ceph/src/boost/libs/math/doc/html/math_toolkit/constants.html

   1 <html>
   2 <head>
   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&#160;4.&#160;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">
  11 </head>
  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>
  20 </tr></table>
  21 <hr>
  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>
  24 </div>
  25 <div class="section">
  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>
  29 <p>
  30       This section lists the mathematical constants, their use(s) (and sometimes
  31       rationale for their inclusion).
  32     </p>
  33 <div class="table">
  34 <a name="math_toolkit.constants.mathematical_constants"></a><p class="title"><b>Table&#160;4.1.&#160;Mathematical Constants</b></p>
  35 <div class="table-contents"><table class="table" summary="Mathematical Constants">
  36 <colgroup>
  37 <col>
  38 <col>
  39 <col>
  40 <col>
  41 </colgroup>
  42 <thead><tr>
  43 <th>
  44               <p>
  45                 name
  46               </p>
  47             </th>
  48 <th>
  49               <p>
  50                 formula
  51               </p>
  52             </th>
  53 <th>
  54               <p>
  55                 Value (6 decimals)
  56               </p>
  57             </th>
  58 <th>
  59               <p>
  60                 Uses and Rationale
  61               </p>
  62             </th>
  63 </tr></thead>
  64 <tbody>
  65 <tr>
  66 <td>
  67               <p>
  68                 <span class="bold"><strong>Rational fractions</strong></span>
  69               </p>
  70             </td>
  71 <td>
  72             </td>
  73 <td>
  74             </td>
  75 <td>
  76             </td>
  77 </tr>
  78 <tr>
  79 <td>
  80               <p>
  81                 half
  82               </p>
  83             </td>
  84 <td>
  85               <p>
  86                 1/2
  87               </p>
  88             </td>
  89 <td>
  90               <p>
  91                 0.5
  92               </p>
  93             </td>
  94 <td>
  95             </td>
  96 </tr>
  97 <tr>
  98 <td>
  99               <p>
 100                 third
 101               </p>
 102             </td>
 103 <td>
 104               <p>
 105                 1/3
 106               </p>
 107             </td>
 108 <td>
 109               <p>
 110                 0.333333
 111               </p>
 112             </td>
 113 <td>
 114             </td>
 115 </tr>
 116 <tr>
 117 <td>
 118               <p>
 119                 two_thirds
 120               </p>
 121             </td>
 122 <td>
 123               <p>
 124                 2/3
 125               </p>
 126             </td>
 127 <td>
 128               <p>
 129                 0.66667
 130               </p>
 131             </td>
 132 <td>
 133             </td>
 134 </tr>
 135 <tr>
 136 <td>
 137               <p>
 138                 three_quarters
 139               </p>
 140             </td>
 141 <td>
 142               <p>
 143                 3/4
 144               </p>
 145             </td>
 146 <td>
 147               <p>
 148                 0.75
 149               </p>
 150             </td>
 151 <td>
 152             </td>
 153 </tr>
 154 <tr>
 155 <td>
 156               <p>
 157                 <span class="bold"><strong>two and related</strong></span>
 158               </p>
 159             </td>
 160 <td>
 161             </td>
 162 <td>
 163             </td>
 164 <td>
 165             </td>
 166 </tr>
 167 <tr>
 168 <td>
 169               <p>
 170                 root_two
 171               </p>
 172             </td>
 173 <td>
 174               <p>
 175                 &#8730;2
 176               </p>
 177             </td>
 178 <td>
 179               <p>
 180                 1.41421
 181               </p>
 182             </td>
 183 <td>
 184             </td>
 185 </tr>
 186 <tr>
 187 <td>
 188               <p>
 189                 root_three
 190               </p>
 191             </td>
 192 <td>
 193               <p>
 194                 &#8730;3
 195               </p>
 196             </td>
