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  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         &gt; 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 &gt; 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>
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