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1753 lines
34 KiB
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<a accesskey="p" href="tutorial/user_def.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../constants.html"><img src="../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="new_const.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a>
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<div class="titlepage"><div><div><h2 class="title" style="clear: both">
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<a name="math_toolkit.constants"></a><a class="link" href="constants.html" title="The Mathematical Constants">The Mathematical Constants</a>
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</h2></div></div></div>
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<p>
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This section lists the mathematical constants, their use(s) (and sometimes
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rationale for their inclusion).
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</p>
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<div class="table">
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<a name="math_toolkit.constants.mathematical_constants"></a><p class="title"><b>Table 4.1. Mathematical Constants</b></p>
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<div class="table-contents"><table class="table" summary="Mathematical Constants">
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<colgroup>
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<col>
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<col>
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<col>
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<col>
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</colgroup>
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<thead><tr>
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<th>
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<p>
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name
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</p>
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||
</th>
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||
<th>
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||
<p>
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formula
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</p>
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</th>
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<th>
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<p>
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Value (6 decimals)
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</p>
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</th>
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<th>
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<p>
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Uses and Rationale
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</p>
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</th>
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</tr></thead>
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<tbody>
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<tr>
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<td>
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<p>
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<span class="bold"><strong>Rational fractions</strong></span>
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</p>
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</td>
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<td>
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</td>
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<td>
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</td>
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<td>
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</td>
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||
</tr>
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<tr>
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<td>
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<p>
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half
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</p>
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</td>
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<td>
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<p>
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1/2
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</p>
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</td>
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||
<td>
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<p>
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0.5
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||
</p>
|
||
</td>
|
||
<td>
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||
</td>
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||
</tr>
|
||
<tr>
|
||
<td>
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||
<p>
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third
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</p>
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</td>
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<td>
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<p>
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1/3
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</p>
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||
</td>
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||
<td>
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||
<p>
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0.333333
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||
</p>
|
||
</td>
|
||
<td>
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||
</td>
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||
</tr>
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||
<tr>
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||
<td>
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<p>
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two_thirds
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</p>
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</td>
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||
<td>
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<p>
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2/3
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</p>
|
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</td>
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||
<td>
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||
<p>
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0.66667
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</p>
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</td>
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||
<td>
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</td>
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</tr>
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<tr>
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<td>
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<p>
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three_quarters
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</p>
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</td>
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<td>
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<p>
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3/4
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</p>
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||
</td>
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||
<td>
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||
<p>
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0.75
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</p>
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</td>
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||
<td>
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||
</td>
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||
</tr>
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||
<tr>
|
||
<td>
|
||
<p>
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<span class="bold"><strong>two and related</strong></span>
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||
</p>
|
||
</td>
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||
<td>
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||
</td>
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||
<td>
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||
</td>
|
||
<td>
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||
</td>
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||
</tr>
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<tr>
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||
<td>
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||
<p>
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root_two
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</p>
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</td>
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<td>
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||
<p>
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√2
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</p>
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||
</td>
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||
<td>
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||
<p>
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||
1.41421
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||
</p>
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||
</td>
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||
<td>
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||
<p>
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||
Equivalent to POSIX constant M_SQRT2
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</p>
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</td>
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</tr>
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||
<tr>
|
||
<td>
|
||
<p>
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root_three
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</p>
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</td>
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<td>
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<p>
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√3
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</p>
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</td>
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<td>
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<p>
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1.73205
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</p>
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</td>
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<td>
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</td>
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||
</tr>
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<tr>
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<td>
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<p>
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half_root_two
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</p>
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</td>
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<td>
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<p>
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√2 /2
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</p>
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</td>
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<td>
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||
<p>
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0.707106
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||
</p>
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||
</td>
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<td>
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</td>
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||
</tr>
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<tr>
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<td>
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||
<p>
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ln_two
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</p>
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</td>
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<td>
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||
<p>
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ln(2)
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||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
0.693147
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||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
Equivalent to POSIX constant M_LN2
|
||
</p>
|
||
</td>
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||
</tr>
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||
<tr>
|
||
<td>
|
||
<p>
|
||
ln_ten
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
ln(10)
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
2.30258
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
Equivalent to POSIX constant M_LN10
|
||
</p>
|
||
</td>
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||
</tr>
|
||
<tr>
|
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<td>
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||
<p>
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ln_ln_two
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||
</p>
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</td>
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<td>
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<p>
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ln(ln(2))
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</p>
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||
</td>
|
||
<td>
|
||
<p>
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||
-0.366512
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||
</p>
|
||
</td>
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||
<td>
|
||
<p>
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||
Gumbel distribution median
|
||
</p>
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||
</td>
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||
</tr>
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||
<tr>
|
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<td>
|
||
<p>
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root_ln_four
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||
</p>
|
||
</td>
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||
<td>
|
||
<p>
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||
√ln(4)
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||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
1.177410
|
||
</p>
|
||
</td>
|
||
<td>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
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one_div_root_two
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
1/√2
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||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
0.707106
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
Equivalent to POSIX constant M_SQRT1_2
|
||
</p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
<span class="bold"><strong>π and related</strong></span>
|
||
</p>
|
||
</td>
|
||
<td>
|
||
</td>
|
||
<td>
|
||
</td>
|
||
<td>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
pi
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||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
π
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
3.14159
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
Ubiquitous. Archimedes constant <a href="http://en.wikipedia.org/wiki/Pi" target="_top">π</a>.
