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  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               <p>
 185                 Equivalent to POSIX constant M_SQRT2
 186               </p>
 187             </td>
 188 </tr>
 189 <tr>
 190 <td>
 191               <p>
 192                 root_three
 193               </p>
 194             </td>
 195 <td>
 196               <p>
 197                 &#8730;3
 198               </p>
 199             </td>
 200 <td>
 201               <p>
 202                 1.73205
 203               </p>
 204             </td>
 205 <td>
 206             </td>
 207 </tr>
 208 <tr>
 209 <td>
 210               <p>
 211                 half_root_two
 212               </p>
 213             </td>
 214 <td>
 215               <p>
 216                 &#8730;2 /2
 217               </p>
 218             </td>
 219 <td>
 220               <p>
 221                 0.707106
 222               </p>
 223             </td>
 224 <td>
 225             </td>
 226 </tr>
 227 <tr>
 228 <td>
 229               <p>
 230                 ln_two
 231               </p>
 232             </td>
 233 <td>
 234               <p>
 235                 ln(2)
 236               </p>
 237             </td>
 238 <td>
 239               <p>
 240                 0.693147
 241               </p>
 242             </td>
 243 <td>
 244               <p>
 245                 Equivalent to POSIX constant M_LN2
 246               </p>
 247             </td>
 248 </tr>
 249 <tr>
 250 <td>
 251               <p>
 252                 ln_ten
 253               </p>
 254             </td>
 255 <td>
 256               <p>
 257                 ln(10)
 258               </p>
 259             </td>
 260 <td>
 261               <p>
 262                 2.30258
 263               </p>
 264             </td>
 265 <td>
 266               <p>
 267                 Equivalent to POSIX constant M_LN10
 268               </p>
 269             </td>
 270 </tr>
 271 <tr>
 272 <td>
 273               <p>
 274                 ln_ln_two
 275               </p>
 276             </td>
 277 <td>
 278               <p>
 279                 ln(ln(2))
 280               </p>
 281             </td>
 282 <td>
 283               <p>
 284                 -0.366512
 285               </p>
 286             </td>
 287 <td>
 288               <p>
 289                 Gumbel distribution median
 290               </p>
 291             </td>
 292 </tr>
 293 <tr>
 294 <td>
 295               <p>
 296                 root_ln_four
 297               </p>
 298             </td>
 299 <td>
 300               <p>
 301                 &#8730;ln(4)
 302               </p>
 303             </td>
 304 <td>
 305               <p>
 306                 1.177410
 307               </p>
 308             </td>
 309 <td>
 310             </td>
 311 </tr>
 312 <tr>
 313 <td>
 314               <p>
 315                 one_div_root_two
 316               </p>
 317             </td>
 318 <td>
 319               <p>
 320                 1/&#8730;2
 321               </p>
 322             </td>
 323 <td>
 324               <p>
 325                 0.707106
 326               </p>
 327             </td>
 328 <td>
 329               <p>
 330                 Equivalent to POSIX constant M_SQRT1_2
 331               </p>
 332             </td>
 333 </tr>
 334 <tr>
 335 <td>
 336               <p>
 337                 <span class="bold"><strong>&#960; and related</strong></span>
