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<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="math_toolkit.constants"></a><a class="link" href="constants.html" title="The Mathematical Constants">The Mathematical Constants</a>
</h2></div></div></div>
<p>
      This section lists the mathematical constants, their use(s) (and sometimes
      rationale for their inclusion).
    </p>
<div class="table">
<a name="math_toolkit.constants.mathematical_constants"></a><p class="title"><b>Table&#160;4.1.&#160;Mathematical Constants</b></p>
<div class="table-contents"><table class="table" summary="Mathematical Constants">
<colgroup>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              <p>
                name
              </p>
            </th>
<th>
              <p>
                formula
              </p>
            </th>
<th>
              <p>
                Value (6 decimals)
              </p>
            </th>
<th>
              <p>
                Uses and Rationale
              </p>
            </th>
</tr></thead>
<tbody>
<tr>
<td>
              <p>
                <span class="bold"><strong>Rational fractions</strong></span>
              </p>
            </td>
<td>
            </td>
<td>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                half
              </p>
            </td>
<td>
              <p>
                1/2
              </p>
            </td>
<td>
              <p>
                0.5
              </p>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                third
              </p>
            </td>
<td>
              <p>
                1/3
              </p>
            </td>
<td>
              <p>
                0.333333
              </p>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                two_thirds
              </p>
            </td>
<td>
              <p>
                2/3
              </p>
            </td>
<td>
              <p>
                0.66667
              </p>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                three_quarters
              </p>
            </td>
<td>
              <p>
                3/4
              </p>
            </td>
<td>
              <p>
                0.75
              </p>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                <span class="bold"><strong>two and related</strong></span>
              </p>
            </td>
<td>
            </td>
<td>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                root_two
              </p>
            </td>
<td>
              <p>
                &#8730;2
              </p>
            </td>
<td>
              <p>
                1.41421
              </p>
            </td>
<td>
              <p>
                Equivalent to POSIX constant M_SQRT2
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                root_three
              </p>
            </td>
<td>
              <p>
                &#8730;3
              </p>
            </td>
<td>
              <p>
                1.73205
              </p>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                half_root_two
              </p>
            </td>
<td>
              <p>
                &#8730;2 /2
              </p>
            </td>
<td>
              <p>
                0.707106
              </p>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                ln_two
              </p>
            </td>
<td>
              <p>
                ln(2)
              </p>
            </td>
<td>
              <p>
                0.693147
              </p>
            </td>
<td>
              <p>
                Equivalent to POSIX constant M_LN2
              </p>
            </td>
</tr>
<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>
</tr>
<tr>
<td>
              <p>
                ln_ln_two
              </p>
            </td>
<td>
              <p>
                ln(ln(2))
              </p>
            </td>
<td>
              <p>
                -0.366512
              </p>
            </td>
<td>
              <p>
                Gumbel distribution median
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                root_ln_four
              </p>
            </td>
<td>
              <p>
                &#8730;ln(4)
              </p>
            </td>
<td>
              <p>
                1.177410
              </p>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                one_div_root_two
              </p>
            </td>
<td>
              <p>
                1/&#8730;2
              </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>&#960; and related</strong></span>
              </p>
            </td>
<td>
            </td>
<td>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                pi
              </p>
            </td>
<td>
              <p>
                pi
              </p>
            </td>
<td>
              <p>
                3.14159
              </p>
            </td>
<td>
              <p>
                Ubiquitous. Archimedes constant <a href="http://en.wikipedia.org/wiki/Pi" target="_top">&#960;</a>.
