Eikonal Blog

2010.03.09

Transcendental numbers: Euler’s constant (= Euler-Mascheroni constant) gamma

Filed under: mathematics — Tags: , , — sandokan65 @ 14:25

Source: http://www.wolframalpha.com/

Euler’s constant (= Euler-Mascheroni constant):
$\gamma =$ $0.577, 215, 664, 901, 532, 860, 606, 512, 090, 082, 402, 431, 042, 159, 335, 939, 923, 598, 805, 767, 234, 884, 867, 726, 777, 664, 670, 936, 947, 063, 291, 746, 749, 514, 631, 447, 249, 807, 082, 480, 960, 504, 014, 486, 542, 836, 224, 173, 997, 644, 923, 536, 253, 500, 333, 742, 937, 337, 737, 673, 942, 792, 595, 258, 247, 094, 916, 008, 735, 203, 948, 165, 670, 853, 233, 151, 776, 611, 528, 621, 199, 501, 507, 984, 793, 745, 085, 705, 740, 029, 921, 354, 786, 146, 694, 029, 604, 325, 421, 519, 058, 775, 535, 267, 331, 399, 254, 012, 967, 420, 513, 754, 139, 549, 111, 685, 102, 807, 984, 234, 877, 587, 205, 038, 431, 093, 997, 361, 372, 553, 060, 889, 331, 267, 600, 172, 479, 537, 836, 759, 271, 351, 577, 226, 102, 734, 929, 139, 407, 984, 301, 034, 177, 717, 780, 881, 549, 570, 661, 075, 010, 161, 916, 633, 401, 522, 789, 358, 679, 654, 972, 520, 362, 128, 792, 265, 559, 536, 696, 281, 763, 887, 927, 268, 013, 243, 101, 047, 650, 596, 370, 394, 739, 495, 763, 890, 657, 296, 792, 960, 100, 901, 512, 519, 595, 092, 224, 350, 140, 934, 987, 122, 824, 794, 974, 719, 564, 697, 631, 850, 667, 612, 906, 381, 105, 182, 419, 744, 486, 783, 638, 086, 174, 945, 516, 989, 279, 230, 187, 739, 107, 294, 578, 155, 431, 600, 500, 218, 284, 409, 605, 377, 243, 420, 328, 547, 836, 701, 517, 739, 439, 870, 030, 237, 033, 951, 832, 869, 000, 155, 819, 398, 804, 270, 741, 154, 222, 781, 971, 652, 301, 107, 356, 583, 396, 734, 871, 765, 049, 194, 181, 230, 004, 065, 469, 314, 299, 929, 777, 956, 930, 310, 050, 308, 630, 341, 856, 980, 323, 108, 369, 164, 002, 589, 297, 089, 098, 548, 682, 577, 736, 428, 825, 395, 492, 587, 362, 959, 613, 329, 857, 473, 930, 237, 343, 884, 707, 037, 028, 441, 292, 016, 641, 785, 024, 873, 337, 908, 056, 275, 499, 843, 459, 076, 164, 316, 710, 314, 671, 072, 237, 002, 181, 074, 504, 441, 866, 475, 913, 480, 366, 902, 553, 245, 862, 544, 222, 534, 518, 138, 791, 243, 457, 350, 136, 129, 778, 227, 828, 814, 894, 590, 986, 384, 600, 629, 316, 947, 188, 714, 958, 752, 549, 236, 649, 352, 047, 324, 364, 109, 726, 827, 616, 087, 759, 508, 809, 512, 620, 840, 454, 447, 799, 229, 915, 724, 829, 251, 625, 127, 842, 765, 965, 708, 321, 461, 029, 821, 461, 795, 195, 795, 909, 592, 270, 420, 898, 962, 797, 125, 536, 321, 794, 887, 376, 421, 066, 060, 706, 598, 256, 199, 010, 288, 075, 612, 519, 913, 751, 167, 821, 764, 361, 905, 705, 844, 078, 357, 350, 158, 005, 607, 745, 793, 421, 314, 498, 850, 078, 641, 517, 161, 519, 456, 570, 617, 043, 245, 075, 008, 168, 705, 230, 789, 093, 704, 614, 306, 684, 817, 916, 496, 842, 549, 150, 496, 724, 312, 183, 783, 875, 356, 489, 495, 086, 845, 410, 234, 060, 162, 250, 851, 558, 386, 723, 494, 418, 788, 044, 094, 077, 010, 688, 379, 511, 130, 787, 202, 342, 639, 522, 692, 097, 160, 885, 690, 838, 251, 137, 871, 283, 682, 049, 117, 892, 594, 478, 486, 199, 118, 529, 391, 029, 309, 905, 925, 526, 691, 727, 446, 892, 044, 386, 971, 114, 717, 457, 157, 457, 320, 393, 520, 912, 231, 608, 508, 682, 755, 889, 010, 945, 168, 118, 101, 687, 