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  26 <div class="titlepage"><div><div><h3 class="title">
  27 <a name="math_toolkit.airy.bi"></a><a class="link" href="bi.html" title="Airy Bi Function">Airy Bi Function</a>
  28 </h3></div></div></div>
  29 <h5>
  30 <a name="math_toolkit.airy.bi.h0"></a>
  31         <span class="phrase"><a name="math_toolkit.airy.bi.synopsis"></a></span><a class="link" href="bi.html#math_toolkit.airy.bi.synopsis">Synopsis</a>
  32       </h5>
  33 <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">airy</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
  34 </pre>
  35 <pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span> <span class="special">{</span>
  36
  37  <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>
  38  <a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">airy_bi</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">x</span><span class="special">);</span>
  39
  40  <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">Policy</span><span class="special">&gt;</span>
  41  <a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">airy_bi</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Policy</span><span class="special">&amp;);</span>
  42
  43 <span class="special">}}</span> <span class="comment">// namespaces</span>
  44 </pre>
  45 <h5>
  46 <a name="math_toolkit.airy.bi.h1"></a>
  47         <span class="phrase"><a name="math_toolkit.airy.bi.description"></a></span><a class="link" href="bi.html#math_toolkit.airy.bi.description">Description</a>
  48       </h5>
  49 <p>
  50         The function <a class="link" href="bi.html" title="Airy Bi Function">airy_bi</a> calculates
  51         the Airy function Bi which is the second solution to the differential equation:
  52       </p>
  53 <p>
  54         <span class="inlinemediaobject"><img src="../../../equations/airy.png"></span>
  55       </p>
  56 <p>
  57         The final <a class="link" href="../../policy.html" title="Chapter&#160;14.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a> argument is optional and can
  58         be used to control the behaviour of the function: how it handles errors,
  59         what level of precision to use etc. Refer to the <a class="link" href="../../policy.html" title="Chapter&#160;14.&#160;Policies: Controlling Precision, Error Handling etc">policy
  60         documentation for more details</a>.
  61       </p>
  62 <p>
  63         The following graph illustrates how this function changes as <span class="emphasis"><em>x</em></span>
  64         changes: for negative <span class="emphasis"><em>x</em></span> the function is cyclic, while
  65         for positive <span class="emphasis"><em>x</em></span> the value tends to infinity:
  66       </p>
  67 <p>
  68         <span class="inlinemediaobject"><img src="../../../graphs/airy_bi.png" align="middle"></span>
  69       </p>
  70 <h5>
  71 <a name="math_toolkit.airy.bi.h2"></a>
  72         <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>
  73       </h5>
  74 <p>
  75         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>
  76         - refer to those functions for detailed accuracy information.
  77       </p>
  78 <p>
  79         In general though, the relative error is low (less than 100 &#949;) for <span class="emphasis"><em>x
  80         &gt; 0</em></span> while only the absolute error is low for <span class="emphasis"><em>x &lt;
  81         0</em></span>.
  82       </p>
  83 <h5>
  84 <a name="math_toolkit.airy.bi.h3"></a>
  85         <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>
  86       </h5>
  87 <p>
  88         Since this function is implemented in terms of other special functions, there
  89         are only a few basic sanity checks, using test values from <a href="http://functions.wolfram.com" target="_top">functions.wolfram.com</a>.
  90       </p>
  91 <h5>
  92 <a name="math_toolkit.airy.bi.h4"></a>
  93         <span class="phrase"><a name="math_toolkit.airy.bi.implementation"></a></span><a class="link" href="bi.html#math_toolkit.airy.bi.implementation">Implementation</a>
  94       </h5>
  95 <p>
  96         This function is implemented in terms of the Bessel functions using the relations:
  97       </p>
  98 <p>
  99         <span class="inlinemediaobject"><img src="../../../equations/airy_bi.png"></span>
 100       </p>
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 105       Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
 106       Holin, Bruno Lalande, John Maddock, Johan R&#229;de, Gautam Sewani, Benjamin Sobotta,
 107       Thijs van den Berg, Daryle Walker and Xiaogang Zhang<p>
 108         Distributed under the Boost Software License, Version 1.0. (See accompanying
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