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||
Equivalent to POSIX constant M_PI
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||
</p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
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half_pi
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||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
π/2
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
1.570796
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
Equivalent to POSIX constant M_PI2
|
||
</p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
third_pi
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
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π/3
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
1.04719
|
||
</p>
|
||
</td>
|
||
<td>
|
||
</td>
|
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</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
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quarter_pi
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</p>
|
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</td>
|
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<td>
|
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<p>
|
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π/4
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</p>
|
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</td>
|
||
<td>
|
||
<p>
|
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0.78539816
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</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
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Equivalent to POSIX constant M_PI_4
|
||
</p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
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sixth_pi
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</p>
|
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</td>
|
||
<td>
|
||
<p>
|
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π/6
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||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
0.523598
|
||
</p>
|
||
</td>
|
||
<td>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
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two_pi
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</p>
|
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</td>
|
||
<td>
|
||
<p>
|
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2π
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||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
6.28318
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
Many uses, most simply, circumference of a circle
|
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</p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
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two_thirds_pi
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</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
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2/3 π
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
2.09439
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
<a href="http://en.wikipedia.org/wiki/Sphere#Volume_of_a_sphere" target="_top">volume
|
||
of a hemi-sphere</a> = 4/3 π r³
|
||
</p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
three_quarters_pi
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
3/4 π
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
2.35619
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
= 3/4 π
|
||
</p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
four_thirds_pi
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
4/3 π
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
4.18879
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
<a href="http://en.wikipedia.org/wiki/Sphere#Volume_of_a_sphere" target="_top">volume
|
||
of a sphere</a> = 4/3 π r³
|
||
</p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
one_div_two_pi
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
1/(2π)
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
1.59155
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
Widely used
|
||
</p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
root_pi
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
√π
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
1.77245
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
Widely used
|
||
</p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
root_half_pi
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
√ π/2
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
1.25331
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
Widely used
|
||
</p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
root_two_pi
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
√ π*2
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
2.50662
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
Widely used
|
||
</p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
one_div_pi
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
1/π
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
0.31830988
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
Equivalent to POSIX constant M_1_PI
|
||
</p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
two_div_pi
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
2/π
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
0.63661977
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
Equivalent to POSIX constant M_2_PI
|
||
</p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
one_div_root_pi
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
1/√π
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
0.564189
|
||
</p>
|
||
</td>
|
||
<td>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
two_div_root_pi
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
2/√π
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
1.128379
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
Equivalent to POSIX constant M_2_SQRTPI
|
||
</p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
one_div_root_two_pi
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
1/√(2π)
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
0.398942
|
||
</p>
|
||
</td>
|
||
<td>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
root_one_div_pi
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
√(1/π
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
0.564189
|
||
</p>
|
||
</td>
|
||
<td>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
pi_minus_three
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
π-3
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
0.141593
|
||
</p>
|
||
</td>
|
||
<td>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
four_minus_pi
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
4 -π
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
0.858407
|
||
</p>
|
||
</td>
|
||
<td>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
pi_pow_e
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
π<sup>e</sup>
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
22.4591
|
||
</p>
|
||
</td>
|
||
<td>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
pi_sqr
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
π<sup>2</sup>
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
9.86960
