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<title>Chapter 23. Backgrounders</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 3.3.0">
<link rel="up" href="index.html" title="Math Toolkit 3.3.0">
<link rel="home" href="index.html" title="Math Toolkit 4.1.0">
<link rel="up" href="index.html" title="Math Toolkit 4.1.0">
<link rel="prev" href="math_toolkit/perf_test_app.html" title="The Performance Test Applications">
<link rel="next" href="math_toolkit/sf_implementation.html" title="Additional Implementation Notes">
</head>

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<title>Chapter 4. Mathematical Constants</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 3.3.0">
<link rel="up" href="index.html" title="Math Toolkit 3.3.0">
<link rel="home" href="index.html" title="Math Toolkit 4.1.0">
<link rel="up" href="index.html" title="Math Toolkit 4.1.0">
<link rel="prev" href="math_toolkit/float128/typeinfo.html" title="typeinfo">
<link rel="next" href="math_toolkit/constants_intro.html" title="Introduction">
</head>

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<title>Chapter 3. Specified-width floating-point typedefs</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 3.3.0">
<link rel="up" href="index.html" title="Math Toolkit 3.3.0">
<link rel="home" href="index.html" title="Math Toolkit 4.1.0">
<link rel="up" href="index.html" title="Math Toolkit 4.1.0">
<link rel="prev" href="math_toolkit/ulps_plots.html" title="ULPs Plots">
<link rel="next" href="math_toolkit/specified_typedefs.html" title="Overview">
</head>

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<title>Chapter 5. Statistical Distributions and Functions</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 3.3.0">
<link rel="up" href="index.html" title="Math Toolkit 3.3.0">
<link rel="home" href="index.html" title="Math Toolkit 4.1.0">
<link rel="up" href="index.html" title="Math Toolkit 4.1.0">
<link rel="prev" href="math_toolkit/constants_faq.html" title="Math Constants FAQs">
<link rel="next" href="math_toolkit/stat_tut.html" title="Statistical Distributions Tutorial">
</head>

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<title>Chapter 9. TR1 and C99 external "C" Functions</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 3.3.0">
<link rel="up" href="index.html" title="Math Toolkit 3.3.0">
<link rel="home" href="index.html" title="Math Toolkit 4.1.0">
<link rel="up" href="index.html" title="Math Toolkit 4.1.0">
<link rel="prev" href="math_toolkit/ccmath.html" title="Constexpr CMath">
<link rel="next" href="math_toolkit/main_tr1.html" title="C99 and TR1 C Functions Overview">
</head>

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<title>Chapter 14. Filters</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 3.3.0">
<link rel="up" href="index.html" title="Math Toolkit 3.3.0">
<link rel="home" href="index.html" title="Math Toolkit 4.1.0">
<link rel="up" href="index.html" title="Math Toolkit 4.1.0">
<link rel="prev" href="math_toolkit/diff0.html" title="Lanczos Smoothing Derivatives">
<link rel="next" href="math_toolkit/daubechies_filters.html" title="Daubechies Filters">
</head>

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<title>Chapter 18. Integer Utilities (Greatest Common Divisor and Least Common Multiple)</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 3.3.0">
<link rel="up" href="index.html" title="Math Toolkit 3.3.0">
<link rel="home" href="index.html" title="Math Toolkit 4.1.0">
<link rel="up" href="index.html" title="Math Toolkit 4.1.0">
<link rel="prev" href="math_toolkit/oct_todo.html" title="To Do">
<link rel="next" href="internals.html" title="Chapter 19. Internal Details: Series, Rationals and Continued Fractions, Testing, and Development Tools">
</head>