 338               </p>
 339             </td>
 340 <td>
 341             </td>
 342 <td>
 343             </td>
 344 <td>
 345             </td>
 346 </tr>
 347 <tr>
 348 <td>
 349               <p>
 350                 pi
 351               </p>
 352             </td>
 353 <td>
 354               <p>
 355                 pi
 356               </p>
 357             </td>
 358 <td>
 359               <p>
 360                 3.14159
 361               </p>
 362             </td>
 363 <td>
 364               <p>
 365                 Ubiquitous. Archimedes constant <a href="http://en.wikipedia.org/wiki/Pi" target="_top">&#960;</a>.
 366                 Equivalent to POSIX constant M_PI
 367               </p>
 368             </td>
 369 </tr>
 370 <tr>
 371 <td>
 372               <p>
 373                 half_pi
 374               </p>
 375             </td>
 376 <td>
 377               <p>
 378                 &#960;/2
 379               </p>
 380             </td>
 381 <td>
 382               <p>
 383                 1.570796
 384               </p>
 385             </td>
 386 <td>
 387               <p>
 388                 Equivalent to POSIX constant M_PI2
 389               </p>
 390             </td>
 391 </tr>
 392 <tr>
 393 <td>
 394               <p>
 395                 third_pi
 396               </p>
 397             </td>
 398 <td>
 399               <p>
 400                 &#960;/3
 401               </p>
 402             </td>
 403 <td>
 404               <p>
 405                 1.04719
 406               </p>
 407             </td>
 408 <td>
 409             </td>
 410 </tr>
 411 <tr>
 412 <td>
 413               <p>
 414                 quarter_pi
 415               </p>
 416             </td>
 417 <td>
 418               <p>
 419                 &#960;/4
 420               </p>
 421             </td>
 422 <td>
 423               <p>
 424                 0.78539816
 425               </p>
 426             </td>
 427 <td>
 428               <p>
 429                 Equivalent to POSIX constant M_PI_4
 430               </p>
 431             </td>
 432 </tr>
 433 <tr>
 434 <td>
 435               <p>
 436                 sixth_pi
 437               </p>
 438             </td>
 439 <td>
 440               <p>
 441                 &#960;/6
 442               </p>
 443             </td>
 444 <td>
 445               <p>
 446                 0.523598
 447               </p>
 448             </td>
 449 <td>
 450             </td>
 451 </tr>
 452 <tr>
 453 <td>
 454               <p>
 455                 two_pi
 456               </p>
 457             </td>
 458 <td>
 459               <p>
 460                 2&#960;
 461               </p>
 462             </td>
 463 <td>
 464               <p>
 465                 6.28318
 466               </p>
 467             </td>
 468 <td>
 469               <p>
 470                 Many uses, most simply, circumference of a circle
 471               </p>
 472             </td>
 473 </tr>
 474 <tr>
 475 <td>
 476               <p>
 477                 two_thirds_pi
 478               </p>
 479             </td>
 480 <td>
 481               <p>
 482                 2/3 &#960;
 483               </p>
 484             </td>
 485 <td>
 486               <p>
 487                 2.09439
 488               </p>
 489             </td>
 490 <td>
 491               <p>
 492                 <a href="http://en.wikipedia.org/wiki/Sphere#Volume_of_a_sphere" target="_top">volume
 493                 of a hemi-sphere</a> = 4/3 &#960; r&#179;
 494               </p>
 495             </td>
 496 </tr>
 497 <tr>
 498 <td>
 499               <p>
 500                 three_quarters_pi
 501               </p>
 502             </td>
 503 <td>
 504               <p>
 505                 3/4 &#960;
 506               </p>
 507             </td>
 508 <td>
 509               <p>
 510                 2.35619
 511               </p>
 512             </td>
 513 <td>
 514               <p>
 515                 = 3/4 &#960;
 516               </p>
 517             </td>
 518 </tr>
 519 <tr>
 520 <td>
 521               <p>
 522                 four_thirds_pi
 523               </p>
 524             </td>
 525 <td>
 526               <p>
 527                 4/3 &#960;
 528               </p>
 529             </td>
 530 <td>
