<title>Finding Zeros of Airy Functions</title>
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<span class="identifier">OutputIterator</span> <span class="identifier">out_it</span><span class="special">);</span> <span class="comment">// Destination for zeros.</span>
</pre>
<p>
- There are also versions which allow control of the <a class="link" href="../../policy.html" title="Chapter 19. Policies: Controlling Precision, Error Handling etc">Policies</a>
+ There are also versions which allow control of the <a class="link" href="../../policy.html" title="Chapter 20. Policies: Controlling Precision, Error Handling etc">Policies</a>
for error handling and precision.
</p>
<pre class="programlisting"> <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">></span>
real axis. The real zeros on the negative real axis can be found by solving
for the roots of
</p>
-<p>
-   <span class="emphasis"><em>Ai(x<sub>m</sub>) = 0</em></span>
- </p>
-<p>
-   <span class="emphasis"><em>Bi(y<sub>m</sub>) = 0</em></span>
- </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+ <span class="emphasis"><em>Ai(x<sub>m</sub>) = 0</em></span>
+ </p></blockquote></div>
+<div class="blockquote"><blockquote class="blockquote"><p>
+ <span class="emphasis"><em>Bi(y<sub>m</sub>) = 0</em></span>
+ </p></blockquote></div>
<p>
Here, <span class="emphasis"><em>x<sub>m</sub></em></span> represents the <span class="emphasis"><em>m<sup>th</sup></em></span> root
of the Airy Ai function, and <span class="emphasis"><em>y<sub>m</sub></em></span> represents the <span class="emphasis"><em>m<sup>th</sup></em></span>
</tr>
</tbody>
</table></div>
-<p>
- <span class="inlinemediaobject"><img src="../../../graphs/airy_zeros.svg" align="middle"></span>
- </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+ <span class="inlinemediaobject"><img src="../../../graphs/airy_zeros.svg" align="middle"></span>
+
+ </p></blockquote></div>
<h5>
<a name="math_toolkit.airy.airy_root.h2"></a>
<span class="phrase"><a name="math_toolkit.airy.airy_root.examples_of_finding_airy_zeros"></a></span><a class="link" href="airy_root.html#math_toolkit.airy.airy_root.examples_of_finding_airy_zeros">Examples
<span class="identifier">OutputIterator</span> <span class="identifier">out_it</span><span class="special">);</span> <span class="comment">// Destination for zeros.</span>
</pre>
<p>
- There are also versions which allows control of the <a class="link" href="../../policy.html" title="Chapter 19. Policies: Controlling Precision, Error Handling etc">Policies</a>
+ There are also versions which allows control of the <a class="link" href="../../policy.html" title="Chapter 20. Policies: Controlling Precision, Error Handling etc">Policies</a>
for error handling and precision.
</p>
<pre class="programlisting"><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> <span class="identifier">OutputIterator</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Policy</span><span class="special">></span>
<p>
Given the following function (A&S 10.4.105):
</p>
-<p>
- <span class="inlinemediaobject"><img src="../../../equations/airy_zero_1.svg"></span>
- </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+ <span class="inlinemediaobject"><img src="../../../equations/airy_zero_1.svg"></span>
+
+ </p></blockquote></div>
<p>
Then an initial estimate for the n<sup>th</sup> zero a<sub>n</sub> of Ai is given by (A&S 10.4.94):
</p>
-<p>
- <span class="inlinemediaobject"><img src="../../../equations/airy_zero_2.svg"></span>
- </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+ <span class="inlinemediaobject"><img src="../../../equations/airy_zero_2.svg"></span>
+
+ </p></blockquote></div>
<p>
and an initial estimate for the n<sup>th</sup> zero b<sub>n</sub> of Bi is given by (A&S 10.4.98):
</p>
-<p>
- <span class="inlinemediaobject"><img src="../../../equations/airy_zero_3.svg"></span>
- </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+ <span class="inlinemediaobject"><img src="../../../equations/airy_zero_3.svg"></span>
+
+ </p></blockquote></div>
<p>
Thereafter the roots are refined using Newton iteration.
</p>