diff options
Diffstat (limited to 'libs/math/doc/html/math_toolkit/expint')
| -rw-r--r-- | libs/math/doc/html/math_toolkit/expint/expint_i.html | 18 | ||||
| -rw-r--r-- | libs/math/doc/html/math_toolkit/expint/expint_n.html | 16 |
2 files changed, 17 insertions, 17 deletions
diff --git a/libs/math/doc/html/math_toolkit/expint/expint_i.html b/libs/math/doc/html/math_toolkit/expint/expint_i.html index deaeb7975..1513422ff 100644 --- a/libs/math/doc/html/math_toolkit/expint/expint_i.html +++ b/libs/math/doc/html/math_toolkit/expint/expint_i.html @@ -3,8 +3,8 @@ <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> <title>Exponential Integral Ei</title> <link rel="stylesheet" href="../../math.css" type="text/css"> -<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> -<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0"> +<meta name="generator" content="DocBook XSL Stylesheets V1.77.1"> +<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0"> <link rel="up" href="../expint.html" title="Exponential Integrals"> <link rel="prev" href="expint_n.html" title="Exponential Integral En"> <link rel="next" href="../powers.html" title="Basic Functions"> @@ -67,10 +67,10 @@ integral</a> of z: </p> <p> - <span class="inlinemediaobject"><img src="../../../equations/expint_i_1.png"></span> + <span class="inlinemediaobject"><img src="../../../equations/expint_i_1.svg"></span> </p> <p> - <span class="inlinemediaobject"><img src="../../../graphs/expint_i.png" align="middle"></span> + <span class="inlinemediaobject"><img src="../../../graphs/expint_i.svg" align="middle"></span> </p> <h5> <a name="math_toolkit.expint.expint_i.h2"></a> @@ -223,7 +223,7 @@ For x > 0 the generic version is implemented using the infinte series: </p> <p> - <span class="inlinemediaobject"><img src="../../../equations/expint_i_2.png"></span> + <span class="inlinemediaobject"><img src="../../../equations/expint_i_2.svg"></span> </p> <p> However, when the precision of the argument type is known at compile time @@ -234,14 +234,14 @@ For 0 < z < 6 a root-preserving approximation of the form: </p> <p> - <span class="inlinemediaobject"><img src="../../../equations/expint_i_3.png"></span> + <span class="inlinemediaobject"><img src="../../../equations/expint_i_3.svg"></span> </p> <p> is used, where z<sub>0</sub> is the positive root of the function, and R(z/3 - 1) is a minimax rational approximation rescaled so that it is evaluated over [-1,1]. Note that while the rational approximation over [0,6] converges rapidly to the minimax solution it is rather ill-conditioned in practice. Cody and Thacher - <a href="#ftn.math_toolkit.expint.expint_i.f0" class="footnote" name="math_toolkit.expint.expint_i.f0"><sup class="footnote">[5]</sup></a> experienced the same issue and converted the polynomials into + <a href="#ftn.math_toolkit.expint.expint_i.f0" class="footnote"><sup class="footnote"><a name="math_toolkit.expint.expint_i.f0"></a>[5]</sup></a> experienced the same issue and converted the polynomials into Chebeshev form to ensure stable computation. By experiment we found that the polynomials are just as stable in polynomial as Chebyshev form, <span class="emphasis"><em>provided</em></span> they are computed over the interval [-1,1]. @@ -251,7 +251,7 @@ takes the form: </p> <p> - <span class="inlinemediaobject"><img src="../../../equations/expint_i_4.png"></span> + <span class="inlinemediaobject"><img src="../../../equations/expint_i_4.svg"></span> </p> <p> where <span class="emphasis"><em>c</em></span> is a constant, and R(t) is a minimax solution @@ -268,7 +268,7 @@ involved. </p> <div class="footnotes"> -<br><hr style="width:100; text-align:left;margin-left: 0"> +<br><hr style="width:100; align:left;"> <div id="ftn.math_toolkit.expint.expint_i.f0" class="footnote"><p><a href="#math_toolkit.expint.expint_i.f0" class="para"><sup class="para">[5] </sup></a> W. J. Cody and H. C. Thacher, Jr., Rational Chebyshev approximations for the exponential integral E<sub>1</sub>(x), Math. Comp. 22 (1968), 641-649, and W. diff --git a/libs/math/doc/html/math_toolkit/expint/expint_n.html b/libs/math/doc/html/math_toolkit/expint/expint_n.html index 032c473da..3e5411322 100644 --- a/libs/math/doc/html/math_toolkit/expint/expint_n.html +++ b/libs/math/doc/html/math_toolkit/expint/expint_n.html @@ -3,8 +3,8 @@ <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> <title>Exponential Integral En</title> <link rel="stylesheet" href="../../math.css" type="text/css"> -<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> -<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0"> +<meta name="generator" content="DocBook XSL Stylesheets V1.77.1"> +<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0"> <link rel="up" href="../expint.html" title="Exponential Integrals"> <link rel="prev" href="../expint.html" title="Exponential Integrals"> <link rel="next" href="expint_i.html" title="Exponential Integral Ei"> @@ -67,10 +67,10 @@ integral En</a> of z: </p> <p> - <span class="inlinemediaobject"><img src="../../../equations/expint_n_1.png"></span> + <span class="inlinemediaobject"><img src="../../../equations/expint_n_1.svg"></span> </p> <p> - <span class="inlinemediaobject"><img src="../../../graphs/expint2.png" align="middle"></span> + <span class="inlinemediaobject"><img src="../../../graphs/expint2.svg" align="middle"></span> </p> <h5> <a name="math_toolkit.expint.expint_n.h2"></a> @@ -237,13 +237,13 @@ The generic version of this function uses the continued fraction: </p> <p> - <span class="inlinemediaobject"><img src="../../../equations/expint_n_3.png"></span> + <span class="inlinemediaobject"><img src="../../../equations/expint_n_3.svg"></span> </p> <p> for large <span class="emphasis"><em>x</em></span> and the infinite series: </p> <p> - <span class="inlinemediaobject"><img src="../../../equations/expint_n_2.png"></span> + <span class="inlinemediaobject"><img src="../../../equations/expint_n_2.svg"></span> </p> <p> for small <span class="emphasis"><em>x</em></span>. @@ -261,7 +261,7 @@ approximation: </p> <p> - <span class="inlinemediaobject"><img src="../../../equations/expint_n_4.png"></span> + <span class="inlinemediaobject"><img src="../../../equations/expint_n_4.svg"></span> </p> <p> and for <code class="computeroutput"><span class="identifier">x</span> <span class="special">></span> @@ -269,7 +269,7 @@ of the form: </p> <p> - <span class="inlinemediaobject"><img src="../../../equations/expint_n_5.png"></span> + <span class="inlinemediaobject"><img src="../../../equations/expint_n_5.svg"></span> </p> <p> is used. |