 531               <p>
 532                 4.18879
 533               </p>
 534             </td>
 535 <td>
 536               <p>
 537                 <a href="http://en.wikipedia.org/wiki/Sphere#Volume_of_a_sphere" target="_top">volume
 538                 of a sphere</a> = 4/3 &#960; r&#179;
 539               </p>
 540             </td>
 541 </tr>
 542 <tr>
 543 <td>
 544               <p>
 545                 one_div_two_pi
 546               </p>
 547             </td>
 548 <td>
 549               <p>
 550                 1/(2&#960;)
 551               </p>
 552             </td>
 553 <td>
 554               <p>
 555                 1.59155
 556               </p>
 557             </td>
 558 <td>
 559               <p>
 560                 Widely used
 561               </p>
 562             </td>
 563 </tr>
 564 <tr>
 565 <td>
 566               <p>
 567                 root_pi
 568               </p>
 569             </td>
 570 <td>
 571               <p>
 572                 &#8730;&#960;
 573               </p>
 574             </td>
 575 <td>
 576               <p>
 577                 1.77245
 578               </p>
 579             </td>
 580 <td>
 581               <p>
 582                 Widely used
 583               </p>
 584             </td>
 585 </tr>
 586 <tr>
 587 <td>
 588               <p>
 589                 root_half_pi
 590               </p>
 591             </td>
 592 <td>
 593               <p>
 594                 &#8730; &#960;/2
 595               </p>
 596             </td>
 597 <td>
 598               <p>
 599                 1.25331
 600               </p>
 601             </td>
 602 <td>
 603               <p>
 604                 Widely used
 605               </p>
 606             </td>
 607 </tr>
 608 <tr>
 609 <td>
 610               <p>
 611                 root_two_pi
 612               </p>
 613             </td>
 614 <td>
 615               <p>
 616                 &#8730; &#960;*2
 617               </p>
 618             </td>
 619 <td>
 620               <p>
 621                 2.50662
 622               </p>
 623             </td>
 624 <td>
 625               <p>
 626                 Widely used
 627               </p>
 628             </td>
 629 </tr>
 630 <tr>
 631 <td>
 632               <p>
 633                 one_div_pi
 634               </p>
 635             </td>
 636 <td>
 637               <p>
 638                 1/&#960;
 639               </p>
 640             </td>
 641 <td>
 642               <p>
 643                 0.31830988
 644               </p>
 645             </td>
 646 <td>
 647               <p>
 648                 Equivalent to POSIX constant M_1_PI
 649               </p>
 650             </td>
 651 </tr>
 652 <tr>
 653 <td>
 654               <p>
 655                 two_div_pi
 656               </p>
 657             </td>
 658 <td>
 659               <p>
 660                 2/&#960;
 661               </p>
 662             </td>
 663 <td>
 664               <p>
 665                 0.63661977
 666               </p>
 667             </td>
 668 <td>
 669               <p>
 670                 Equivalent to POSIX constant M_2_PI
 671               </p>
 672             </td>
 673 </tr>
 674 <tr>
 675 <td>
 676               <p>
 677                 one_div_root_pi
 678               </p>
 679             </td>
 680 <td>
 681               <p>
 682                 1/&#8730;&#960;
 683               </p>
 684             </td>
 685 <td>
 686               <p>
 687                 0.564189
 688               </p>
 689             </td>
 690 <td>
 691             </td>
 692 </tr>
 693 <tr>
 694 <td>
 695               <p>
 696                 two_div_root_pi
 697               </p>
 698             </td>
 699 <td>
 700               <p>
 701                 2/&#8730;&#960;
 702               </p>
 703             </td>
 704 <td>
 705               <p>
 706                 1.128379
 707               </p>
 708             </td>
 709 <td>
 710               <p>
 711                 Equivalent to POSIX constant M_2_SQRTPI
 712               </p>
 713             </td>
 714 </tr>
 715 <tr>
 716 <td>
 717               <p>
 718                 one_div_root_two_pi
 719               </p>
 720             </td>
 721 <td>
 722               <p>
 723                 1/&#8730;(2&#960;)
