1<html> 2<head> 3<meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> 4<title>The Mathematical Constants</title> 5<link rel="stylesheet" href="../math.css" type="text/css"> 6<meta name="generator" content="DocBook XSL Stylesheets V1.79.1"> 7<link rel="home" href="../index.html" title="Math Toolkit 2.12.0"> 8<link rel="up" href="../constants.html" title="Chapter 4. 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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 √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 √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 √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 √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/√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>π 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">π</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 π/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 π/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 π/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 π/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 2π 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 π 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 π r³ 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 π 506 </p> 507 </td> 508<td> 509 <p> 510 2.35619 511 </p> 512 </td> 513<td> 514 <p> 515 = 3/4 π 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 π 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 π r³ 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/(2π) 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 √π 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 √ π/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 √ π*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/π 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/π 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/√π 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/√π 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/√(2π) 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 √(1/π 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 π-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 -π 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 π<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 π<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 π<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 π<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 √<sup>3</sup> π 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/√<sup>3</sup> π 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>π</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 √ 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 = π / 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 / π 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 + √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(φ) 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(φ) 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 ζ(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 ζ(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√6 ζ(3)/ π<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√π(π-3)/(4 - π)<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 -(6π<sup>2</sup>-24π+16)/(4-π)<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+(6π<sup>2</sup>-24π+16)/(4-π)<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"><</span><span class="identifier">cpp_float</span><span class="special">>(</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 © 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 Råde, 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> 1618</div> 1619</body> 1620</html> 1621