497, 547, 096, 936, 667, 121, 020, 630, 482, 716, 589, 504, 932, 731, 486, 087, 494, 020, 700, 674, 259, 091, 824, 875, 962, 137, 384, 231, 144, 265, 313, 502, 923, 031, 751, 722, 572, 216, 283, 248, 838, 112, 458, 957, 438, 623, 987, 037, 576, 628, 551, 303, 314, 392, 999, 540, 185, 313, 414, 158, 621, 278, 864, 807, 611, 003, 015, 211, 965, 780, 068, 117, 773, 763, 501, 681, 838, 973, 389, 663, 986, 895, 793, 299, 145, 638, 864, 431, 037, 060, 807, 817, 448, 995, 795, 832, 457, 941, 896, 202, 604, 984, 104, 392, 250, 786, 046, 036, 252, 772, 602, 291, 968, 299, 586, 098, 833, 901, 378, 717, 142, 269, 178, 838, 195, 298, 445, 607, 916, 051, 972, 797, 360, 475, 910, 251, 099, 577, 913, 351, 579, 177, 225, 150, 254, 929, 324, 632, 502, 874, 767, 794, 842, 158, 405, 075, 992, 904, 018, 557, 645, 990, 186, 269, 267, 764, 372, 660, 571, 176, 813, 365, 590, 881, 554, 810, 747, 000, 062, 336, 372, 528, 894, 955, 463, 697, 143, 301, 200, 791, 308, 555, 263, 959, 549, 782, 302, 314, 403, 914, 974, 049, 474, 682, 594, 732, 084, 618, 524, 605, 877, 669, 488, 287, 953, 010, 406, 349, 172, 292, 185, 800, 870, 677, 069, 042, 792, 674, 328, 444, 696, 851, 497, 182, 567, 809, 584, 165, 449, 185, 145, 753, 319, 640, 633, 119, 937, 382, 157, 345, 087, 498, 832, 556, 088, 887, 352, 801, 901, 915, 508, 968, 855, 468, 259, 245, 444, 527, 728, 173, 057, 301, 080, 606, 177, 011, 363, 773, 182, 462, 924, 660, 081, 277, 162, 101, 867, 744, 684, 959, 514, 281, 790, 145, 111, 948, 934, 228, 834, 482, 530, 753, 118, 701, 860, 976, 122, 462, 317, 674, 977, 556, 412, 461, 983, 856, 401, 484, 123, 587, 177, 249, 554, 224, 820, 161, 517, 657, 994, 080, 629, 683, 424, 289, 057, 259, 473, 926, 963, 863, 383, 874, 380, 547, 131, 967, 642, 926, 837, 249, 076, 087, 507, 378, 528, 370, 230, 468, 650, 349, 051, 203, 422, 721, 743, 668, 979, 284, 862, 972, 908, 892, 678, 977, 703, 262, 462, 391, 226, 188, 876, 530, 057, 786, 274, 360, 609, 444, 360, 392, 809, 770, 813, 383, 693, 423, 550, 858, 394, 112, 670, 921, 873, 441, 451, 218, 780, 327, 615, 050, 947, 805, 546, 630, 058, 684, 556, 315, 245, 460, 531, 511, 325, 281, 889, 107, 923, 149, 131, 103, 234, 430, 245, 093, 345, 000, 307, 655, 864, 874, 222, 971, 770, 033, 178, 453, 915, 056, 694, 015, 998, 849, 291, 609, 114, 002, 948, 690, 208, 848, 538, 169, 700, 955, 156, 634, 705, 544, 522, 176, 403, 586, 293, 982, 865, 813, 123, 870, 132, 535, 880, 062, 568, 662, 692, 699, 776, 773, 773, 068, 322, 690, 091, 608, 510, 451, 500, 226, 107, 180, 255, 465, 928, 493, 894, 927, 759, 589, 754, 076, 155, 993, 378, 264, 824, 197, 950, 641, 868, 143, 788, 171, 850, 885, 408, 036, 799, 631, 423, 954, 009, 196, 438, 875, 007, 890, 000, 062, 799, 794, 280, 988, 637, 299, 259, 197, 776, 504, 040, 992, 203, 794, 042, 761, 681, 783, 715, 668, 653, 066, 939, 830, 916, 524, 322, 705, 955, 304, 176, 673, 664, 011, 679, 295, 901, 293, 053, 744, 971, 830, 800, 427, 584, 863, 508, 380, 804, 246, 673, 509, 355, 983, 232, 411, 696, 921, 486, 064, 989, 276, 362, 443, 295, 885, 487, 378, 970, 148, 971, 334, 353, 844, 800, 289, 046, 665, 090, 284, 537, 689, 622, 398, 304, 881, 406, 273, 054, 087, 959, 118, 967, 05...$

For definition and some properties see the separate posting https://eikonal.wordpress.com/2010/01/04/euler-mascheroni-constant/.