 724               </p>
 725             </td>
 726 <td>
 727               <p>
 728                 0.398942
 729               </p>
 730             </td>
 731 <td>
 732             </td>
 733 </tr>
 734 <tr>
 735 <td>
 736               <p>
 737                 root_one_div_pi
 738               </p>
 739             </td>
 740 <td>
 741               <p>
 742                 &#8730;(1/&#960;
 743               </p>
 744             </td>
 745 <td>
 746               <p>
 747                 0.564189
 748               </p>
 749             </td>
 750 <td>
 751             </td>
 752 </tr>
 753 <tr>
 754 <td>
 755               <p>
 756                 pi_minus_three
 757               </p>
 758             </td>
 759 <td>
 760               <p>
 761                 &#960;-3
 762               </p>
 763             </td>
 764 <td>
 765               <p>
 766                 0.141593
 767               </p>
 768             </td>
 769 <td>
 770             </td>
 771 </tr>
 772 <tr>
 773 <td>
 774               <p>
 775                 four_minus_pi
 776               </p>
 777             </td>
 778 <td>
 779               <p>
 780                 4 -&#960;
 781               </p>
 782             </td>
 783 <td>
 784               <p>
 785                 0.858407
 786               </p>
 787             </td>
 788 <td>
 789             </td>
 790 </tr>
 791 <tr>
 792 <td>
 793               <p>
 794                 pi_pow_e
 795               </p>
 796             </td>
 797 <td>
 798               <p>
 799                 &#960;<sup>e</sup>
 800               </p>
 801             </td>
 802 <td>
 803               <p>
 804                 22.4591
 805               </p>
 806             </td>
 807 <td>
 808             </td>
 809 </tr>
 810 <tr>
 811 <td>
 812               <p>
 813                 pi_sqr
 814               </p>
 815             </td>
 816 <td>
 817               <p>
 818                 &#960;<sup>2</sup>
 819               </p>
 820             </td>
 821 <td>
 822               <p>
 823                 9.86960
 824               </p>
 825             </td>
 826 <td>
 827             </td>
 828 </tr>
 829 <tr>
 830 <td>
 831               <p>
 832                 pi_sqr_div_six
 833               </p>
 834             </td>
 835 <td>
 836               <p>
 837                 &#960;<sup>2</sup>/6
 838               </p>
 839             </td>
 840 <td>
 841               <p>
 842                 1.64493
 843               </p>
 844             </td>
 845 <td>
 846             </td>
 847 </tr>
 848 <tr>
 849 <td>
 850               <p>
 851                 pi_cubed
 852               </p>
 853             </td>
 854 <td>
 855               <p>
 856                 &#960;<sup>3</sup>
 857               </p>
 858             </td>
 859 <td>
 860               <p>
 861                 31.00627
 862               </p>
 863             </td>
 864 <td>
 865             </td>
 866 </tr>
 867 <tr>
 868 <td>
 869               <p>
 870                 cbrt_pi
 871               </p>
 872             </td>
 873 <td>
 874               <p>
 875                 &#8730;<sup>3</sup> &#960;
 876               </p>
 877             </td>
 878 <td>
 879               <p>
 880                 1.46459
 881               </p>
 882             </td>
 883 <td>
 884             </td>
 885 </tr>
 886 <tr>
 887 <td>
 888               <p>
 889                 one_div_cbrt_pi
 890               </p>
 891             </td>
 892 <td>
 893               <p>
 894                 1/&#8730;<sup>3</sup> &#960;
 895               </p>
 896             </td>
 897 <td>
 898               <p>
 899                 0.682784
 900               </p>
 901             </td>
 902 <td>
 903             </td>
 904 </tr>
 905 <tr>
 906 <td>
 907               <p>
 908                 <span class="bold"><strong>Euler's e and related</strong></span>
 909               </p>
 910             </td>
 911 <td>
 912             </td>
 913 <td>
 914             </td>
 915 <td>
 916             </td>
 917 </tr>
 918 <tr>
 919 <td>
 920               <p>
 921                 e
 922               </p>
 923             </td>
 924 <td>
 925               <p>
 926                 e
 927               </p>
 928             </td>
 929 <td>
 930               <p>