 197 <td>
 198               <p>
 199                 1.73205
 200               </p>
 201             </td>
 202 <td>
 203             </td>
 204 </tr>
 205 <tr>
 206 <td>
 207               <p>
 208                 half_root_two
 209               </p>
 210             </td>
 211 <td>
 212               <p>
 213                 &#8730;2 /2
 214               </p>
 215             </td>
 216 <td>
 217               <p>
 218                 0.707106
 219               </p>
 220             </td>
 221 <td>
 222             </td>
 223 </tr>
 224 <tr>
 225 <td>
 226               <p>
 227                 ln_two
 228               </p>
 229             </td>
 230 <td>
 231               <p>
 232                 ln(2)
 233               </p>
 234             </td>
 235 <td>
 236               <p>
 237                 0.693147
 238               </p>
 239             </td>
 240 <td>
 241             </td>
 242 </tr>
 243 <tr>
 244 <td>
 245               <p>
 246                 ln_ten
 247               </p>
 248             </td>
 249 <td>
 250               <p>
 251                 ln(10)
 252               </p>
 253             </td>
 254 <td>
 255               <p>
 256                 2.30258
 257               </p>
 258             </td>
 259 <td>
 260             </td>
 261 </tr>
 262 <tr>
 263 <td>
 264               <p>
 265                 ln_ln_two
 266               </p>
 267             </td>
 268 <td>
 269               <p>
 270                 ln(ln(2))
 271               </p>
 272             </td>
 273 <td>
 274               <p>
 275                 -0.366512
 276               </p>
 277             </td>
 278 <td>
 279               <p>
 280                 Gumbel distribution median
 281               </p>
 282             </td>
 283 </tr>
 284 <tr>
 285 <td>
 286               <p>
 287                 root_ln_four
 288               </p>
 289             </td>
 290 <td>
 291               <p>
 292                 &#8730;ln(4)
 293               </p>
 294             </td>
 295 <td>
 296               <p>
 297                 1.177410
 298               </p>
 299             </td>
 300 <td>
 301             </td>
 302 </tr>
 303 <tr>
 304 <td>
 305               <p>
 306                 one_div_root_two
 307               </p>
 308             </td>
 309 <td>
 310               <p>
 311                 1/&#8730;2
 312               </p>
 313             </td>
 314 <td>
 315               <p>
 316                 0.707106
 317               </p>
 318             </td>
 319 <td>
 320             </td>
 321 </tr>
 322 <tr>
 323 <td>
 324               <p>
 325                 <span class="bold"><strong>&#960; and related</strong></span>
 326               </p>
 327             </td>
 328 <td>
 329             </td>
 330 <td>
 331             </td>
 332 <td>
 333             </td>
 334 </tr>
 335 <tr>
 336 <td>
 337               <p>
 338                 pi
 339               </p>
 340             </td>
 341 <td>
 342               <p>
 343                 pi
 344               </p>
 345             </td>
 346 <td>
 347               <p>
 348                 3.14159
 349               </p>
 350             </td>
 351 <td>
 352               <p>
 353                 Ubiquitous. Archimedes constant <a href="http://en.wikipedia.org/wiki/Pi" target="_top">&#960;</a>
 354               </p>
 355             </td>
 356 </tr>
 357 <tr>
 358 <td>
 359               <p>
 360                 half_pi
 361               </p>
 362             </td>
 363 <td>
 364               <p>
 365                 &#960;/2
 366               </p>
 367             </td>
 368 <td>
 369               <p>
 370                 1.570796
 371               </p>
 372             </td>
 373 <td>
 374             </td>
 375 </tr>
 376 <tr>
 377 <td>
 378               <p>
 379                 third_pi
 380               </p>
 381             </td>
 382 <td>
 383               <p>
 384                 &#960;/3
 385               </p>
 386             </td>
 387 <td>
 388               <p>
 389                 1.04719
 390               </p>
 391             </td>
