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| <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 |
| and Hyperbolic Sinus Cardinal Functions Overview</a> |
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| The <a href="http://mathworld.wolfram.com/SincFunction.html" target="_top">Sinus Cardinal |
| family of functions</a> (indexed by the family of indices <code class="literal">a |
| > 0</code>) is defined by |
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| <span class="inlinemediaobject"><img src="../../../../equations/special_functions_blurb20.png"></span> |
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| it sees heavy use in signal processing tasks. |
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| <p> |
| By analogy, the <a href="http://mathworld.wolfram.com/SinhcFunction.htm" target="_top">Hyperbolic |
| Sinus Cardinal</a> family of functions (also indexed by the family |
| of indices <code class="literal">a > 0</code>) is defined by |
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| <p> |
| <span class="inlinemediaobject"><img src="../../../../equations/special_functions_blurb22.png"></span> |
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| These two families of functions are composed of entire functions. |
| </p> |
| <p> |
| These functions (<a class="link" href="sinc_pi.html" title="sinc_pi">sinc_pi</a> |
| and <a class="link" href="sinhc_pi.html" title="sinhc_pi">sinhc_pi</a>) |
| are needed by <a href="http://www.boost.org/libs/math/quaternion/quaternion.html" target="_top">our |
| implementation</a> of <a href="http://mathworld.wolfram.com/Quaternion.html" target="_top">quaternions</a> |
| and <a href="http://mathworld.wolfram.com/Octonion.html" target="_top">octonions</a>. |
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| <div class="blockquote"><blockquote class="blockquote"><p> |
| <span class="emphasis"><em><span class="bold"><strong>Sinus Cardinal of index pi (purple) and |
| Hyperbolic Sinus Cardinal of index pi (red) on R</strong></span></em></span> |
| </p></blockquote></div> |
| <div class="blockquote"><blockquote class="blockquote"><p> |
| <span class="inlinemediaobject"><img src="../../../../graphs/sinc_pi_and_sinhc_pi_on_r.png" alt="sinc_pi_and_sinhc_pi_on_r"></span> |
| </p></blockquote></div> |
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| Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani and |
| Thijs van den Berg<p> |
| Distributed under the Boost Software License, Version 1.0. (See accompanying |
| 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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