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Diffstat (limited to 'libs/math/doc/html/math_toolkit/lanczos.html')
| -rw-r--r-- | libs/math/doc/html/math_toolkit/lanczos.html | 24 |
1 files changed, 12 insertions, 12 deletions
diff --git a/libs/math/doc/html/math_toolkit/lanczos.html b/libs/math/doc/html/math_toolkit/lanczos.html index e178ba6f2..daa6cb855 100644 --- a/libs/math/doc/html/math_toolkit/lanczos.html +++ b/libs/math/doc/html/math_toolkit/lanczos.html @@ -3,8 +3,8 @@ <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> <title>The Lanczos Approximation</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="../backgrounders.html" title="Chapter 16. Backgrounders"> <link rel="prev" href="relative_error.html" title="Relative Error"> <link rel="next" href="remez.html" title="The Remez Method"> @@ -106,7 +106,7 @@ The Lanczos Approximation to the Gamma Function is given by: </p> <p> - <span class="inlinemediaobject"><img src="../../equations/lanczos0.png"></span> + <span class="inlinemediaobject"><img src="../../equations/lanczos0.svg"></span> </p> <p> Where S<sub>g</sub>(z) is an infinite sum, that is convergent for all z > 0, and <span class="emphasis"><em>g</em></span> @@ -114,13 +114,13 @@ in the sum which is given by: </p> <p> - <span class="inlinemediaobject"><img src="../../equations/lanczos0a.png"></span> + <span class="inlinemediaobject"><img src="../../equations/lanczos0a.svg"></span> </p> <p> With individual coefficients defined in closed form by: </p> <p> - <span class="inlinemediaobject"><img src="../../equations/lanczos0b.png"></span> + <span class="inlinemediaobject"><img src="../../equations/lanczos0b.svg"></span> </p> <p> However, evaluation of the sum in that form can lead to numerical instability @@ -133,13 +133,13 @@ with the leading constants absorbed by the coefficients in the sum: </p> <p> - <span class="inlinemediaobject"><img src="../../equations/lanczos1.png"></span> + <span class="inlinemediaobject"><img src="../../equations/lanczos1.svg"></span> </p> <p> where: </p> <p> - <span class="inlinemediaobject"><img src="../../equations/lanczos2.png"></span> + <span class="inlinemediaobject"><img src="../../equations/lanczos2.svg"></span> </p> <p> Again parameter <span class="emphasis"><em>g</em></span> is an arbitrarily chosen constant, and @@ -178,25 +178,25 @@ where B is an NxN matrix: </p> <p> - <span class="inlinemediaobject"><img src="../../equations/lanczos4.png"></span> + <span class="inlinemediaobject"><img src="../../equations/lanczos4.svg"></span> </p> <p> D is an NxN matrix: </p> <p> - <span class="inlinemediaobject"><img src="../../equations/lanczos3.png"></span> + <span class="inlinemediaobject"><img src="../../equations/lanczos3.svg"></span> </p> <p> C is an NxN matrix: </p> <p> - <span class="inlinemediaobject"><img src="../../equations/lanczos5.png"></span> + <span class="inlinemediaobject"><img src="../../equations/lanczos5.svg"></span> </p> <p> and F is an N element column vector: </p> <p> - <span class="inlinemediaobject"><img src="../../equations/lanczos6.png"></span> + <span class="inlinemediaobject"><img src="../../equations/lanczos6.svg"></span> </p> <p> Note than the matrices B, D and C contain all integer terms and depend only @@ -526,7 +526,7 @@ by exp(g): </p> <p> - <span class="inlinemediaobject"><img src="../../equations/lanczos7.png"></span> + <span class="inlinemediaobject"><img src="../../equations/lanczos7.svg"></span> </p> <p> This form is more convenient for calculating lgamma, but for the gamma function |