[DEV] add v1.76.0

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2021-10-05 21:37:46 +02:00
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commit d0115b733d
45133 changed files with 4744437 additions and 1026325 deletions

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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>

View File

@@ -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="bi.html" title="Airy Bi Function">
<link rel="next" href="bip.html" title="Airy Bi' Function">
@@ -51,13 +51,14 @@
the Airy function Ai' which is the derivative of the first solution to the
differential equation:
</p>
<div class="blockquote"><blockquote class="blockquote"><p>
<span class="inlinemediaobject"><img src="../../../equations/airy.svg"></span>
</p></blockquote></div>
<p>
<span class="inlinemediaobject"><img src="../../../equations/airy.svg"></span>
</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
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>
@@ -65,9 +66,10 @@
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_aip.svg" align="middle"></span>
</p>
<div class="blockquote"><blockquote class="blockquote"><p>
<span class="inlinemediaobject"><img src="../../../graphs/airy_aip.svg" align="middle"></span>
</p></blockquote></div>
<h5>
<a name="math_toolkit.airy.aip.h2"></a>
<span class="phrase"><a name="math_toolkit.airy.aip.accuracy"></a></span><a class="link" href="aip.html#math_toolkit.airy.aip.accuracy">Accuracy</a>
@@ -77,10 +79,14 @@
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_prime__double.svg" align="middle"></span>
</p></blockquote></div>
<h5>
<a name="math_toolkit.airy.aip.h3"></a>
<span class="phrase"><a name="math_toolkit.airy.aip.testing"></a></span><a class="link" href="aip.html#math_toolkit.airy.aip.testing">Testing</a>
@@ -96,17 +102,18 @@
<p>
This function is implemented in terms of the Bessel functions using the relations:
</p>
<p>
<span class="inlinemediaobject"><img src="../../../equations/airy_aip.svg"></span>
</p>
<div class="blockquote"><blockquote class="blockquote"><p>
<span class="inlinemediaobject"><img src="../../../equations/airy_aip.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>

View File

@@ -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>Finding Zeros of Airy 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 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="bip.html" title="Airy Bi' Function">
<link rel="next" href="../ellint.html" title="Elliptic Integrals">
@@ -65,7 +65,7 @@
<span class="identifier">OutputIterator</span> <span class="identifier">out_it</span><span class="special">);</span> <span class="comment">// Destination for zeros.</span>
</pre>
<p>
There are also versions which allow control of the <a class="link" href="../../policy.html" title="Chapter&#160;18.&#160;Policies: Controlling Precision, Error Handling etc">Policies</a>
There are also versions which allow control of the <a class="link" href="../../policy.html" title="Chapter 21. Policies: Controlling Precision, Error Handling etc">Policies</a>
for error handling and precision.
</p>
<pre class="programlisting"> <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
@@ -102,12 +102,12 @@
real axis. The real zeros on the negative real axis can be found by solving
for the roots of
</p>
<p>
&#8193; <span class="emphasis"><em>Ai(x<sub>m</sub>) = 0</em></span>
</p>
<p>
&#8193; <span class="emphasis"><em>Bi(y<sub>m</sub>) = 0</em></span>
</p>
<div class="blockquote"><blockquote class="blockquote"><p>
<span class="emphasis"><em>Ai(x<sub>m</sub>) = 0</em></span>
</p></blockquote></div>
<div class="blockquote"><blockquote class="blockquote"><p>
<span class="emphasis"><em>Bi(y<sub>m</sub>) = 0</em></span>
</p></blockquote></div>
<p>
Here, <span class="emphasis"><em>x<sub>m</sub></em></span> represents the <span class="emphasis"><em>m<sup>th</sup></em></span> root
of the Airy Ai function, and <span class="emphasis"><em>y<sub>m</sub></em></span> represents the <span class="emphasis"><em>m<sup>th</sup></em></span>
@@ -265,9 +265,10 @@
</tr>
</tbody>
</table></div>
<p>
<span class="inlinemediaobject"><img src="../../../graphs/airy_zeros.svg" align="middle"></span>
</p>
<div class="blockquote"><blockquote class="blockquote"><p>
<span class="inlinemediaobject"><img src="../../../graphs/airy_zeros.svg" align="middle"></span>
</p></blockquote></div>
<h5>
<a name="math_toolkit.airy.airy_root.h2"></a>
<span class="phrase"><a name="math_toolkit.airy.airy_root.examples_of_finding_airy_zeros"></a></span><a class="link" href="airy_root.html#math_toolkit.airy.airy_root.examples_of_finding_airy_zeros">Examples
@@ -312,7 +313,7 @@
<span class="identifier">OutputIterator</span> <span class="identifier">out_it</span><span class="special">);</span> <span class="comment">// Destination for zeros.</span>
</pre>
<p>
There are also versions which allows control of the <a class="link" href="../../policy.html" title="Chapter&#160;18.&#160;Policies: Controlling Precision, Error Handling etc">Policies</a>
There are also versions which allows control of the <a class="link" href="../../policy.html" title="Chapter 21. Policies: Controlling Precision, Error Handling etc">Policies</a>
for error handling and precision.
</p>
<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">OutputIterator</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Policy</span><span class="special">&gt;</span>
@@ -427,21 +428,24 @@ airy_ai_zeros:
<p>
Given the following function (A&amp;S 10.4.105):
</p>
<p>
<span class="inlinemediaobject"><img src="../../../equations/airy_zero_1.svg"></span>
</p>
<div class="blockquote"><blockquote class="blockquote"><p>
<span class="inlinemediaobject"><img src="../../../equations/airy_zero_1.svg"></span>
</p></blockquote></div>
<p>
Then an initial estimate for the n<sup>th</sup> zero a<sub>n</sub> of Ai is given by (A&amp;S 10.4.94):
</p>
<p>
<span class="inlinemediaobject"><img src="../../../equations/airy_zero_2.svg"></span>
</p>
<div class="blockquote"><blockquote class="blockquote"><p>
<span class="inlinemediaobject"><img src="../../../equations/airy_zero_2.svg"></span>
</p></blockquote></div>
<p>
and an initial estimate for the n<sup>th</sup> zero b<sub>n</sub> of Bi is given by (A&amp;S 10.4.98):
</p>
<p>
<span class="inlinemediaobject"><img src="../../../equations/airy_zero_3.svg"></span>
</p>
<div class="blockquote"><blockquote class="blockquote"><p>
<span class="inlinemediaobject"><img src="../../../equations/airy_zero_3.svg"></span>
</p></blockquote></div>
<p>
Thereafter the roots are refined using Newton iteration.
</p>
@@ -458,11 +462,11 @@ airy_ai_zeros:
</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>