 392 <td>
 393             </td>
 394 </tr>
 395 <tr>
 396 <td>
 397               <p>
 398                 sixth_pi
 399               </p>
 400             </td>
 401 <td>
 402               <p>
 403                 &#960;/6
 404               </p>
 405             </td>
 406 <td>
 407               <p>
 408                 0.523598
 409               </p>
 410             </td>
 411 <td>
 412             </td>
 413 </tr>
 414 <tr>
 415 <td>
 416               <p>
 417                 two_pi
 418               </p>
 419             </td>
 420 <td>
 421               <p>
 422                 2&#960;
 423               </p>
 424             </td>
 425 <td>
 426               <p>
 427                 6.28318
 428               </p>
 429             </td>
 430 <td>
 431               <p>
 432                 Many uses, most simply, circumference of a circle
 433               </p>
 434             </td>
 435 </tr>
 436 <tr>
 437 <td>
 438               <p>
 439                 two_thirds_pi
 440               </p>
 441             </td>
 442 <td>
 443               <p>
 444                 2/3 &#960;
 445               </p>
 446             </td>
 447 <td>
 448               <p>
 449                 2.09439
 450               </p>
 451             </td>
 452 <td>
 453               <p>
 454                 <a href="http://en.wikipedia.org/wiki/Sphere#Volume_of_a_sphere" target="_top">volume
 455                 of a hemi-sphere</a> = 4/3 &#960; r&#179;
 456               </p>
 457             </td>
 458 </tr>
 459 <tr>
 460 <td>
 461               <p>
 462                 three_quarters_pi
 463               </p>
 464             </td>
 465 <td>
 466               <p>
 467                 3/4 &#960;
 468               </p>
 469             </td>
 470 <td>
 471               <p>
 472                 2.35619
 473               </p>
 474             </td>
 475 <td>
 476               <p>
 477                 = 3/4 &#960;
 478               </p>
 479             </td>
 480 </tr>
 481 <tr>
 482 <td>
 483               <p>
 484                 four_thirds_pi
 485               </p>
 486             </td>
 487 <td>
 488               <p>
 489                 4/3 &#960;
 490               </p>
 491             </td>
 492 <td>
 493               <p>
 494                 4.18879
 495               </p>
 496             </td>
 497 <td>
 498               <p>
 499                 <a href="http://en.wikipedia.org/wiki/Sphere#Volume_of_a_sphere" target="_top">volume
 500                 of a sphere</a> = 4/3 &#960; r&#179;
 501               </p>
 502             </td>
 503 </tr>
 504 <tr>
 505 <td>
 506               <p>
 507                 one_div_two_pi
 508               </p>
 509             </td>
 510 <td>
 511               <p>
 512                 1/(2&#960;)
 513               </p>
 514             </td>
 515 <td>
 516               <p>
 517                 1.59155
 518               </p>
 519             </td>
 520 <td>
 521               <p>
 522                 Widely used
 523               </p>
 524             </td>
 525 </tr>
 526 <tr>
 527 <td>
 528               <p>
 529                 root_pi
 530               </p>
 531             </td>
 532 <td>
 533               <p>
 534                 &#8730;&#960;
 535               </p>
 536             </td>
 537 <td>
 538               <p>
 539                 1.77245
 540               </p>
 541             </td>
 542 <td>
 543               <p>
 544                 Widely used
 545               </p>
 546             </td>
 547 </tr>
 548 <tr>
 549 <td>
 550               <p>
 551                 root_half_pi
 552               </p>
 553             </td>
 554 <td>
 555               <p>
 556                 &#8730; &#960;/2
 557               </p>
 558             </td>
 559 <td>
 560               <p>
 561                 1.25331
 562               </p>
 563             </td>
 564 <td>
 565               <p>
 566                 Widely used
 567               </p>
 568             </td>
 569 </tr>
 570 <tr>
 571 <td>
 572               <p>
 573                 root_two_pi
 574               </p>
