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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 4.1. 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> |
| √2 |
| </p> |
| </td> |
| <td> |
| <p> |
| 1.41421 |
| </p> |
| </td> |
| <td> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| root_three |
| </p> |
| </td> |
| <td> |
| <p> |
| √3 |
| </p> |
| </td> |
| <td> |
| <p> |
| 1.73205 |
| </p> |
| </td> |
| <td> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| half_root_two |
| </p> |
| </td> |
| <td> |
| <p> |
| √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> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| ln_ten |
| </p> |
| </td> |
| <td> |
| <p> |
| ln(10) |
| </p> |
| </td> |
| <td> |
| <p> |
| 2.30258 |
| </p> |
| </td> |
| <td> |
| </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> |
| √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/√2 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.707106 |
| </p> |
| </td> |
| <td> |
| </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 |
| </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">π</a> |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| half_pi |
| </p> |
| </td> |
| <td> |
| <p> |
| π/2 |
| </p> |
| </td> |
| <td> |
| <p> |
| 1.570796 |
| </p> |
| </td> |
| <td> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| third_pi |
| </p> |
| </td> |
| <td> |
| <p> |
| π/3 |
| </p> |
| </td> |
| <td> |
| <p> |
| 1.04719 |
| </p> |
| </td> |
| <td> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| sixth_pi |
| </p> |
| </td> |
| <td> |
| <p> |
| π/6 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.523598 |
| </p> |
| </td> |
| <td> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| two_pi |
| </p> |
| </td> |
| <td> |
| <p> |
| 2π |
| </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 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_root_pi |
| </p> |
| </td> |
| <td> |
| <p> |
| 1/√π |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.564189 |
| </p> |
| </td> |
| <td> |
| </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> |
| </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> |
| </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> |
| <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> |
| </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 © 2006-2010, 2012-2014 Nikhar Agrawal, |
| Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert |
| Holin, Bruno Lalande, John Maddock, Johan Råde, Gautam Sewani, Benjamin Sobotta, |
| 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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