<title>Double Factorial</title>
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<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">></span>
<span class="identifier">T</span> <span class="identifier">double_factorial</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">i</span><span class="special">);</span>
-<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Chapter 19. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">></span>
-<span class="identifier">T</span> <span class="identifier">double_factorial</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">i</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Chapter 19. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&);</span>
+<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Chapter 20. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">></span>
+<span class="identifier">T</span> <span class="identifier">double_factorial</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">i</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Chapter 20. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&);</span>
<span class="special">}}</span> <span class="comment">// namespaces</span>
</pre>
Returns <code class="literal">i!!</code>.
</p>
<p>
- The final <a class="link" href="../../policy.html" title="Chapter 19. Policies: Controlling Precision, Error Handling etc">Policy</a> argument is optional and can
+ The final <a class="link" href="../../policy.html" title="Chapter 20. Policies: Controlling Precision, Error Handling etc">Policy</a> argument is optional and can
be used to control the behaviour of the function: how it handles errors,
- what level of precision to use etc. Refer to the <a class="link" href="../../policy.html" title="Chapter 19. Policies: Controlling Precision, Error Handling etc">policy
+ what level of precision to use etc. Refer to the <a class="link" href="../../policy.html" title="Chapter 20. Policies: Controlling Precision, Error Handling etc">policy
documentation for more details</a>.
</p>
<p>
<span class="phrase"><a name="math_toolkit.factorials.sf_double_factorial.testing"></a></span><a class="link" href="sf_double_factorial.html#math_toolkit.factorials.sf_double_factorial.testing">Testing</a>
</h5>
<p>
- The spot tests for the double factorial use data generated by functions.wolfram.com.
+ The spot tests for the double factorial use data generated by <a href="http://www.wolframalpha.com/" target="_top">Wolfram
+ Alpha</a>.
</p>
<h5>
<a name="math_toolkit.factorials.sf_double_factorial.h2"></a>
The double factorial is implemented in terms of the factorial and gamma functions
using the relations:
</p>
-<p>
- (2n)!! = 2<sup>n </sup> * n!
- </p>
-<p>
- (2n+1)!! = (2n+1)! / (2<sup>n </sup> n!)
- </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+ <span class="serif_italic"><span class="emphasis"><em>(2n)!! = 2<sup>n </sup> * n!</em></span></span>
+ </p></blockquote></div>
+<div class="blockquote"><blockquote class="blockquote"><p>
+ <span class="serif_italic"><span class="emphasis"><em>(2n+1)!! = (2n+1)! / (2<sup>n </sup> n!)</em></span></span>
+ </p></blockquote></div>
<p>
and
</p>
-<p>
- (2n-1)!! = Γ((2n+1)/2) * 2<sup>n </sup> / sqrt(pi)
- </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+ <span class="serif_italic"><span class="emphasis"><em>(2n-1)!! = Γ((2n+1)/2) * 2<sup>n </sup> / sqrt(pi)</em></span></span>
+ </p></blockquote></div>
</div>
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