 575             </td>
 576 <td>
 577               <p>
 578                 &#8730; &#960;*2
 579               </p>
 580             </td>
 581 <td>
 582               <p>
 583                 2.50662
 584               </p>
 585             </td>
 586 <td>
 587               <p>
 588                 Widely used
 589               </p>
 590             </td>
 591 </tr>
 592 <tr>
 593 <td>
 594               <p>
 595                 one_div_root_pi
 596               </p>
 597             </td>
 598 <td>
 599               <p>
 600                 1/&#8730;&#960;
 601               </p>
 602             </td>
 603 <td>
 604               <p>
 605                 0.564189
 606               </p>
 607             </td>
 608 <td>
 609             </td>
 610 </tr>
 611 <tr>
 612 <td>
 613               <p>
 614                 one_div_root_two_pi
 615               </p>
 616             </td>
 617 <td>
 618               <p>
 619                 1/&#8730;(2&#960;)
 620               </p>
 621             </td>
 622 <td>
 623               <p>
 624                 0.398942
 625               </p>
 626             </td>
 627 <td>
 628             </td>
 629 </tr>
 630 <tr>
 631 <td>
 632               <p>
 633                 root_one_div_pi
 634               </p>
 635             </td>
 636 <td>
 637               <p>
 638                 &#8730;(1/&#960;
 639               </p>
 640             </td>
 641 <td>
 642               <p>
 643                 0.564189
 644               </p>
 645             </td>
 646 <td>
 647             </td>
 648 </tr>
 649 <tr>
 650 <td>
 651               <p>
 652                 pi_minus_three
 653               </p>
 654             </td>
 655 <td>
 656               <p>
 657                 &#960;-3
 658               </p>
 659             </td>
 660 <td>
 661               <p>
 662                 0.141593
 663               </p>
 664             </td>
 665 <td>
 666             </td>
 667 </tr>
 668 <tr>
 669 <td>
 670               <p>
 671                 four_minus_pi
 672               </p>
 673             </td>
 674 <td>
 675               <p>
 676                 4 -&#960;
 677               </p>
 678             </td>
 679 <td>
 680               <p>
 681                 0.858407
 682               </p>
 683             </td>
 684 <td>
 685             </td>
 686 </tr>
 687 <tr>
 688 <td>
 689               <p>
 690                 pi_pow_e
 691               </p>
 692             </td>
 693 <td>
 694               <p>
 695                 &#960;<sup>e</sup>
 696               </p>
 697             </td>
 698 <td>
 699               <p>
 700                 22.4591
 701               </p>
 702             </td>
 703 <td>
 704             </td>
 705 </tr>
 706 <tr>
 707 <td>
 708               <p>
 709                 pi_sqr
 710               </p>
 711             </td>
 712 <td>
 713               <p>
 714                 &#960;<sup>2</sup>
 715               </p>
 716             </td>
 717 <td>
 718               <p>
 719                 9.86960
 720               </p>
 721             </td>
 722 <td>
 723             </td>
 724 </tr>
 725 <tr>
 726 <td>
 727               <p>
 728                 pi_sqr_div_six
 729               </p>
 730             </td>
 731 <td>
 732               <p>
 733                 &#960;<sup>2</sup>/6
 734               </p>
 735             </td>
 736 <td>
 737               <p>
 738                 1.64493
 739               </p>
 740             </td>
 741 <td>
 742             </td>
 743 </tr>
 744 <tr>
 745 <td>
 746               <p>
 747                 pi_cubed
 748               </p>
 749             </td>
 750 <td>
 751               <p>
 752                 &#960;<sup>3</sup>
 753               </p>
 754             </td>
 755 <td>
 756               <p>
 757                 31.00627
 758               </p>
 759             </td>
 760 <td>
 761             </td>
 762 </tr>
 763 <tr>
 764 <td>
 765               <p>
 766                 cbrt_pi
 767               </p>
 768             </td>
 769 <td>
 770               <p>
 771                 &#8730;<sup>3</sup> &#960;
