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+<title>Overview of the Jacobi Elliptic Functions</title>
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<div class="titlepage"><div><div><h3 class="title">
-<a name="math_toolkit.jacobi.jac_over"></a><a class="link" href="jac_over.html" title="Overvew of the Jacobi Elliptic Functions">Overvew of the Jacobi Elliptic
- Functions</a>
+<a name="math_toolkit.jacobi.jac_over"></a><a class="link" href="jac_over.html" title="Overview of the Jacobi Elliptic Functions">Overview of the Jacobi
+ Elliptic Functions</a>
</h3></div></div></div>
<p>
There are twelve Jacobi Elliptic functions, of which the three copolar functions
= k<sup>2</sup></em></span>.
</li>
<li class="listitem">
- In terms of the modular angle α, where <span class="emphasis"><em>m = sin<sup>2</sup>α</em></span>.
+ In terms of the modular angle α, where <span class="emphasis"><em>m = sin<sup>2</sup>  α</em></span>.
</li>
</ul></div>
<p>
an amplitude φ, in our implementation we always use <span class="emphasis"><em>u</em></span>.
</p>
<p>
- Finally note that our functions all take the elliptic modulus as the first
- argument - this is for alignment with the Elliptic Integrals.
+ Finally note that our functions all take the elliptic modulus <span class="emphasis"><em>k</em></span>
+ as the <span class="bold"><strong>first</strong></span> argument - this is for alignment
+ with the Elliptic Integrals (but is different from other implementations,
+ for example Mathworks).
</p>
<p>
- There are twenve functions for computing the twelve individual Jacobi elliptic
+ A simple example comparing use of <a href="http://www.wolframalpha.com/" target="_top">Wolfram
+ Alpha</a> with Boost.Math (including much higher precision using Boost.Multiprecision)
+ is <a href="../../../../example/jacobi_zeta_example.cpp" target="_top">jacobi_zeta_example.cpp</a>.
+ </p>
+<p>
+ There are twelve functions for computing the twelve individual Jacobi elliptic
functions: <a class="link" href="jacobi_cd.html" title="Jacobi Elliptic Function cd">jacobi_cd</a>,
<a class="link" href="jacobi_cn.html" title="Jacobi Elliptic Function cn">jacobi_cn</a>, <a class="link" href="jacobi_cs.html" title="Jacobi Elliptic Function cs">jacobi_cs</a>,
<a class="link" href="jacobi_dc.html" title="Jacobi Elliptic Function dc">jacobi_dc</a>, <a class="link" href="jacobi_dn.html" title="Jacobi Elliptic Function dn">jacobi_dn</a>,
Note however that these individual functions are all really thin wrappers
around the function <a class="link" href="jacobi_elliptic.html" title="Jacobi Elliptic SN, CN and DN">jacobi_elliptic</a>
which calculates the three copolar functions <span class="emphasis"><em>sn</em></span>, <span class="emphasis"><em>cn</em></span>
- and <span class="emphasis"><em>dn</em></span> in a single function call. Thus if you need more
- than one of these functions for a given set of arguments, it's most efficient
- to use <a class="link" href="jacobi_elliptic.html" title="Jacobi Elliptic SN, CN and DN">jacobi_elliptic</a>.
+ and <span class="emphasis"><em>dn</em></span> in a single function call.
</p>
+<div class="tip"><table border="0" summary="Tip">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Tip]" src="../../../../../../doc/src/images/tip.png"></td>
+<th align="left">Tip</th>
+</tr>
+<tr><td align="left" valign="top"><p>
+ If you need more than one of these functions for a given set of arguments,
+ it's most efficient to use <a class="link" href="jacobi_elliptic.html" title="Jacobi Elliptic SN, CN and DN">jacobi_elliptic</a>.
+ </p></td></tr>
+</table></div>
<div class="footnotes">
<br><hr style="width:100; text-align:left;margin-left: 0">
<div id="ftn.math_toolkit.jacobi.jac_over.f0" class="footnote"><p><a href="#math_toolkit.jacobi.jac_over.f0" class="para"><sup class="para">[2] </sup></a>
</p></div>
<div id="ftn.math_toolkit.jacobi.jac_over.f2" class="footnote"><p><a href="#math_toolkit.jacobi.jac_over.f2" class="para"><sup class="para">[4] </sup></a>
<a href="http://dlmf.nist.gov/22" target="_top">Digital Library of Mathematical Functions:
- Jacobian Elliptic Functions</a>
+ Jacobian Elliptic Functions, Reinhardt, W. P., Walker, O. L.</a>
</p></div>
</div>
</div>
projects / platform / upstream / boost.git / blobdiff