87 lines
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87 lines
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<div class="titlepage"><div><div><h3 class="title">
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<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
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Sinus Cardinal Functions Overview</a>
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</h3></div></div></div>
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<p>
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The <a href="http://mathworld.wolfram.com/SincFunction.html" target="_top">Sinus Cardinal
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family of functions</a> (indexed by the family of indices <code class="literal">a
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> 0</code>) is defined by
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</p>
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<div class="blockquote"><blockquote class="blockquote"><p>
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<span class="inlinemediaobject"><img src="../../../equations/special_functions_blurb20.svg"></span>
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</p></blockquote></div>
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<p>
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it sees heavy use in signal processing tasks.
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<p>
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By analogy, the <a href="http://mathworld.wolfram.com/SinhcFunction.htm" target="_top">Hyperbolic
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Sinus Cardinal</a> family of functions (also indexed by the family of
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indices <code class="literal">a > 0</code>) is defined by
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</p>
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<div class="blockquote"><blockquote class="blockquote"><p>
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<span class="inlinemediaobject"><img src="../../../equations/special_functions_blurb22.svg"></span>
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</p></blockquote></div>
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<p>
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These two families of functions are composed of entire functions.
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</p>
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<p>
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These functions (<a class="link" href="sinc_pi.html" title="sinc_pi">sinc_pi</a>
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and <a class="link" href="sinhc_pi.html" title="sinhc_pi">sinhc_pi</a>) are needed
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by <a href="http://www.boost.org/libs/math/quaternion/quaternion.html" target="_top">our
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implementation</a> of <a href="http://mathworld.wolfram.com/Quaternion.html" target="_top">quaternions</a>
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and <a href="http://mathworld.wolfram.com/Octonion.html" target="_top">octonions</a>.
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</p>
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<div class="blockquote"><blockquote class="blockquote"><p>
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<span class="emphasis"><em><span class="bold"><strong>Sinus Cardinal of index pi (purple) and
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Hyperbolic Sinus Cardinal of index pi (red) on R</strong></span></em></span>
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</p></blockquote></div>
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<div class="blockquote"><blockquote class="blockquote"><p>
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<span class="inlinemediaobject"><img src="../../../graphs/sinc_pi_and_sinhc_pi_on_r.png"></span>
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</p></blockquote></div>
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<td align="right"><div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
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Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
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Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
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Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
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Walker and Xiaogang Zhang<p>
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Distributed under the Boost Software License, Version 1.0. (See accompanying
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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>)
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