 772               </p>
 773             </td>
 774 <td>
 775               <p>
 776                 1.46459
 777               </p>
 778             </td>
 779 <td>
 780             </td>
 781 </tr>
 782 <tr>
 783 <td>
 784               <p>
 785                 one_div_cbrt_pi
 786               </p>
 787             </td>
 788 <td>
 789               <p>
 790                 1/&#8730;<sup>3</sup> &#960;
 791               </p>
 792             </td>
 793 <td>
 794               <p>
 795                 0.682784
 796               </p>
 797             </td>
 798 <td>
 799             </td>
 800 </tr>
 801 <tr>
 802 <td>
 803               <p>
 804                 <span class="bold"><strong>Euler's e and related</strong></span>
 805               </p>
 806             </td>
 807 <td>
 808             </td>
 809 <td>
 810             </td>
 811 <td>
 812             </td>
 813 </tr>
 814 <tr>
 815 <td>
 816               <p>
 817                 e
 818               </p>
 819             </td>
 820 <td>
 821               <p>
 822                 e
 823               </p>
 824             </td>
 825 <td>
 826               <p>
 827                 2.71828
 828               </p>
 829             </td>
 830 <td>
 831               <p>
 832                 <a href="http://en.wikipedia.org/wiki/E_(mathematical_constant)" target="_top">Euler's
 833                 constant e</a>
 834               </p>
 835             </td>
 836 </tr>
 837 <tr>
 838 <td>
 839               <p>
 840                 exp_minus_half
 841               </p>
 842             </td>
 843 <td>
 844               <p>
 845                 e <sup>-1/2</sup>
 846               </p>
 847             </td>
 848 <td>
 849               <p>
 850                 0.606530
 851               </p>
 852             </td>
 853 <td>
 854             </td>
 855 </tr>
 856 <tr>
 857 <td>
 858               <p>
 859                 e_pow_pi
 860               </p>
 861             </td>
 862 <td>
 863               <p>
 864                 e <sup>&#960;</sup>
 865               </p>
 866             </td>
 867 <td>
 868               <p>
 869                 23.14069
 870               </p>
 871             </td>
 872 <td>
 873             </td>
 874 </tr>
 875 <tr>
 876 <td>
 877               <p>
 878                 root_e
 879               </p>
 880             </td>
 881 <td>
 882               <p>
 883                 &#8730; e
 884               </p>
 885             </td>
 886 <td>
 887               <p>
 888                 1.64872
 889               </p>
 890             </td>
 891 <td>
 892             </td>
 893 </tr>
 894 <tr>
 895 <td>
 896               <p>
 897                 log10_e
 898               </p>
 899             </td>
 900 <td>
 901               <p>
 902                 log10(e)
 903               </p>
 904             </td>
 905 <td>
 906               <p>
 907                 0.434294
 908               </p>
 909             </td>
 910 <td>
 911             </td>
 912 </tr>
 913 <tr>
 914 <td>
 915               <p>
 916                 one_div_log10_e
 917               </p>
 918             </td>
 919 <td>
 920               <p>
 921                 1/log10(e)
 922               </p>
 923             </td>
 924 <td>
 925               <p>
 926                 2.30258
 927               </p>
 928             </td>
 929 <td>
 930             </td>
 931 </tr>
 932 <tr>
 933 <td>
 934               <p>
 935                 <span class="bold"><strong>Trigonometric</strong></span>
 936               </p>
 937             </td>
 938 <td>
 939             </td>
 940 <td>
 941             </td>
 942 <td>
 943             </td>
 944 </tr>
 945 <tr>
 946 <td>
 947               <p>
 948                 degree
 949               </p>
 950             </td>
 951 <td>
 952               <p>
 953                 radians = &#960; / 180
 954               </p>
 955             </td>
 956 <td>
 957               <p>
 958                 0.017453
 959               </p>
 960             </td>
 961 <td>
 962             </td>
 963 </tr>
 964 <tr>
 965 <td>