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<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<title>Math Toolkit 3.3.0</title>
<title>Math Toolkit 4.1.0</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 3.3.0">
<link rel="home" href="index.html" title="Math Toolkit 4.1.0">
<link rel="next" href="overview.html" title="Chapter 1. Overview">
</head>
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
@@ -22,7 +22,7 @@
<div class="titlepage">
<div>
<div><h1 class="title">
<a name="math_toolkit"></a>Math Toolkit 3.3.0</h1></div>
<a name="math_toolkit"></a>Math Toolkit 4.1.0</h1></div>
<div><div class="authorgroup">
<div class="author"><h3 class="author">
<span class="firstname">Nikhar</span> <span class="surname">Agrawal</span>
@@ -134,7 +134,7 @@ This manual is also available in <a href="http://sourceforge.net/projects/boost/
</div>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"><p><small>Last revised: February 23, 2023 at 17:09:15 GMT</small></p></td>
<td align="left"><p><small>Last revised: February 23, 2023 at 18:11:17 GMT</small></p></td>
<td align="right"><div class="copyright-footer"></div></td>
</tr></table>
<hr>

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<title>Chapter 25. Indexes</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 3.3.0">
<link rel="up" href="index.html" title="Math Toolkit 3.3.0">
<link rel="home" href="index.html" title="Math Toolkit 4.1.0">
<link rel="up" href="index.html" title="Math Toolkit 4.1.0">
<link rel="prev" href="math_toolkit/credits.html" title="Credits and Acknowledgements">
<link rel="next" href="indexes/s01.html" title="Function Index">
</head>

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<title>Function Index</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 3.3.0">
<link rel="home" href="../index.html" title="Math Toolkit 4.1.0">
<link rel="up" href="../indexes.html" title="Chapter 25. Indexes">
<link rel="prev" href="../indexes.html" title="Chapter 25. Indexes">
<link rel="next" href="s02.html" title="Class Index">
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</div>
<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="id2082294"></a>Function Index</h2></div></div></div>
<a name="id2090569"></a>Function Index</h2></div></div></div>
<p><a class="link" href="s01.html#idx_id_0">1</a> <a class="link" href="s01.html#idx_id_1">2</a> <a class="link" href="s01.html#idx_id_2">4</a> <a class="link" href="s01.html#idx_id_5">A</a> <a class="link" href="s01.html#idx_id_6">B</a> <a class="link" href="s01.html#idx_id_7">C</a> <a class="link" href="s01.html#idx_id_8">D</a> <a class="link" href="s01.html#idx_id_9">E</a> <a class="link" href="s01.html#idx_id_10">F</a> <a class="link" href="s01.html#idx_id_11">G</a> <a class="link" href="s01.html#idx_id_12">H</a> <a class="link" href="s01.html#idx_id_13">I</a> <a class="link" href="s01.html#idx_id_14">J</a> <a class="link" href="s01.html#idx_id_15">K</a> <a class="link" href="s01.html#idx_id_16">L</a> <a class="link" href="s01.html#idx_id_17">M</a> <a class="link" href="s01.html#idx_id_18">N</a> <a class="link" href="s01.html#idx_id_19">O</a> <a class="link" href="s01.html#idx_id_20">P</a> <a class="link" href="s01.html#idx_id_21">Q</a> <a class="link" href="s01.html#idx_id_22">R</a> <a class="link" href="s01.html#idx_id_23">S</a> <a class="link" href="s01.html#idx_id_24">T</a> <a class="link" href="s01.html#idx_id_25">U</a> <a class="link" href="s01.html#idx_id_26">V</a> <a class="link" href="s01.html#idx_id_27">W</a> <a class="link" href="s01.html#idx_id_28">X</a> <a class="link" href="s01.html#idx_id_29">Y</a> <a class="link" href="s01.html#idx_id_30">Z</a> <a class="link" href="s01.html#idx_id_31">_</a></p>
<div class="variablelist"><dl class="variablelist">
<dt>

