3 <meta http-equiv=
"Content-Type" content=
"text/html; charset=US-ASCII">
4 <title>The Mathematical Constants
</title>
5 <link rel=
"stylesheet" href=
"../math.css" type=
"text/css">
6 <meta name=
"generator" content=
"DocBook XSL Stylesheets V1.77.1">
7 <link rel=
"home" href=
"../index.html" title=
"Math Toolkit 2.5.1">
8 <link rel=
"up" href=
"../constants.html" title=
"Chapter 4. Mathematical Constants">
9 <link rel=
"prev" href=
"tutorial/user_def.html" title=
"Use With User-Defined Types">
10 <link rel=
"next" href=
"new_const.html" title=
"Defining New Constants">
12 <body bgcolor=
"white" text=
"black" link=
"#0000FF" vlink=
"#840084" alink=
"#0000FF">
13 <table cellpadding=
"2" width=
"100%"><tr>
14 <td valign=
"top"><img alt=
"Boost C++ Libraries" width=
"277" height=
"86" src=
"../../../../../boost.png"></td>
15 <td align=
"center"><a href=
"../../../../../index.html">Home
</a></td>
16 <td align=
"center"><a href=
"../../../../../libs/libraries.htm">Libraries
</a></td>
17 <td align=
"center"><a href=
"http://www.boost.org/users/people.html">People
</a></td>
18 <td align=
"center"><a href=
"http://www.boost.org/users/faq.html">FAQ
</a></td>
19 <td align=
"center"><a href=
"../../../../../more/index.htm">More
</a></td>
22 <div class=
"spirit-nav">
23 <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>
26 <div class=
"titlepage"><div><div><h2 class=
"title" style=
"clear: both">
27 <a name=
"math_toolkit.constants"></a><a class=
"link" href=
"constants.html" title=
"The Mathematical Constants">The Mathematical Constants
</a>
28 </h2></div></div></div>
30 This section lists the mathematical constants, their use(s) (and sometimes
31 rationale for their inclusion).
34 <a name=
"math_toolkit.constants.mathematical_constants"></a><p class=
"title"><b>Table
 4.1.
 Mathematical Constants
</b></p>
35 <div class=
"table-contents"><table class=
"table" summary=
"Mathematical Constants">
68 <span class=
"bold"><strong>Rational fractions
</strong></span>
157 <span class=
"bold"><strong>two and related
</strong></span>
280 Gumbel distribution median
325 <span class=
"bold"><strong>π and related
</strong></span>
353 Ubiquitous. Archimedes constant
<a href=
"http://en.wikipedia.org/wiki/Pi" target=
"_top">π</a>
432 Many uses, most simply, circumference of a circle
454 <a href=
"http://en.wikipedia.org/wiki/Sphere#Volume_of_a_sphere" target=
"_top">volume
455 of a hemi-sphere
</a> =
4/
3 π r
³
499 <a href=
"http://en.wikipedia.org/wiki/Sphere#Volume_of_a_sphere" target=
"_top">volume
500 of a sphere
</a> =
4/
3 π r
³
771 √<sup>3</sup> π
790 1/
√<sup>3</sup> π
804 <span class=
"bold"><strong>Euler's e and related
</strong></span>
832 <a href=
"http://en.wikipedia.org/wiki/E_(mathematical_constant)" target=
"_top">Euler's
935 <span class=
"bold"><strong>Trigonometric
</strong></span>
953 radians =
π /
180
972 degrees =
180 /
π
1062 <span class=
"bold"><strong>Phi
</strong></span>
1067 Phidias golden ratio
1072 <a href=
"http://en.wikipedia.org/wiki/Golden_ratio" target=
"_top">Phidias golden
1142 <span class=
"bold"><strong>Euler's Gamma
</strong></span>
1170 <a href=
"http://en.wikipedia.org/wiki/Euler%E2%80%93Mascheroni_constant" target=
"_top">Euler-Mascheroni
1216 <span class=
"bold"><strong>Misc
</strong></span>
1244 <a href=
"http://en.wikipedia.org/wiki/Riemann_zeta_function" target=
"_top">Riemann
1267 <a href=
"http://en.wikipedia.org/wiki/Riemann_zeta_function" target=