 966               <p>
 967                 radian
 968               </p>
 969             </td>
 970 <td>
 971               <p>
 972                 degrees = 180 / &#960;
 973               </p>
 974             </td>
 975 <td>
 976               <p>
 977                 57.2957
 978               </p>
 979             </td>
 980 <td>
 981             </td>
 982 </tr>
 983 <tr>
 984 <td>
 985               <p>
 986                 sin_one
 987               </p>
 988             </td>
 989 <td>
 990               <p>
 991                 sin(1)
 992               </p>
 993             </td>
 994 <td>
 995               <p>
 996                 0.841470
 997               </p>
 998             </td>
 999 <td>
1000             </td>
1001 </tr>
1002 <tr>
1003 <td>
1004               <p>
1005                 cos_one
1006               </p>
1007             </td>
1008 <td>
1009               <p>
1010                 cos(1)
1011               </p>
1012             </td>
1013 <td>
1014               <p>
1015                 0.54030
1016               </p>
1017             </td>
1018 <td>
1019             </td>
1020 </tr>
1021 <tr>
1022 <td>
1023               <p>
1024                 sinh_one
1025               </p>
1026             </td>
1027 <td>
1028               <p>
1029                 sinh(1)
1030               </p>
1031             </td>
1032 <td>
1033               <p>
1034                 1.17520
1035               </p>
1036             </td>
1037 <td>
1038             </td>
1039 </tr>
1040 <tr>
1041 <td>
1042               <p>
1043                 cosh_one
1044               </p>
1045             </td>
1046 <td>
1047               <p>
1048                 cosh(1)
1049               </p>
1050             </td>
1051 <td>
1052               <p>
1053                 1.54308
1054               </p>
1055             </td>
1056 <td>
1057             </td>
1058 </tr>
1059 <tr>
1060 <td>
1061               <p>
1062                 <span class="bold"><strong>Phi</strong></span>
1063               </p>
1064             </td>
1065 <td>
1066               <p>
1067                 Phidias golden ratio
1068               </p>
1069             </td>
1070 <td>
1071               <p>
1072                 <a href="http://en.wikipedia.org/wiki/Golden_ratio" target="_top">Phidias golden
1073                 ratio</a>
1074               </p>
1075             </td>
1076 <td>
1077             </td>
1078 </tr>
1079 <tr>
1080 <td>
1081               <p>
1082                 phi
1083               </p>
1084             </td>
1085 <td>
1086               <p>
1087                 (1 + &#8730;5) /2
1088               </p>
1089             </td>
1090 <td>
1091               <p>
1092                 1.61803
1093               </p>
1094             </td>
1095 <td>
1096               <p>
1097                 finance
1098               </p>
1099             </td>
1100 </tr>
1101 <tr>
1102 <td>
1103               <p>
1104                 ln_phi
1105               </p>
1106             </td>
1107 <td>
1108               <p>
1109                 ln(&#966;)
1110               </p>
1111             </td>
1112 <td>
1113               <p>
1114                 0.48121
1115               </p>
1116             </td>
1117 <td>
1118             </td>
1119 </tr>
1120 <tr>
1121 <td>
1122               <p>
1123                 one_div_ln_phi
1124               </p>
1125             </td>
1126 <td>
1127               <p>
1128                 1/ln(&#966;)
1129               </p>
1130             </td>
1131 <td>
1132               <p>
1133                 2.07808
1134               </p>
1135             </td>
1136 <td>
1137             </td>
1138 </tr>
1139 <tr>
1140 <td>
1141               <p>
1142                 <span class="bold"><strong>Euler's Gamma</strong></span>
1143               </p>
1144             </td>
1145 <td>
1146             </td>
1147 <td>
1148             </td>
1149 <td>
1150             </td>
1151 </tr>
1152 <tr>
1153 <td>
1154               <p>
1155                 euler
1156               </p>
1157             </td>
1158 <td>
1159               <p>
1160                 euler
