libs/math/doc/sf_and_dist/html/math_toolkit/special/sinc/sinc_overview.html

   1 <html>
   2 <head>
   3 <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
   4 <title>Sinus Cardinal and Hyperbolic Sinus Cardinal Functions Overview</title>
   5 <link rel="stylesheet" href="../../../../../../../../doc/src/boostbook.css" type="text/css">
   6 <meta name="generator" content="DocBook XSL Stylesheets V1.76.1">
   7 <link rel="home" href="../../../index.html" title="Math Toolkit">
   8 <link rel="up" href="../sinc.html" title="Sinus Cardinal and Hyperbolic Sinus Cardinal Functions">
   9 <link rel="prev" href="../sinc.html" title="Sinus Cardinal and Hyperbolic Sinus Cardinal Functions">
  10 <link rel="next" href="sinc_pi.html" title="sinc_pi">
  11 </head>
  12 <body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
  13 <table cellpadding="2" width="100%"><tr>
  14 <td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../../../boost.png"></td>
  15 <td align="center"><a href="../../../../../../../../index.html">Home</a></td>
  16 <td align="center"><a href="../../../../../../../../libs/libraries.htm">Libraries</a></td>
  17 <td align="center"><a href="http://www.boost.org/users/people.html">People</a></td>
  18 <td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td>
  19 <td align="center"><a href="../../../../../../../../more/index.htm">More</a></td>
  20 </tr></table>
  21 <hr>
  22 <div class="spirit-nav">
  23 <a accesskey="p" href="../sinc.html"><img src="../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../sinc.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="sinc_pi.html"><img src="../../../../../../../../doc/src/images/next.png" alt="Next"></a>
  24 </div>
  25 <div class="section math_toolkit_special_sinc_sinc_overview">
  26 <div class="titlepage"><div><div><h4 class="title">
  27 <a name="math_toolkit.special.sinc.sinc_overview"></a><a class="link" href="sinc_overview.html" title="Sinus Cardinal and Hyperbolic Sinus Cardinal Functions Overview">Sinus Cardinal
  28         and Hyperbolic Sinus Cardinal Functions Overview</a>
  29 </h4></div></div></div>
  30 <p>
  31           The <a href="http://mathworld.wolfram.com/SincFunction.html" target="_top">Sinus Cardinal
  32           family of functions</a> (indexed by the family of indices <code class="literal">a
  33           &gt; 0</code>) is defined by
  34         </p>
  35 <p>
  36           <span class="inlinemediaobject"><img src="../../../../equations/special_functions_blurb20.png"></span>
  37         </p>
  38 <p>
  39           it sees heavy use in signal processing tasks.
  40         </p>
  41 <p>
  42           By analogy, the <a href="http://mathworld.wolfram.com/SinhcFunction.htm" target="_top">Hyperbolic
  43           Sinus Cardinal</a> family of functions (also indexed by the family
  44           of indices <code class="literal">a &gt; 0</code>) is defined by
  45         </p>
  46 <p>
  47           <span class="inlinemediaobject"><img src="../../../../equations/special_functions_blurb22.png"></span>
  48         </p>
  49 <p>
  50           These two families of functions are composed of entire functions.
  51         </p>
  52 <p>
  53           These functions (<a class="link" href="sinc_pi.html" title="sinc_pi">sinc_pi</a>
  54           and <a class="link" href="sinhc_pi.html" title="sinhc_pi">sinhc_pi</a>)
  55           are needed by <a href="http://www.boost.org/libs/math/quaternion/quaternion.html" target="_top">our
  56           implementation</a> of <a href="http://mathworld.wolfram.com/Quaternion.html" target="_top">quaternions</a>
  57           and <a href="http://mathworld.wolfram.com/Octonion.html" target="_top">octonions</a>.
  58         </p>
  59 <div class="blockquote"><blockquote class="blockquote"><p>
  60             <span class="emphasis"><em><span class="bold"><strong>Sinus Cardinal of index pi (purple) and
  61             Hyperbolic Sinus Cardinal of index pi (red) on R</strong></span></em></span>
  62           </p></blockquote></div>
  63 <div class="blockquote"><blockquote class="blockquote"><p>
  64             <span class="inlinemediaobject"><img src="../../../../graphs/sinc_pi_and_sinhc_pi_on_r.png" alt="sinc_pi_and_sinhc_pi_on_r"></span>
  65           </p></blockquote></div>
  66 </div>
  67 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
  68 <td align="left"></td>
  69 <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno
  70       Lalande, Johan R&#229;de, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p>
  71         Distributed under the Boost Software License, Version 1.0. (See accompanying
  72         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>)
  73       </p>
  74 </div></td>
  75 </tr></table>
  76 <hr>
  77 <div class="spirit-nav">
  78 <a accesskey="p" href="../sinc.html"><img src="../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../sinc.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="sinc_pi.html"><img src="../../../../../../../../doc/src/images/next.png" alt="Next"></a>
  79 </div>
  80 </body>
  81 </html>