 931                 2.71828
 932               </p>
 933             </td>
 934 <td>
 935               <p>
 936                 <a href="http://en.wikipedia.org/wiki/E_(mathematical_constant)" target="_top">Euler's
 937                 constant e</a>, equivalent to POSIX constant M_E
 938               </p>
 939             </td>
 940 </tr>
 941 <tr>
 942 <td>
 943               <p>
 944                 exp_minus_half
 945               </p>
 946             </td>
 947 <td>
 948               <p>
 949                 e <sup>-1/2</sup>
 950               </p>
 951             </td>
 952 <td>
 953               <p>
 954                 0.606530
 955               </p>
 956             </td>
 957 <td>
 958             </td>
 959 </tr>
 960 <tr>
 961 <td>
 962               <p>
 963                 e_pow_pi
 964               </p>
 965             </td>
 966 <td>
 967               <p>
 968                 e <sup>&#960;</sup>
 969               </p>
 970             </td>
 971 <td>
 972               <p>
 973                 23.14069
 974               </p>
 975             </td>
 976 <td>
 977             </td>
 978 </tr>
 979 <tr>
 980 <td>
 981               <p>
 982                 root_e
 983               </p>
 984             </td>
 985 <td>
 986               <p>
 987                 &#8730; e
 988               </p>
 989             </td>
 990 <td>
 991               <p>
 992                 1.64872
 993               </p>
 994             </td>
 995 <td>
 996             </td>
 997 </tr>
 998 <tr>
 999 <td>
1000               <p>
1001                 log10_e
1002               </p>
1003             </td>
1004 <td>
1005               <p>
1006                 log10(e)
1007               </p>
1008             </td>
1009 <td>
1010               <p>
1011                 0.434294
1012               </p>
1013             </td>
1014 <td>
1015               <p>
1016                 Equivalent to POSIX constant M_LOG10E
1017               </p>
1018             </td>
1019 </tr>
1020 <tr>
1021 <td>
1022               <p>
1023                 one_div_log10_e
1024               </p>
1025             </td>
1026 <td>
1027               <p>
1028                 1/log10(e)
1029               </p>
1030             </td>
1031 <td>
1032               <p>
1033                 2.30258
1034               </p>
1035             </td>
1036 <td>
1037             </td>
1038 </tr>
1039 <tr>
1040 <td>
1041               <p>
1042                 log2_e
1043               </p>
1044             </td>
1045 <td>
1046               <p>
1047                 log<sub>2</sub>(e)
1048               </p>
1049             </td>
1050 <td>
1051               <p>
1052                 1.442695
1053               </p>
1054             </td>
1055 <td>
1056               <p>
1057                 This is the same as 1/ln(2) and is equivalent to POSIX constant M_LOG2E
1058               </p>
1059             </td>
1060 </tr>
1061 <tr>
1062 <td>
1063               <p>
1064                 <span class="bold"><strong>Trigonometric</strong></span>
1065               </p>
1066             </td>
1067 <td>
1068             </td>
1069 <td>
1070             </td>
1071 <td>
1072             </td>
1073 </tr>
1074 <tr>
1075 <td>
1076               <p>
1077                 degree
1078               </p>
1079             </td>
1080 <td>
1081               <p>
1082                 radians = &#960; / 180
1083               </p>
1084             </td>
1085 <td>
1086               <p>
1087                 0.017453
1088               </p>
1089             </td>
1090 <td>
1091             </td>
1092 </tr>
1093 <tr>
1094 <td>
1095               <p>
1096                 radian
1097               </p>
1098             </td>
1099 <td>
1100               <p>
1101                 degrees = 180 / &#960;
1102               </p>
1103             </td>
1104 <td>
1105               <p>
1106                 57.2957
1107               </p>
1108             </td>
1109 <td>
1110             </td>
1111 </tr>
1112 <tr>
1113 <td>
1114               <p>
1115                 sin_one
1116               </p>
1117             </td>
1118 <td>
1119               <p>
1120                 sin(1)
1121               </p>
1122             </td>
1123 <td>
1124               <p>
1125                 0.841470
1126               </p>