|
||
</p>
|
||
</td>
|
||
<td>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
pi_sqr_div_six
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
π<sup>2</sup>/6
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
1.64493
|
||
</p>
|
||
</td>
|
||
<td>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
pi_cubed
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
π<sup>3</sup>
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
31.00627
|
||
</p>
|
||
</td>
|
||
<td>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
cbrt_pi
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
√<sup>3</sup> π
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
1.46459
|
||
</p>
|
||
</td>
|
||
<td>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
one_div_cbrt_pi
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
1/√<sup>3</sup> π
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
0.682784
|
||
</p>
|
||
</td>
|
||
<td>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
<span class="bold"><strong>Euler's e and related</strong></span>
|
||
</p>
|
||
</td>
|
||
<td>
|
||
</td>
|
||
<td>
|
||
</td>
|
||
<td>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
e
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
e
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
2.71828
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
<a href="http://en.wikipedia.org/wiki/E_(mathematical_constant)" target="_top">Euler's
|
||
constant e</a>, equivalent to POSIX constant M_E
|
||
</p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
exp_minus_half
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
e <sup>-1/2</sup>
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
0.606530
|
||
</p>
|
||
</td>
|
||
<td>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
e_pow_pi
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
e <sup>π</sup>
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
23.14069
|
||
</p>
|
||
</td>
|
||
<td>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
root_e
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
√ e
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
1.64872
|
||
</p>
|
||
</td>
|
||
<td>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
log10_e
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
log10(e)
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
0.434294
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
Equivalent to POSIX constant M_LOG10E
|
||
</p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
one_div_log10_e
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
1/log10(e)
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
2.30258
|
||
</p>
|
||
</td>
|
||
<td>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
log2_e
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
log<sub>2</sub>(e)
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
1.442695
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
This is the same as 1/ln(2) and is equivalent to POSIX constant M_LOG2E
|
||
</p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
<span class="bold"><strong>Trigonometric</strong></span>
|
||
</p>
|
||
</td>
|
||
<td>
|
||
</td>
|
||
<td>
|
||
</td>
|
||
<td>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
degree
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
radians = π / 180
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
0.017453
|
||
</p>
|
||
</td>
|
||
<td>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
radian
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
degrees = 180 / π
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
57.2957
|
||
</p>
|
||
</td>
|
||
<td>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
sin_one
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
sin(1)
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
0.841470
|
||
</p>
|
||
</td>
|
||
<td>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
cos_one
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
cos(1)
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
0.54030
|
||
</p>
|
||
</td>
|
||
<td>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
sinh_one
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
sinh(1)
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
1.17520
|
||
</p>
|
||
</td>
|
||
<td>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
cosh_one
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
cosh(1)
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
1.54308
|
||
</p>
|
||
</td>
|
||
<td>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
<span class="bold"><strong>Phi</strong></span>
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
Phidias golden ratio
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
<a href="http://en.wikipedia.org/wiki/Golden_ratio" target="_top">Phidias golden
|
||
ratio</a>
|
||
</p>
|
||
</td>
|
||
<td>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
phi
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
(1 + √5) /2
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
1.61803
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
finance
|
||
</p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
ln_phi
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
ln(φ)
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
0.48121
|
||
</p>
|
||
</td>
|
||
<td>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
one_div_ln_phi
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
1/ln(φ)
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
2.07808
|
||
</p>
|
||
</td>
|
||
<td>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
<span class="bold"><strong>Euler's Gamma</strong></span>
|
||
</p>
|
||
</td>
|
||
<td>
|
||
</td>
|
||
<td>
|
||
</td>
|
||
<td>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
euler
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
euler
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
0.577215
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
<a href="http://en.wikipedia.org/wiki/Euler%E2%80%93Mascheroni_constant" target="_top">Euler-Mascheroni
|
||
gamma constant</a>
|
||
</p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
one_div_euler
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
1/euler
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
1.73245
|
||
</p>
|
||
</td>
|
||
<td>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
euler_sqr
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
euler<sup>2</sup>
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
0.333177
|
||
</p>
|
||
</td>
|
||
<td>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
<span class="bold"><strong>Misc</strong></span>
|
||
</p>
|
||
</td>
|
||
<td>
|
||
</td>
|
||
<td>
|
||
</td>
|
||
<td>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
zeta_two
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
ζ(2)
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
1.64493
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
<a href="http://en.wikipedia.org/wiki/Riemann_zeta_function" target="_top">Riemann
|
||
zeta function</a>
|
||
</p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
zeta_three
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
ζ(3)
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
1.20205
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
