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<a name="Airy-Functions-and-Derivatives"></a>
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<p>
Next: <a href="Bessel-Functions.html#Bessel-Functions" accesskey="n" rel="next">Bessel Functions</a>, Previous: <a href="Special-Function-Modes.html#Special-Function-Modes" accesskey="p" rel="previous">Special Function Modes</a>, Up: <a href="Special-Functions.html#Special-Functions" accesskey="u" rel="up">Special Functions</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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<a name="Airy-Functions-and-Derivatives-1"></a>
<h3 class="section">7.4 Airy Functions and Derivatives</h3>
<a name="index-Airy-functions"></a>
<a name="index-Ai_0028x_0029"></a>
<a name="index-Bi_0028x_0029"></a>

<p>The Airy functions <em>Ai(x)</em> and <em>Bi(x)</em> are defined by the
integral representations,
</p>
<div class="example">
<pre class="example">Ai(x) = (1/\pi) \int_0^\infty \cos((1/3) t^3 + xt) dt
Bi(x) = (1/\pi) \int_0^\infty (e^(-(1/3) t^3 + xt) + \sin((1/3) t^3 + xt)) dt
</pre></div>

<p>For further information see Abramowitz &amp; Stegun, Section 10.4. The Airy
functions are defined in the header file <samp>gsl_sf_airy.h</samp>.
</p>
<table class="menu" border="0" cellspacing="0">
<tr><td align="left" valign="top">&bull; <a href="Airy-Functions.html#Airy-Functions" accesskey="1">Airy Functions</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="Derivatives-of-Airy-Functions.html#Derivatives-of-Airy-Functions" accesskey="2">Derivatives of Airy Functions</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="Zeros-of-Airy-Functions.html#Zeros-of-Airy-Functions" accesskey="3">Zeros of Airy Functions</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="Zeros-of-Derivatives-of-Airy-Functions.html#Zeros-of-Derivatives-of-Airy-Functions" accesskey="4">Zeros of Derivatives of Airy Functions</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
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