1127             </td>
1128 <td>
1129             </td>
1130 </tr>
1131 <tr>
1132 <td>
1133               <p>
1134                 cos_one
1135               </p>
1136             </td>
1137 <td>
1138               <p>
1139                 cos(1)
1140               </p>
1141             </td>
1142 <td>
1143               <p>
1144                 0.54030
1145               </p>
1146             </td>
1147 <td>
1148             </td>
1149 </tr>
1150 <tr>
1151 <td>
1152               <p>
1153                 sinh_one
1154               </p>
1155             </td>
1156 <td>
1157               <p>
1158                 sinh(1)
1159               </p>
1160             </td>
1161 <td>
1162               <p>
1163                 1.17520
1164               </p>
1165             </td>
1166 <td>
1167             </td>
1168 </tr>
1169 <tr>
1170 <td>
1171               <p>
1172                 cosh_one
1173               </p>
1174             </td>
1175 <td>
1176               <p>
1177                 cosh(1)
1178               </p>
1179             </td>
1180 <td>
1181               <p>
1182                 1.54308
1183               </p>
1184             </td>
1185 <td>
1186             </td>
1187 </tr>
1188 <tr>
1189 <td>
1190               <p>
1191                 <span class="bold"><strong>Phi</strong></span>
1192               </p>
1193             </td>
1194 <td>
1195               <p>
1196                 Phidias golden ratio
1197               </p>
1198             </td>
1199 <td>
1200               <p>
1201                 <a href="http://en.wikipedia.org/wiki/Golden_ratio" target="_top">Phidias golden
1202                 ratio</a>
1203               </p>
1204             </td>
1205 <td>
1206             </td>
1207 </tr>
1208 <tr>
1209 <td>
1210               <p>
1211                 phi
1212               </p>
1213             </td>
1214 <td>
1215               <p>
1216                 (1 + &#8730;5) /2
1217               </p>
1218             </td>
1219 <td>
1220               <p>
1221                 1.61803
1222               </p>
1223             </td>
1224 <td>
1225               <p>
1226                 finance
1227               </p>
1228             </td>
1229 </tr>
1230 <tr>
1231 <td>
1232               <p>
1233                 ln_phi
1234               </p>
1235             </td>
1236 <td>
1237               <p>
1238                 ln(&#966;)
1239               </p>
1240             </td>
1241 <td>
1242               <p>
1243                 0.48121
1244               </p>
1245             </td>
1246 <td>
1247             </td>
1248 </tr>
1249 <tr>
1250 <td>
1251               <p>
1252                 one_div_ln_phi
1253               </p>
1254             </td>
1255 <td>
1256               <p>
1257                 1/ln(&#966;)
1258               </p>
1259             </td>
1260 <td>
1261               <p>
1262                 2.07808
1263               </p>
1264             </td>
1265 <td>
1266             </td>
1267 </tr>
1268 <tr>
1269 <td>
1270               <p>
1271                 <span class="bold"><strong>Euler's Gamma</strong></span>
1272               </p>
1273             </td>
1274 <td>
1275             </td>
1276 <td>
1277             </td>
1278 <td>
1279             </td>
1280 </tr>
1281 <tr>
1282 <td>
1283               <p>
1284                 euler
1285               </p>
1286             </td>
1287 <td>
1288               <p>
1289                 euler
1290               </p>
1291             </td>
1292 <td>
1293               <p>
1294                 0.577215
1295               </p>
1296             </td>
1297 <td>
1298               <p>
1299                 <a href="http://en.wikipedia.org/wiki/Euler%E2%80%93Mascheroni_constant" target="_top">Euler-Mascheroni
1300                 gamma constant</a>
1301               </p>
1302             </td>
1303 </tr>
1304 <tr>
1305 <td>
1306               <p>
1307                 one_div_euler
1308               </p>
1309             </td>
1310 <td>
1311               <p>
1312                 1/euler
1313               </p>
1314             </td>
1315 <td>
1316               <p>
1317                 1.73245
1318               </p>
1319             </td>
1320 <td>
1321             </td>
1322 </tr>
1323 <tr>
1324 <td>
1325               <p>
1326                 euler_sqr