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<title>Class Index</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 3.3.0">
<link rel="home" href="../index.html" title="Math Toolkit 4.1.0">
<link rel="up" href="../indexes.html" title="Chapter 25. Indexes">
<link rel="prev" href="s01.html" title="Function Index">
<link rel="next" href="s03.html" title="Typedef Index">
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</div>
<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="id2113829"></a>Class Index</h2></div></div></div>
<a name="id2120124"></a>Class Index</h2></div></div></div>
<p><a class="link" href="s02.html#idx_id_37">A</a> <a class="link" href="s02.html#idx_id_38">B</a> <a class="link" href="s02.html#idx_id_39">C</a> <a class="link" href="s02.html#idx_id_40">D</a> <a class="link" href="s02.html#idx_id_41">E</a> <a class="link" href="s02.html#idx_id_42">F</a> <a class="link" href="s02.html#idx_id_43">G</a> <a class="link" href="s02.html#idx_id_44">H</a> <a class="link" href="s02.html#idx_id_45">I</a> <a class="link" href="s02.html#idx_id_47">K</a> <a class="link" href="s02.html#idx_id_48">L</a> <a class="link" href="s02.html#idx_id_49">M</a> <a class="link" href="s02.html#idx_id_50">N</a> <a class="link" href="s02.html#idx_id_51">O</a> <a class="link" href="s02.html#idx_id_52">P</a> <a class="link" href="s02.html#idx_id_53">Q</a> <a class="link" href="s02.html#idx_id_54">R</a> <a class="link" href="s02.html#idx_id_55">S</a> <a class="link" href="s02.html#idx_id_56">T</a> <a class="link" href="s02.html#idx_id_57">U</a> <a class="link" href="s02.html#idx_id_58">V</a> <a class="link" href="s02.html#idx_id_59">W</a></p>
<div class="variablelist"><dl class="variablelist">
<dt>

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<title>Typedef Index</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 3.3.0">
<link rel="home" href="../index.html" title="Math Toolkit 4.1.0">
<link rel="up" href="../indexes.html" title="Chapter 25. Indexes">
<link rel="prev" href="s02.html" title="Class Index">
<link rel="next" href="s04.html" title="Macro Index">
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</div>
<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="id2118168"></a>Typedef Index</h2></div></div></div>
<a name="id2122186"></a>Typedef Index</h2></div></div></div>
<p><a class="link" href="s03.html#idx_id_69">A</a> <a class="link" href="s03.html#idx_id_70">B</a> <a class="link" href="s03.html#idx_id_71">C</a> <a class="link" href="s03.html#idx_id_72">D</a> <a class="link" href="s03.html#idx_id_73">E</a> <a class="link" href="s03.html#idx_id_74">F</a> <a class="link" href="s03.html#idx_id_75">G</a> <a class="link" href="s03.html#idx_id_76">H</a> <a class="link" href="s03.html#idx_id_77">I</a> <a class="link" href="s03.html#idx_id_79">K</a> <a class="link" href="s03.html#idx_id_80">L</a> <a class="link" href="s03.html#idx_id_82">N</a> <a class="link" href="s03.html#idx_id_84">P</a> <a class="link" href="s03.html#idx_id_86">R</a> <a class="link" href="s03.html#idx_id_87">S</a> <a class="link" href="s03.html#idx_id_88">T</a> <a class="link" href="s03.html#idx_id_89">U</a> <a class="link" href="s03.html#idx_id_90">V</a> <a class="link" href="s03.html#idx_id_91">W</a></p>
<div class="variablelist"><dl class="variablelist">
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<title>Macro Index</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 3.3.0">
<link rel="home" href="../index.html" title="Math Toolkit 4.1.0">
<link rel="up" href="../indexes.html" title="Chapter 25. Indexes">
<link rel="prev" href="s03.html" title="Typedef Index">
<link rel="next" href="s05.html" title="Index">
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</div>
<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="id2121352"></a>Macro Index</h2></div></div></div>
<a name="id2125884"></a>Macro Index</h2></div></div></div>
<p><a class="link" href="s04.html#idx_id_102">B</a> <a class="link" href="s04.html#idx_id_106">F</a></p>
<div class="variablelist"><dl class="variablelist">
<dt>