"_top">Riemann
1280 <span class=
"emphasis"><em>K
</em></span>
1290 <a href=
"http://mathworld.wolfram.com/CatalansConstant.html" target=
"_top">Catalan
1291 (or Glaisher) combinatorial constant
</a>
1303 <span class=
"emphasis"><em>A
</em></span>
1313 <a href=
"https://oeis.org/A074962/constant" target=
"_top">Decimal expansion
1314 of Glaisher-Kinkelin constant
</a>
1326 <span class=
"emphasis"><em>k
</em></span>
1336 <a href=
"https://oeis.org/A002210/constant" target=
"_top">Decimal expansion
1337 of Khinchin constant
</a>
1344 extreme_value_skewness
1349 12√6 ζ(
3)/
π<sup>3</sup>
1359 Extreme value distribution
1371 2√π(
π-
3)/(
4 -
π)
<sup>3/
2</sup>
1381 Rayleigh distribution skewness
1388 rayleigh_kurtosis_excess
1393 -(
6π<sup>2</sup>-
24π+
16)/(
4-
π)
<sup>2</sup>
1403 <a href=
"http://en.wikipedia.org/wiki/Rayleigh_distribution" target=
"_top">Rayleigh
1404 distribution kurtosis excess
</a>
1416 3+(
6π<sup>2</sup>-
24π+
16)/(
4-
π)
<sup>2</sup>
1426 Rayleigh distribution kurtosis
1433 <br class=
"table-break"><div class=
"note"><table border=
"0" summary=
"Note">
1435 <td rowspan=
"2" align=
"center" valign=
"top" width=
"25"><img alt=
"[Note]" src=
"../../../../../doc/src/images/note.png"></td>
1436 <th align=
"left">Note
</th>
1438 <tr><td align=
"left" valign=
"top"><p>
1439 Integer values are
<span class=
"bold"><strong>not included
</strong></span> in this
1440 list of math constants, however interesting, because they can be so easily
1441 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>.
1444 <div class=
"tip"><table border=
"0" summary=
"Tip">
1446 <td rowspan=
"2" align=
"center" valign=
"top" width=
"25"><img alt=
"[Tip]" src=
"../../../../../doc/src/images/tip.png"></td>
1447 <th align=
"left">Tip
</th>
1449 <tr><td align=
"left" valign=
"top"><p>
1450 If you know the approximate value of the constant, you can search for the
1451 value to find Boost.Math chosen name in this table.
1454 <div class=
"tip"><table border=
"0" summary=
"Tip">
1456 <td rowspan=
"2" align=
"center" valign=
"top" width=
"25"><img alt=
"[Tip]" src=
"../../../../../doc/src/images/tip.png"></td>
1457 <th align=
"left">Tip
</th>
1459 <tr><td align=
"left" valign=
"top"><p>
1460 Bernoulli numbers are available at
<a class=
"link" href=
"number_series/bernoulli_numbers.html" title=
"Bernoulli Numbers">Bernoulli
1464 <div class=
"tip"><table border=
"0" summary=
"Tip">
1466 <td rowspan=
"2" align=
"center" valign=
"top" width=
"25"><img alt=
"[Tip]" src=
"../../../../../doc/src/images/tip.png"></td>
1467 <th align=
"left">Tip
</th>
1469 <tr><td align=
"left" valign=
"top"><p>
1470 Factorials are available at
<a class=
"link" href=
"factorials/sf_factorial.html" title=
"Factorial">factorial
</a>.
1474 <table xmlns:
rev=
"http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width=
"100%"><tr>
1475 <td align=
"left"></td>
1476 <td align=
"right"><div class=
"copyright-footer">Copyright
© 2006-
2010,
2012-
2014 Nikhar Agrawal,
1477 Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
1478 Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R
åde, Gautam Sewani,
1479 Benjamin Sobotta, Thijs van den Berg, Daryle Walker and Xiaogang Zhang
<p>
1480 Distributed under the Boost Software License, Version
1.0. (See accompanying
1481 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>)
1486 <div class=
"spirit-nav">
1487 <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>