1161               </p>
1162             </td>
1163 <td>
1164               <p>
1165                 0.577215
1166               </p>
1167             </td>
1168 <td>
1169               <p>
1170                 <a href="http://en.wikipedia.org/wiki/Euler%E2%80%93Mascheroni_constant" target="_top">Euler-Mascheroni
1171                 gamma constant</a>
1172               </p>
1173             </td>
1174 </tr>
1175 <tr>
1176 <td>
1177               <p>
1178                 one_div_euler
1179               </p>
1180             </td>
1181 <td>
1182               <p>
1183                 1/euler
1184               </p>
1185             </td>
1186 <td>
1187               <p>
1188                 1.73245
1189               </p>
1190             </td>
1191 <td>
1192             </td>
1193 </tr>
1194 <tr>
1195 <td>
1196               <p>
1197                 euler_sqr
1198               </p>
1199             </td>
1200 <td>
1201               <p>
1202                 euler<sup>2</sup>
1203               </p>
1204             </td>
1205 <td>
1206               <p>
1207                 0.333177
1208               </p>
1209             </td>
1210 <td>
1211             </td>
1212 </tr>
1213 <tr>
1214 <td>
1215               <p>
1216                 <span class="bold"><strong>Misc</strong></span>
1217               </p>
1218             </td>
1219 <td>
1220             </td>
1221 <td>
1222             </td>
1223 <td>
1224             </td>
1225 </tr>
1226 <tr>
1227 <td>
1228               <p>
1229                 zeta_two
1230               </p>
1231             </td>
1232 <td>
1233               <p>
1234                 &#950;(2)
1235               </p>
1236             </td>
1237 <td>
1238               <p>
1239                 1.64493
1240               </p>
1241             </td>
1242 <td>
1243               <p>
1244                 <a href="http://en.wikipedia.org/wiki/Riemann_zeta_function" target="_top">Riemann
1245                 zeta function</a>
1246               </p>
1247             </td>
1248 </tr>
1249 <tr>
1250 <td>
1251               <p>
1252                 zeta_three
1253               </p>
1254             </td>
1255 <td>
1256               <p>
1257                 &#950;(3)
1258               </p>
1259             </td>
1260 <td>
1261               <p>
1262                 1.20205
1263               </p>
1264             </td>
1265 <td>
1266               <p>
1267                 <a href="http://en.wikipedia.org/wiki/Riemann_zeta_function" target="_top">Riemann
1268                 zeta function</a>
1269               </p>
1270             </td>
1271 </tr>
1272 <tr>
1273 <td>
1274               <p>
1275                 catalan
1276               </p>
1277             </td>
1278 <td>
1279               <p>
1280                 <span class="emphasis"><em>K</em></span>
1281               </p>
1282             </td>
1283 <td>
1284               <p>
1285                 0.915965
1286               </p>
1287             </td>
1288 <td>
1289               <p>
1290                 <a href="http://mathworld.wolfram.com/CatalansConstant.html" target="_top">Catalan
1291                 (or Glaisher) combinatorial constant</a>
1292               </p>
1293             </td>
1294 </tr>
1295 <tr>
1296 <td>
1297               <p>
1298                 glaisher
1299               </p>
1300             </td>
1301 <td>
1302               <p>
1303                 <span class="emphasis"><em>A</em></span>
1304               </p>
1305             </td>
1306 <td>
1307               <p>
1308                 1.28242
1309               </p>
1310             </td>
1311 <td>
1312               <p>
1313                 <a href="https://oeis.org/A074962/constant" target="_top">Decimal expansion
1314                 of Glaisher-Kinkelin constant</a>
1315               </p>
1316             </td>
1317 </tr>
1318 <tr>
1319 <td>
1320               <p>
1321                 khinchin
1322               </p>
1323             </td>
1324 <td>
1325               <p>
1326                 <span class="emphasis"><em>k</em></span>
1327               </p>
1328             </td>