                Equivalent to POSIX constant M_PI
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                half_pi
              </p>
            </td>
<td>
              <p>
                &#960;/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>
                &#960;/3
              </p>
            </td>
<td>
              <p>
                1.04719
              </p>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                quarter_pi
              </p>
            </td>
<td>
              <p>
                &#960;/4
              </p>
            </td>
<td>
              <p>
                0.78539816
              </p>
            </td>
<td>
              <p>
                Equivalent to POSIX constant M_PI_4
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                sixth_pi
              </p>
            </td>
<td>
              <p>
                &#960;/6
              </p>
            </td>
<td>
              <p>
                0.523598
              </p>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                two_pi
              </p>
            </td>
<td>
              <p>
                2&#960;
              </p>
            </td>
<td>
              <p>
                6.28318
              </p>
            </td>
<td>
              <p>
                Many uses, most simply, circumference of a circle
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                two_thirds_pi
              </p>
            </td>
<td>
              <p>
                2/3 &#960;
              </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 &#960; r&#179;
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                three_quarters_pi
              </p>
            </td>
<td>
              <p>
                3/4 &#960;
              </p>
            </td>
<td>
              <p>
                2.35619
              </p>
            </td>
<td>
              <p>
                = 3/4 &#960;
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                four_thirds_pi
              </p>
            </td>
<td>
              <p>
                4/3 &#960;
              </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 &#960; r&#179;
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                one_div_two_pi
              </p>
            </td>
<td>
              <p>
                1/(2&#960;)
              </p>
            </td>
<td>
              <p>
                1.59155
              </p>
            </td>
<td>
              <p>
                Widely used
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                root_pi
              </p>
            </td>
<td>
              <p>
                &#8730;&#960;
              </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>
                &#8730; &#960;/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>
                &#8730; &#960;*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/&#960;
              </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/&#960;
              </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/&#8730;&#960;
              </p>
            </td>
<td>
              <p>
                0.564189
              </p>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                two_div_root_pi
              </p>
            </td>
<td>
              <p>
                2/&#8730;&#960;
              </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/&#8730;(2&#960;)
              </p>
            </td>
<td>
              <p>
                0.398942
              </p>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                root_one_div_pi
              </p>
            </td>
<td>
              <p>
                &#8730;(1/&#960;
              </p>
            </td>
<td>
              <p>
                0.564189
              </p>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                pi_minus_three
              </p>
            </td>
<td>
              <p>
                &#960;-3
              </p>
            </td>
<td>
              <p>
                0.141593
              </p>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                four_minus_pi
              </p>
            </td>
<td>
              <p>
                4 -&#960;
              </p>
            </td>
<td>
              <p>
                0.858407
              </p>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                pi_pow_e
              </p>
            </td>
<td>
              <p>
                &#960;<sup>e</sup>
              </p>
            </td>
<td>
              <p>
                22.4591
              </p>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                pi_sqr
              </p>
            </td>
<td>
              <p>
                &#960;<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>
                &#960;<sup>2</sup>/6
              </p>
            </td>
<td>
              <p>
                1.64493
              </p>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                pi_cubed
              </p>
            </td>
<td>
              <p>
                &#960;<sup>3</sup>
              </p>
            </td>
<td>
              <p>
                31.00627
              </p>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                cbrt_pi
              </p>
            </td>
<td>
              <p>
                &#8730;<sup>3</sup> &#960;
              </p>
            </td>
<td>
              <p>
                1.46459
              </p>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                one_div_cbrt_pi
              </p>
            </td>
<td>
              <p>
                1/&#8730;<sup>3</sup> &#960;
              </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>&#960;</sup>
              </p>
            </td>
<td>
              <p>
                23.14069
              </p>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                root_e
              </p>
            </td>
<td>
              <p>
                &#8730; 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 = &#960; / 180
              </p>
            </td>
<td>
              <p>
                0.017453
              </p>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                radian
              </p>
            </td>
<td>
              <p>
                degrees = 180 / &#960;
              </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 + &#8730;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(&#966;)
              </p>
            </td>
<td>
              <p>
                0.48121
              </p>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                one_div_ln_phi
              </p>
            </td>
<td>
              <p>
                1/ln(&#966;)
              </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>
                &#950;(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>
                &#950;(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&#8730;6 &#950;(3)/ &#960;<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&#8730;&#960;(&#960;-3)/(4 - &#960;)<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>
                -(6&#960;<sup>2</sup>-24&#960;+16)/(4-&#960;)<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+(6&#960;<sup>2</sup>-24&#960;+16)/(4-&#960;)<sup>2</sup>
              </p>
            </td>
<td>
              <p>
                3.245089
              </p>
            </td>
<td>
              <p>
                Rayleigh distribution kurtosis
              </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">&lt;</span><span class="identifier">cpp_float</span><span class="special">&gt;(</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 &#169; 2006-2019 Nikhar
      Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
      R&#229;de, 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>
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