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<html> <head> <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> <title>Airy Bi' Function</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"> <link rel="up" href="../airy.html" title="Airy Functions"> <link rel="prev" href="aip.html" title="Airy Ai' Function"> <link rel="next" href="../ellint.html" title="Elliptic Integrals"> </head> <body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> <table cellpadding="2" width="100%"><tr> <td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td> <td align="center"><a href="../../../../../../index.html">Home</a></td> <td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td> <td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> <td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> <td align="center"><a href="../../../../../../more/index.htm">More</a></td> </tr></table> <hr> <div class="spirit-nav"> <a accesskey="p" href="aip.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../airy.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="../ellint.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> </div> <div class="section"> <div class="titlepage"><div><div><h3 class="title"> <a name="math_toolkit.airy.bip"></a><a class="link" href="bip.html" title="Airy Bi' Function">Airy Bi' Function</a> </h3></div></div></div> <h5> <a name="math_toolkit.airy.bip.h0"></a> <a name="math_toolkit.airy.bip.synopsis"></a><a class="link" href="bip.html#math_toolkit.airy.bip.synopsis">Synopsis</a> </h5> <pre class="programlisting">#include <boost/math/special_functions/airy.hpp> </pre> <pre class="programlisting">namespace boost { namespace math { template <class T> <a class="link" href="../result_type.html" title="Calculation of the Type of the Result">calculated-result-type</a> airy_bi_prime(T x); template <class T, class Policy> <a class="link" href="../result_type.html" title="Calculation of the Type of the Result">calculated-result-type</a> airy_bi_prime(T x, const Policy&); }} // namespaces </pre> <h5> <a name="math_toolkit.airy.bip.h1"></a> <a name="math_toolkit.airy.bip.description"></a><a class="link" href="bip.html#math_toolkit.airy.bip.description">Description</a> </h5> The function <a class="link" href="bip.html" title="Airy Bi' Function">airy_bi_prime</a> calculates the Airy function Bi' which is the derivative of the second solution to the differential equation: <img src="../../../equations/airy.png"> The final <a class="link" href="../../policy.html" title="Chapter 14. 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 14. Policies: Controlling Precision, Error Handling etc">policy documentation for more details</a>. The following graph illustrates how this function changes as x changes: for negative x the function is cyclic, while for positive x the value tends to infinity: <img src="../../../graphs/airy_bi.png" align="middle"> <h5> <a name="math_toolkit.airy.bip.h2"></a> <a name="math_toolkit.airy.bip.accuracy"></a><a class="link" href="bip.html#math_toolkit.airy.bip.accuracy">Accuracy</a> </h5> This function is implemented entirely in terms of the Bessel functions <a class="link" href="../bessel/mbessel.html" title="Modified Bessel Functions of the First and Second Kinds">cyl_bessel_i</a> and <a class="link" href="../bessel/bessel_first.html" title="Bessel Functions of the First and Second Kinds">cyl_bessel_j</a> - refer to those functions for detailed accuracy information. In general though, the relative error is low (less than 100 ε) for x > 0 while only the absolute error is low for x < 0. <h5> <a name="math_toolkit.airy.bip.h3"></a> <a name="math_toolkit.airy.bip.testing"></a><a class="link" href="bip.html#math_toolkit.airy.bip.testing">Testing</a> </h5> Since this function is implemented in terms of other special functions, there are only a few basic sanity checks, using test values from <a href="http://functions.wolfram.com" target="_top">functions.wolfram.com</a>. <h5> <a name="math_toolkit.airy.bip.h4"></a> <a name="math_toolkit.airy.bip.implementation"></a><a class="link" href="bip.html#math_toolkit.airy.bip.implementation">Implementation</a> </h5> This function is implemented in terms of the Bessel functions using the relations: <img src="../../../equations/airy_bip.png"> </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 © 2006-2010, 2012-2014 Nikhar Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno Lalande, John Maddock, Johan Råde, Gautam Sewani, Benjamin Sobotta, Thijs van den Berg, Daryle Walker and Xiaogang Zhang 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>) </div></td> </tr></table> <hr> <div class="spirit-nav"> <a accesskey="p" href="aip.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../airy.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="../ellint.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> </div> </body> </html>