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<title>Index</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 3.3.0">
<link rel="home" href="../index.html" title="Math Toolkit 4.1.0">
<link rel="up" href="../indexes.html" title="Chapter 25. Indexes">
<link rel="prev" href="s04.html" title="Macro Index">
</head>
@@ -23,7 +23,7 @@
</div>
<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="id2123021"></a>Index</h2></div></div></div>
<a name="id2129952"></a>Index</h2></div></div></div>
<p><a class="link" href="s05.html#idx_id_128">1</a> <a class="link" href="s05.html#idx_id_129">2</a> <a class="link" href="s05.html#idx_id_130">4</a> <a class="link" href="s05.html#idx_id_131">5</a> <a class="link" href="s05.html#idx_id_132">7</a> <a class="link" href="s05.html#idx_id_133">A</a> <a class="link" href="s05.html#idx_id_134">B</a> <a class="link" href="s05.html#idx_id_135">C</a> <a class="link" href="s05.html#idx_id_136">D</a> <a class="link" href="s05.html#idx_id_137">E</a> <a class="link" href="s05.html#idx_id_138">F</a> <a class="link" href="s05.html#idx_id_139">G</a> <a class="link" href="s05.html#idx_id_140">H</a> <a class="link" href="s05.html#idx_id_141">I</a> <a class="link" href="s05.html#idx_id_142">J</a> <a class="link" href="s05.html#idx_id_143">K</a> <a class="link" href="s05.html#idx_id_144">L</a> <a class="link" href="s05.html#idx_id_145">M</a> <a class="link" href="s05.html#idx_id_146">N</a> <a class="link" href="s05.html#idx_id_147">O</a> <a class="link" href="s05.html#idx_id_148">P</a> <a class="link" href="s05.html#idx_id_149">Q</a> <a class="link" href="s05.html#idx_id_150">R</a> <a class="link" href="s05.html#idx_id_151">S</a> <a class="link" href="s05.html#idx_id_152">T</a> <a class="link" href="s05.html#idx_id_153">U</a> <a class="link" href="s05.html#idx_id_154">V</a> <a class="link" href="s05.html#idx_id_155">W</a> <a class="link" href="s05.html#idx_id_156">X</a> <a class="link" href="s05.html#idx_id_157">Y</a> <a class="link" href="s05.html#idx_id_158">Z</a> <a class="link" href="s05.html#idx_id_159">_</a></p>
<div class="variablelist"><dl class="variablelist">
<dt>

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<title>Chapter 19. Internal Details: Series, Rationals and Continued Fractions, Testing, and Development Tools</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 3.3.0">
<link rel="up" href="index.html" title="Math Toolkit 3.3.0">
<link rel="home" href="index.html" title="Math Toolkit 4.1.0">
<link rel="up" href="index.html" title="Math Toolkit 4.1.0">
<link rel="prev" href="gcd_lcm.html" title="Chapter 18. Integer Utilities (Greatest Common Divisor and Least Common Multiple)">
<link rel="next" href="math_toolkit/internals_overview.html" title="Overview">
</head>

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<title>Chapter 12. Interpolation</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 3.3.0">
<link rel="up" href="index.html" title="Math Toolkit 3.3.0">
<link rel="home" href="index.html" title="Math Toolkit 4.1.0">
<link rel="up" href="index.html" title="Math Toolkit 4.1.0">
<link rel="prev" href="math_toolkit/rational.html" title="Polynomial and Rational Function Evaluation">
<link rel="next" href="math_toolkit/cardinal_cubic_b.html" title="Cardinal Cubic B-spline interpolation">
</head>

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<title>Chapter 15. Complex Number Functions</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 3.3.0">
<link rel="up" href="index.html" title="Math Toolkit 3.3.0">
<link rel="home" href="index.html" title="Math Toolkit 4.1.0">
<link rel="up" href="index.html" title="Math Toolkit 4.1.0">
<link rel="prev" href="math_toolkit/daubechies_filters.html" title="Daubechies Filters">
<link rel="next" href="math_toolkit/complex_implementation.html" title="Implementation and Accuracy">
</head>