<a href="http://en.wikipedia.org/wiki/Riemann_zeta_function" target="_top">Riemann
|
||
zeta function</a>
|
||
</p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
catalan
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
<span class="emphasis"><em>K</em></span>
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
0.915965
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
<a href="http://mathworld.wolfram.com/CatalansConstant.html" target="_top">Catalan
|
||
(or Glaisher) combinatorial constant</a>
|
||
</p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
glaisher
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
<span class="emphasis"><em>A</em></span>
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
1.28242
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
<a href="https://oeis.org/A074962/constant" target="_top">Decimal expansion
|
||
of Glaisher-Kinkelin constant</a>
|
||
</p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
khinchin
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
<span class="emphasis"><em>k</em></span>
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
2.685452
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
<a href="https://oeis.org/A002210/constant" target="_top">Decimal expansion
|
||
of Khinchin constant</a>
|
||
</p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
extreme_value_skewness
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
12√6 ζ(3)/ π<sup>3</sup>
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
1.139547
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
Extreme value distribution
|
||
</p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
rayleigh_skewness
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
2√π(π-3)/(4 - π)<sup>3/2</sup>
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
0.631110
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
Rayleigh distribution skewness
|
||
</p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
rayleigh_kurtosis_excess
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
-(6π<sup>2</sup>-24π+16)/(4-π)<sup>2</sup>
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
0.245089
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
<a href="http://en.wikipedia.org/wiki/Rayleigh_distribution" target="_top">Rayleigh
|
||
distribution kurtosis excess</a>
|
||
</p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
rayleigh_kurtosis
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
3+(6π<sup>2</sup>-24π+16)/(4-π)<sup>2</sup>
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
3.245089
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
Rayleigh distribution kurtosis
|
||
</p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
first_feigenbaum
|
||
</p>
|
||
</td>
|
||
<td>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
4.6692016
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
<a href="https://en.wikipedia.org/wiki/Feigenbaum_constants" target="_top">First
|
||
Feigenbaum constant</a>
|
||
</p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
plastic
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
Real solution of x<sup>3</sup> = x + 1
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
1.324717957
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
<a href="https://en.wikipedia.org/wiki/Plastic_number" target="_top">Plastic
|
||
constant</a>
|
||
</p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
gauss
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
Reciprocal of agm(1, √2)
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
0.8346268
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
<a href="https://en.wikipedia.org/wiki/Gauss%27s_constant" target="_top">Gauss's
|
||
constant</a>
|
||
</p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
dottie
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
Solution of cos(x) = x
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
0.739085
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
<a href="https://en.wikipedia.org/wiki/Dottie_number" target="_top">Dottie's
|
||
number</a>
|
||
</p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
reciprocal_fibonacci
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
Sum of reciprocals of Fibonacci numbers
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
3.359885666
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
<a href="https://en.wikipedia.org/wiki/Reciprocal_Fibonacci_constant" target="_top">Reciprocal
|
||
Fibonacci constant</a>
|
||
</p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
laplace_limit
|
||
</p>
|
||
</td>
|
||
<td>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
.6627434193
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
<a href="https://en.wikipedia.org/wiki/Laplace_limit" target="_top">Laplace
|
||
Limit</a>
|
||
</p>
|
||
</td>
|
||
</tr>
|
||
</tbody>
|
||
</table></div>
|
||
</div>
|
||
<br class="table-break"><div class="note"><table border="0" summary="Note">
|
||
<tr>
|
||
<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../doc/src/images/note.png"></td>
|
||
<th align="left">Note</th>
|
||
</tr>
|
||
<tr><td align="left" valign="top"><p>
|
||
Integer values are <span class="bold"><strong>not included</strong></span> in this
|
||
list of math constants, however interesting, because they can be so easily
|
||
and exactly constructed, even for UDT, for example: <code class="computeroutput"><span class="keyword">static_cast</span><span class="special"><</span><span class="identifier">cpp_float</span><span class="special">>(</span><span class="number">42</span><span class="special">)</span></code>.
|
||
</p></td></tr>
|
||
</table></div>
|
||
<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 know the approximate value of the constant, you can search for the
|
||
value to find Boost.Math chosen name in this table.
|
||
</p></td></tr>
|
||
</table></div>
|
||
<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>
|
||
Bernoulli numbers are available at <a class="link" href="number_series/bernoulli_numbers.html" title="Bernoulli Numbers">Bernoulli
|
||
numbers</a>.
|
||
</p></td></tr>
|
||
</table></div>
|
||
<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>
|
||
Factorials are available at <a class="link" href="factorials/sf_factorial.html" title="Factorial">factorial</a>.
|
||
</p></td></tr>
|
||
</table></div>
|
||
</div>
|
||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
|
||
<td align="left"></td>
|
||
<td align="right"><div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
|
||
Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
|
||
Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
|
||
Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
|
||
Walker and Xiaogang Zhang<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>)
|
||
</p>
|
||
</div></td>
|
||
</tr></table>
|
||
<hr>
|
||
<div class="spirit-nav">
|
||
<a accesskey="p" href="tutorial/user_def.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../constants.html"><img src="../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="new_const.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a>
|
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|
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</body>
|
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</html>
|