1<html> 2<head> 3<meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> 4<title>Sinus Cardinal and Hyperbolic Sinus Cardinal Functions Overview</title> 5<link rel="stylesheet" href="../../math.css" type="text/css"> 6<meta name="generator" content="DocBook XSL Stylesheets V1.79.1"> 7<link rel="home" href="../../index.html" title="Math Toolkit 2.12.0"> 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"> 26<div class="titlepage"><div><div><h3 class="title"> 27<a name="math_toolkit.sinc.sinc_overview"></a><a class="link" href="sinc_overview.html" title="Sinus Cardinal and Hyperbolic Sinus Cardinal Functions Overview">Sinus Cardinal and Hyperbolic 28 Sinus Cardinal Functions Overview</a> 29</h3></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 > 0</code>) is defined by 34 </p> 35<div class="blockquote"><blockquote class="blockquote"><p> 36 <span class="inlinemediaobject"><img src="../../../equations/special_functions_blurb20.svg"></span> 37 38 </p></blockquote></div> 39<p> 40 it sees heavy use in signal processing tasks. 41 </p> 42<p> 43 By analogy, the <a href="http://mathworld.wolfram.com/SinhcFunction.htm" target="_top">Hyperbolic 44 Sinus Cardinal</a> family of functions (also indexed by the family of 45 indices <code class="literal">a > 0</code>) is defined by 46 </p> 47<div class="blockquote"><blockquote class="blockquote"><p> 48 <span class="inlinemediaobject"><img src="../../../equations/special_functions_blurb22.svg"></span> 49 50 </p></blockquote></div> 51<p> 52 These two families of functions are composed of entire functions. 53 </p> 54<p> 55 These functions (<a class="link" href="sinc_pi.html" title="sinc_pi">sinc_pi</a> 56 and <a class="link" href="sinhc_pi.html" title="sinhc_pi">sinhc_pi</a>) are needed 57 by <a href="http://www.boost.org/libs/math/quaternion/quaternion.html" target="_top">our 58 implementation</a> of <a href="http://mathworld.wolfram.com/Quaternion.html" target="_top">quaternions</a> 59 and <a href="http://mathworld.wolfram.com/Octonion.html" target="_top">octonions</a>. 60 </p> 61<div class="blockquote"><blockquote class="blockquote"><p> 62 <span class="emphasis"><em><span class="bold"><strong>Sinus Cardinal of index pi (purple) and 63 Hyperbolic Sinus Cardinal of index pi (red) on R</strong></span></em></span> 64 </p></blockquote></div> 65<div class="blockquote"><blockquote class="blockquote"><p> 66 <span class="inlinemediaobject"><img src="../../../graphs/sinc_pi_and_sinhc_pi_on_r.png"></span> 67 </p></blockquote></div> 68</div> 69<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> 70<td align="left"></td> 71<td align="right"><div class="copyright-footer">Copyright © 2006-2019 Nikhar 72 Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, 73 Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan 74 Råde, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, 75 Daryle Walker and Xiaogang Zhang<p> 76 Distributed under the Boost Software License, Version 1.0. (See accompanying 77 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>) 78 </p> 79</div></td> 80</tr></table> 81<hr> 82<div class="spirit-nav"> 83<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> 84</div> 85</body> 86</html> 87