1329 <td>
1330               <p>
1331                 2.685452
1332               </p>
1333             </td>
1334 <td>
1335               <p>
1336                 <a href="https://oeis.org/A002210/constant" target="_top">Decimal expansion
1337                 of Khinchin constant</a>
1338               </p>
1339             </td>
1340 </tr>
1341 <tr>
1342 <td>
1343               <p>
1344                 extreme_value_skewness
1345               </p>
1346             </td>
1347 <td>
1348               <p>
1349                 12&#8730;6 &#950;(3)/ &#960;<sup>3</sup>
1350               </p>
1351             </td>
1352 <td>
1353               <p>
1354                 1.139547
1355               </p>
1356             </td>
1357 <td>
1358               <p>
1359                 Extreme value distribution
1360               </p>
1361             </td>
1362 </tr>
1363 <tr>
1364 <td>
1365               <p>
1366                 rayleigh_skewness
1367               </p>
1368             </td>
1369 <td>
1370               <p>
1371                 2&#8730;&#960;(&#960;-3)/(4 - &#960;)<sup>3/2</sup>
1372               </p>
1373             </td>
1374 <td>
1375               <p>
1376                 0.631110
1377               </p>
1378             </td>
1379 <td>
1380               <p>
1381                 Rayleigh distribution skewness
1382               </p>
1383             </td>
1384 </tr>
1385 <tr>
1386 <td>
1387               <p>
1388                 rayleigh_kurtosis_excess
1389               </p>
1390             </td>
1391 <td>
1392               <p>
1393                 -(6&#960;<sup>2</sup>-24&#960;+16)/(4-&#960;)<sup>2</sup>
1394               </p>
1395             </td>
1396 <td>
1397               <p>
1398                 0.245089
1399               </p>
1400             </td>
1401 <td>
1402               <p>
1403                 <a href="http://en.wikipedia.org/wiki/Rayleigh_distribution" target="_top">Rayleigh
1404                 distribution kurtosis excess</a>
1405               </p>
1406             </td>
1407 </tr>
1408 <tr>
1409 <td>
1410               <p>
1411                 rayleigh_kurtosis
1412               </p>
1413             </td>
1414 <td>
1415               <p>
1416                 3+(6&#960;<sup>2</sup>-24&#960;+16)/(4-&#960;)<sup>2</sup>
1417               </p>
1418             </td>
1419 <td>
1420               <p>
1421                 3.245089
1422               </p>
1423             </td>
1424 <td>
1425               <p>
1426                 Rayleigh distribution kurtosis
1427               </p>
1428             </td>
1429 </tr>
1430 </tbody>
1431 </table></div>
1432 </div>
1433 <br class="table-break"><div class="note"><table border="0" summary="Note">
1434 <tr>
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>
1437 </tr>
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">&lt;</span><span class="identifier">cpp_float</span><span class="special">&gt;(</span><span class="number">42</span><span class="special">)</span></code>.
1442       </p></td></tr>
1443 </table></div>
1444 <div class="tip"><table border="0" summary="Tip">
1445 <tr>
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>
1448 </tr>
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.
1452       </p></td></tr>
1453 </table></div>
1454 <div class="tip"><table border="0" summary="Tip">
1455 <tr>
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>
1458 </tr>
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
1461         numbers</a>.
1462       </p></td></tr>
1463 </table></div>
1464 <div class="tip"><table border="0" summary="Tip">
1465 <tr>
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>
1468 </tr>
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>.
1471       </p></td></tr>
1472 </table></div>
1473 </div>
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 &#169; 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&#229;de, 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>)
1482       </p>
1483 </div></td>
1484 </tr></table>
1485 <hr>
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>
1488 </div>
1489 </body>
1490 </html>