/html/math_toolkit/sf_poly/legendre_stieltjes.html
@@ -4,7 +4,7 @@
 <title>Legendre-Stieltjes 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="legendre.html" title="Legendre (and Associated) Polynomials">
 <link rel="next" href="laguerre.html" title="Laguerre (and Associated) Polynomials">
@@ -70,30 +70,37 @@
         of degree n+1.
       </p>
 <p>
-        The Legendre-Stieltjes polynomials <span class="emphasis"><em>E</em></span><sub>n+1</sub> are defined by
-        the property that they have <span class="emphasis"><em>n</em></span> vanishing moments against
-        the oscillatory measure P<sub>n</sub>, i.e., &#8747;<sub>-1</sub><sup>1</sup> E<sub>n+1</sub>(x)P<sub>n</sub>(x) x<sup>k</sup> dx = 0 for <span class="emphasis"><em>k
-        = 0, 1, ..., n</em></span>. The first few are
+        The Legendre-Stieltjes polynomials <span class="emphasis"><em>E<sub>n+1</sub></em></span> are defined
+        by the property that they have <span class="emphasis"><em>n</em></span> vanishing moments against
+        the oscillatory measure <span class="emphasis"><em>P<sub>n</sub></em></span>, i.e.,
       </p>
-<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
-<li class="listitem">
-            E<sub>1</sub>(x) = P<sub>1</sub>(x)
-          </li>
-<li class="listitem">
-            E<sub>2</sub>(x) = P<sub>2</sub>(x) - 2P<sub>0</sub>(x)/5
-          </li>
-<li class="listitem">
-            E<sub>3</sub>(x) = P<sub>3</sub>(x) - 9P<sub>1</sub>(x)/14
-          </li>
-<li class="listitem">
-            E<sub>4</sub>(x) = P<sub>4</sub>(x) - 20P<sub>2</sub>(x)/27 + 14P<sub>0</sub>(x)/891
-          </li>
-<li class="listitem">
-            E<sub>5</sub>(x) = P<sub>5</sub>(x) - 35P<sub>3</sub>(x)/44 + 135P<sub>1</sub>(x)/12584
-          </li>
-</ul></div>
+<div class="blockquote"><blockquote class="blockquote"><p>
+          <span class="serif_italic">&#8747; <sub>-1</sub><sup>1</sup> E<sub>n+1</sub>(x)P<sub>n</sub>(x) x<sup>k</sup>dx = 0</span>
+        </p></blockquote></div>
 <p>
-        where P<sub>i</sub> are the Legendre polynomials. The scaling follows <a href="http://www.ams.org/journals/mcom/1968-22-104/S0025-5718-68-99866-9/S0025-5718-68-99866-9.pdf" target="_top">Patterson</a>,
+        for <span class="emphasis"><em>k = 0, 1, ..., n</em></span>.
+      </p>
+<p>
+        The first few are
+      </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+          <span class="serif_italic">E<sub>1</sub>(x) = P<sub>1</sub>(x)</span>
+        </p></blockquote></div>
+<div class="blockquote"><blockquote class="blockquote"><p>
+          <span class="serif_italic">E<sub>2</sub>(x) = P<sub>2</sub>(x) - 2P<sub>0</sub>(x)/5</span>
+        </p></blockquote></div>
+<div class="blockquote"><blockquote class="blockquote"><p>
+          <span class="serif_italic">E<sub>3</sub>(x) = P<sub>3</sub>(x) - 9P<sub>1</sub>(x)/14</span>
+        </p></blockquote></div>
+<div class="blockquote"><blockquote class="blockquote"><p>
+          <span class="serif_italic">E<sub>4</sub>(x) = P<sub>4</sub>(x) - 20P<sub>2</sub>(x)/27 + 14P<sub>0</sub>(x)/891</span>
+        </p></blockquote></div>
+<div class="blockquote"><blockquote class="blockquote"><p>
+          <span class="serif_italic">E<sub>5</sub>(x) = P<sub>5</sub>(x) - 35P<sub>3</sub>(x)/44 + 135P<sub>1</sub>(x)/12584</span>
+        </p></blockquote></div>
+<p>
+        where <span class="emphasis"><em>P<sub>i</sub></em></span> are the Legendre polynomials. The scaling follows
+        <a href="http://www.ams.org/journals/mcom/1968-22-104/S0025-5718-68-99866-9/S0025-5718-68-99866-9.pdf" target="_top">Patterson</a>,
         who expanded the Legendre-Stieltjes polynomials in a Legendre series and
         took the coefficient of the highest-order Legendre polynomial in the series
         to be unity.