View File

@@ -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 Bi 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="ai.html" title="Airy Ai Function">
<link rel="next" href="aip.html" title="Airy Ai' Function">
@@ -50,13 +50,14 @@
The function <a class="link" href="bi.html" title="Airy Bi Function">airy_bi</a> calculates
the Airy function Bi which is the second solution to the differential equation:
</p>
<div class="blockquote"><blockquote class="blockquote"><p>
<span class="inlinemediaobject"><img src="../../../equations/airy.svg"></span>
</p></blockquote></div>
<p>
<span class="inlinemediaobject"><img src="../../../equations/airy.svg"></span>
</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
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>
@@ -64,9 +65,10 @@
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 infinity:
</p>
<p>
<span class="inlinemediaobject"><img src="../../../graphs/airy_bi.svg" align="middle"></span>
</p>
<div class="blockquote"><blockquote class="blockquote"><p>
<span class="inlinemediaobject"><img src="../../../graphs/airy_bi.svg" align="middle"></span>
</p></blockquote></div>
<h5>
<a name="math_toolkit.airy.bi.h2"></a>
<span class="phrase"><a name="math_toolkit.airy.bi.accuracy"></a></span><a class="link" href="bi.html#math_toolkit.airy.bi.accuracy">Accuracy</a>
@@ -76,10 +78,14 @@
- refer to those 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 illustrate:
</p>
<div class="blockquote"><blockquote class="blockquote"><p>
<span class="inlinemediaobject"><img src="../../../graphs/bi__double.svg" align="middle"></span>
</p></blockquote></div>
<h5>
<a name="math_toolkit.airy.bi.h3"></a>
<span class="phrase"><a name="math_toolkit.airy.bi.testing"></a></span><a class="link" href="bi.html#math_toolkit.airy.bi.testing">Testing</a>
@@ -95,17 +101,18 @@
<p>
This function is implemented in terms of the Bessel functions using the relations:
</p>
<p>
<span class="inlinemediaobject"><img src="../../../equations/airy_bi.svg"></span>
</p>
<div class="blockquote"><blockquote class="blockquote"><p>
<span class="inlinemediaobject"><img src="../../../equations/airy_bi.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>

View File

@@ -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 Bi' 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="aip.html" title="Airy Ai' Function">
<link rel="next" href="airy_root.html" title="Finding Zeros of Airy Functions">
@@ -51,13 +51,14 @@
the Airy function Bi' which is the derivative of the second solution to the
differential equation:
</p>
<div class="blockquote"><blockquote class="blockquote"><p>
<span class="inlinemediaobject"><img src="../../../equations/airy.svg"></span>
</p></blockquote></div>
<p>
<span class="inlinemediaobject"><img src="../../../equations/airy.svg"></span>
</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
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>
@@ -65,9 +66,10 @@
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 infinity:
</p>
<p>
<span class="inlinemediaobject"><img src="../../../graphs/airy_bi.svg" align="middle"></span>
</p>
<div class="blockquote"><blockquote class="blockquote"><p>
<span class="inlinemediaobject"><img src="../../../graphs/airy_bi.svg" align="middle"></span>
</p></blockquote></div>
<h5>
<a name="math_toolkit.airy.bip.h2"></a>
<span class="phrase"><a name="math_toolkit.airy.bip.accuracy"></a></span><a class="link" href="bip.html#math_toolkit.airy.bip.accuracy">Accuracy</a>
@@ -77,10 +79,14 @@
- refer to those 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/bi_prime__double.svg" align="middle"></span>
</p></blockquote></div>
<h5>
<a name="math_toolkit.airy.bip.h3"></a>
<span class="phrase"><a name="math_toolkit.airy.bip.testing"></a></span><a class="link" href="bip.html#math_toolkit.airy.bip.testing">Testing</a>
@@ -96,17 +102,18 @@
<p>
This function is implemented in terms of the Bessel functions using the relations:
</p>
<p>
<span class="inlinemediaobject"><img src="../../../equations/airy_bip.svg"></span>
</p>
<div class="blockquote"><blockquote class="blockquote"><p>
<span class="inlinemediaobject"><img src="../../../equations/airy_bip.svg"></span>
</p></blockquote></div>
</div>
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<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>