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Edouard DUPIN
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@@ -1,10 +1,10 @@
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<title>Airy Ai Function</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 2.6.0">
<link rel="home" href="../../index.html" title="Math Toolkit 3.0.0">
<link rel="up" href="../airy.html" title="Airy Functions">
<link rel="prev" href="../airy.html" title="Airy Functions">
<link rel="next" href="bi.html" title="Airy Bi Function">
@@ -50,17 +50,22 @@
The function <a class="link" href="ai.html" title="Airy Ai Function">airy_ai</a> calculates
the Airy function Ai which is the first solution to the differential equation:
</p>
<p>
<span class="inlinemediaobject"><img src="../../../equations/airy.svg"></span>
</p>
<div class="blockquote"><blockquote class="blockquote"><p>
<span class="inlinemediaobject"><img src="../../../equations/airy.svg"></span>
</p></blockquote></div>
<p>
See Weisstein, Eric W. "Airy Functions." From MathWorld--A Wolfram
Web Resource. <a href="http://mathworld.wolfram.com/AiryFunctions.html" target="_top">http://mathworld.wolfram.com/AiryFunctions.html</a>;
Web Resource. <a href="http://mathworld.wolfram.com/AiryFunctions.html" target="_top">http://mathworld.wolfram.com/AiryFunctions.html</a>
</p>
<p>
The final <a class="link" href="../../policy.html" title="Chapter&#160;18.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a> argument is optional and can
and <a href="https://en.wikipedia.org/wiki/Airy_zeta_function" target="_top">Airy Zeta
function</a>.
</p>
<p>
The final <a class="link" href="../../policy.html" title="Chapter 21. 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;18.&#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 21. Policies: Controlling Precision, Error Handling etc">policy
documentation for more details</a>.
</p>
<p>
@@ -68,9 +73,10 @@
changes: for negative <span class="emphasis"><em>x</em></span> the function is cyclic, while
for positive <span class="emphasis"><em>x</em></span> the value tends to zero:
</p>
<p>
<span class="inlinemediaobject"><img src="../../../graphs/airy_ai.svg" align="middle"></span>
</p>
<div class="blockquote"><blockquote class="blockquote"><p>
<span class="inlinemediaobject"><img src="../../../graphs/airy_ai.svg" align="middle"></span>
</p></blockquote></div>
<h5>
<a name="math_toolkit.airy.ai.h2"></a>
<span class="phrase"><a name="math_toolkit.airy.ai.accuracy"></a></span><a class="link" href="ai.html#math_toolkit.airy.ai.accuracy">Accuracy</a>
@@ -80,10 +86,14 @@
functions for detailed accuracy information.
</p>
<p>
In general though, the relative error is low (less than 100 &#949;) for <span class="emphasis"><em>x
In general though, the relative error is low (less than 100 ε) for <span class="emphasis"><em>x
&gt; 0</em></span> while only the absolute error is low for <span class="emphasis"><em>x &lt;
0</em></span>.
0</em></span> as the following error plot illustrates:
</p>
<div class="blockquote"><blockquote class="blockquote"><p>
<span class="inlinemediaobject"><img src="../../../graphs/ai__double.svg" align="middle"></span>
</p></blockquote></div>
<h5>
<a name="math_toolkit.airy.ai.h3"></a>
<span class="phrase"><a name="math_toolkit.airy.ai.testing"></a></span><a class="link" href="ai.html#math_toolkit.airy.ai.testing">Testing</a>
@@ -100,17 +110,18 @@
<p>
This function is implemented in terms of the Bessel functions using the relations:
</p>
<p>
<span class="inlinemediaobject"><img src="../../../equations/airy_ai.svg"></span>
</p>
<div class="blockquote"><blockquote class="blockquote"><p>
<span class="inlinemediaobject"><img src="../../../equations/airy_ai.svg"></span>
</p></blockquote></div>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
and Xiaogang Zhang<p>
<td align="right"><div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
Walker and Xiaogang Zhang<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
</p>