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<title>Acknowledgements</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 3.3.0">
<link rel="home" href="../index.html" title="Math Toolkit 4.1.0">
<link rel="up" href="../quaternions.html" title="Chapter 16. Quaternions">
<link rel="prev" href="exp.html" title="The Quaternionic Exponential">
<link rel="next" href="quat_history.html" title="History">

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<title>Acknowledgements</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 3.3.0">
<link rel="home" href="../index.html" title="Math Toolkit 4.1.0">
<link rel="up" href="../octonions.html" title="Chapter 17. Octonions">
<link rel="prev" href="oct_tests.html" title="Test Program">
<link rel="next" href="oct_history.html" title="History">

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<title>acos</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 3.3.0">
<link rel="home" href="../index.html" title="Math Toolkit 4.1.0">
<link rel="up" href="../inverse_complex.html" title="Chapter 15. Complex Number Functions">
<link rel="prev" href="asin.html" title="asin">
<link rel="next" href="atan.html" title="atan">

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<title>acosh</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 3.3.0">
<link rel="home" href="../index.html" title="Math Toolkit 4.1.0">
<link rel="up" href="../inverse_complex.html" title="Chapter 15. Complex Number Functions">
<link rel="prev" href="asinh.html" title="asinh">
<link rel="next" href="atanh.html" title="atanh">

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<title>Airy Functions</title>
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<title>The Mathematical Constants</title>
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<title>Introduction</title>
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<title>Contact Info and Support</title>
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<title>Document Conventions</title>
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<a name="math_toolkit.conventions"></a><a class="link" href="conventions.html" title="Document Conventions">Document Conventions</a>
</h2></div></div></div>
<p>
<a class="indexterm" name="id968419"></a>
<a class="indexterm" name="id974673"></a>
</p>
<p>
This documentation aims to use of the following naming and formatting conventions.

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<title>Quaternion Creation Functions</title>
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<title>Cubic Hermite interpolation</title>
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<title>Roots of Cubic Polynomials</title>
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<title>Daubechies Wavelets and Scaling Functions</title>
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<title>Daubechies Filters</title>
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<title>Numerical Differentiation</title>
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<title>Lanczos Smoothing Derivatives</title>
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<title>Directory and File Structure</title>
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<title>Conceptual Requirements for Distribution Types</title>
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<title>Statistical Distributions Reference</title>
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<title>Distribution Algorithms</title>
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<title>Distributions</title>
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<title>Arcsine Distribution</title>
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<title>Bernoulli Distribution</title>
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<title>Beta Distribution</title>
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<title>Binomial Distribution</title>
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<title>Cauchy-Lorentz Distribution</title>
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<title>Chi Squared Distribution</title>
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<title>Empirical Cumulative Distribution Function</title>
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<title>Exponential Distribution</title>
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<title>Extreme Value Distribution</title>
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<title>F Distribution</title>
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<title>Gamma (and Erlang) Distribution</title>
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<title>Geometric Distribution</title>
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<title>Hyperexponential Distribution</title>
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<title>Hypergeometric Distribution</title>
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<title>Inverse Chi Squared Distribution</title>
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<title>Inverse Gamma Distribution</title>
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<link rel="prev" href="inverse_chi_squared_dist.html" title="Inverse Chi Squared Distribution">
<link rel="next" href="inverse_gaussian_dist.html" title="Inverse Gaussian (or Inverse Normal) Distribution">

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<title>Inverse Gaussian (or Inverse Normal) Distribution</title>
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<title>Kolmogorov-Smirnov Distribution</title>
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<link rel="prev" href="inverse_gaussian_dist.html" title="Inverse Gaussian (or Inverse Normal) Distribution">
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<title>Laplace Distribution</title>
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