1327               </p>
1328             </td>
1329 <td>
1330               <p>
1331                 euler<sup>2</sup>
1332               </p>
1333             </td>
1334 <td>
1335               <p>
1336                 0.333177
1337               </p>
1338             </td>
1339 <td>
1340             </td>
1341 </tr>
1342 <tr>
1343 <td>
1344               <p>
1345                 <span class="bold"><strong>Misc</strong></span>
1346               </p>
1347             </td>
1348 <td>
1349             </td>
1350 <td>
1351             </td>
1352 <td>
1353             </td>
1354 </tr>
1355 <tr>
1356 <td>
1357               <p>
1358                 zeta_two
1359               </p>
1360             </td>
1361 <td>
1362               <p>
1363                 &#950;(2)
1364               </p>
1365             </td>
1366 <td>
1367               <p>
1368                 1.64493
1369               </p>
1370             </td>
1371 <td>
1372               <p>
1373                 <a href="http://en.wikipedia.org/wiki/Riemann_zeta_function" target="_top">Riemann
1374                 zeta function</a>
1375               </p>
1376             </td>
1377 </tr>
1378 <tr>
1379 <td>
1380               <p>
1381                 zeta_three
1382               </p>
1383             </td>
1384 <td>
1385               <p>
1386                 &#950;(3)
1387               </p>
1388             </td>
1389 <td>
1390               <p>
1391                 1.20205
1392               </p>
1393             </td>
1394 <td>
1395               <p>
1396                 <a href="http://en.wikipedia.org/wiki/Riemann_zeta_function" target="_top">Riemann
1397                 zeta function</a>
1398               </p>
1399             </td>
1400 </tr>
1401 <tr>
1402 <td>
1403               <p>
1404                 catalan
1405               </p>
1406             </td>
1407 <td>
1408               <p>
1409                 <span class="emphasis"><em>K</em></span>
1410               </p>
1411             </td>
1412 <td>
1413               <p>
1414                 0.915965
1415               </p>
1416             </td>
1417 <td>
1418               <p>
1419                 <a href="http://mathworld.wolfram.com/CatalansConstant.html" target="_top">Catalan
1420                 (or Glaisher) combinatorial constant</a>
1421               </p>
1422             </td>
1423 </tr>
1424 <tr>
1425 <td>
1426               <p>
1427                 glaisher
1428               </p>
1429             </td>
1430 <td>
1431               <p>
1432                 <span class="emphasis"><em>A</em></span>
1433               </p>
1434             </td>
1435 <td>
1436               <p>
1437                 1.28242
1438               </p>
1439             </td>
1440 <td>
1441               <p>
1442                 <a href="https://oeis.org/A074962/constant" target="_top">Decimal expansion
1443                 of Glaisher-Kinkelin constant</a>
1444               </p>
1445             </td>
1446 </tr>
1447 <tr>
1448 <td>
1449               <p>
1450                 khinchin
1451               </p>
1452             </td>
1453 <td>
1454               <p>
1455                 <span class="emphasis"><em>k</em></span>
1456               </p>
1457             </td>
1458 <td>
1459               <p>
1460                 2.685452
1461               </p>
1462             </td>
1463 <td>
1464               <p>
1465                 <a href="https://oeis.org/A002210/constant" target="_top">Decimal expansion
1466                 of Khinchin constant</a>
1467               </p>
1468             </td>
1469 </tr>
1470 <tr>
1471 <td>
1472               <p>
1473                 extreme_value_skewness
1474               </p>
1475             </td>
1476 <td>
1477               <p>
1478                 12&#8730;6 &#950;(3)/ &#960;<sup>3</sup>
1479               </p>
1480             </td>
1481 <td>
1482               <p>
1483                 1.139547
1484               </p>
1485             </td>
1486 <td>
1487               <p>
1488                 Extreme value distribution
1489               </p>
1490             </td>
1491 </tr>
1492 <tr>
1493 <td>
1494               <p>
1495                 rayleigh_skewness
1496               </p>
1497             </td>
1498 <td>
1499               <p>
1500                 2&#8730;&#960;(&#960;-3)/(4 - &#960;)<sup>3/2</sup>
1501               </p>
1502             </td>
1503 <td>
1504               <p>
1505                 0.631110
1506               </p>
1507             </td>
1508 <td>
1509               <p>
1510                 Rayleigh distribution skewness
1511               </p>
1512             </td>
1513 </tr>
1514 <tr>
1515 <td>
1516               <p>
1517                 rayleigh_kurtosis_excess
1518               </p>
1519             </td>
1520 <td>
1521               <p>
1522                 -(6&#960;<sup>2</sup>-24&#960;+16)/(4-&#960;)<sup>2</sup>
1523               </p>
1524             </td>
1525 <td>
1526               <p>
1527                 0.245089
1528               </p>
1529             </td>
1530 <td>
1531               <p>
1532                 <a href="http://en.wikipedia.org/wiki/Rayleigh_distribution" target="_top">Rayleigh
1533                 distribution kurtosis excess</a>
1534               </p>
1535             </td>
1536 </tr>
1537 <tr>
1538 <td>
1539               <p>
1540                 rayleigh_kurtosis
1541               </p>
1542             </td>
1543 <td>
1544               <p>
1545                 3+(6&#960;<sup>2</sup>-24&#960;+16)/(4-&#960;)<sup>2</sup>
1546               </p>
1547             </td>
1548 <td>
1549               <p>
1550                 3.245089
1551               </p>
1552             </td>
1553 <td>
1554               <p>
1555                 Rayleigh distribution kurtosis
1556               </p>
1557             </td>
1558 </tr>
1559 </tbody>
1560 </table></div>
1561 </div>
1562 <br class="table-break"><div class="note"><table border="0" summary="Note">
1563 <tr>
1564 <td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../doc/src/images/note.png"></td>
1565 <th align="left">Note</th>
1566 </tr>
1567 <tr><td align="left" valign="top"><p>
1568         Integer values are <span class="bold"><strong>not included</strong></span> in this
1569         list of math constants, however interesting, because they can be so easily
1570         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>.
1571       </p></td></tr>
1572 </table></div>
1573 <div class="tip"><table border="0" summary="Tip">
1574 <tr>
1575 <td rowspan="2" align="center" valign="top" width="25"><img alt="[Tip]" src="../../../../../doc/src/images/tip.png"></td>
1576 <th align="left">Tip</th>
1577 </tr>
1578 <tr><td align="left" valign="top"><p>
1579         If you know the approximate value of the constant, you can search for the
1580         value to find Boost.Math chosen name in this table.
1581       </p></td></tr>
1582 </table></div>
1583 <div class="tip"><table border="0" summary="Tip">
1584 <tr>
1585 <td rowspan="2" align="center" valign="top" width="25"><img alt="[Tip]" src="../../../../../doc/src/images/tip.png"></td>
1586 <th align="left">Tip</th>
1587 </tr>
1588 <tr><td align="left" valign="top"><p>
1589         Bernoulli numbers are available at <a class="link" href="number_series/bernoulli_numbers.html" title="Bernoulli Numbers">Bernoulli
1590         numbers</a>.
1591       </p></td></tr>
1592 </table></div>
1593 <div class="tip"><table border="0" summary="Tip">
1594 <tr>
1595 <td rowspan="2" align="center" valign="top" width="25"><img alt="[Tip]" src="../../../../../doc/src/images/tip.png"></td>
1596 <th align="left">Tip</th>
1597 </tr>
1598 <tr><td align="left" valign="top"><p>
1599         Factorials are available at <a class="link" href="factorials/sf_factorial.html" title="Factorial">factorial</a>.
1600       </p></td></tr>
1601 </table></div>
1602 </div>
1603 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
1604 <td align="left"></td>
1605 <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
1606       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
1607       Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
1608       R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
1609       Daryle Walker and Xiaogang Zhang<p>
1610         Distributed under the Boost Software License, Version 1.0. (See accompanying
1611         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>)
1612       </p>
1613 </div></td>
1614 </tr></table>
1615 <hr>
1616 <div class="spirit-nav">
1617 <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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