The acceleration formula for Zeta(, 7, ) is Charpoly depends on, x The acceleration rate is too hard to compute, so the usefulness of the acceleration formula is not rigorously established 4 3 2 3 1 (3 x + 5) (87 x + 558 x + 1348 x + 1454 x + 591) (x + 1) [--------, [[------------------------------------------------------------, - ( 7 7 (1 + z) 128 (7 x + 6) (2 x + 3) 7 6 5 4 3 2 1778 x + 16800 x + 67131 x + 146689 x + 188740 x + 142510 x + 58269 x 3 / 7 9 + 9933) (x + 1) / (64 (7 x + 6) (7 x + 5) (2 x + 3) ), (18669 x / 8 7 6 5 4 + 198275 x + 918741 x + 2433081 x + 4050404 x + 4387224 x 3 2 3 / + 3086837 x + 1358706 x + 339185 x + 36564) (x + 1) / (64 (7 x + 6) / 7 10 9 8 (7 x + 5) (7 x + 4) (2 x + 3) ), - (130683 x + 1375822 x + 6346291 x 7 6 5 4 3 + 16843903 x + 28404665 x + 31706372 x + 23653716 x + 11608898 x 2 4 / + 3574418 x + 620722 x + 45888) (x + 1) / (64 (7 x + 6) (7 x + 5) / 7 10 (7 x + 4) (7 x + 3) (2 x + 3) ), - (150432 + 2371408 x + 41781782 x 12 11 9 8 2 + 646212 x + 7746998 x + 133972979 x + 284276940 x + 16519903 x 3 4 5 6 7 + 67524856 x + 180946811 x + 335750524 x + 443255078 x + 420210337 x ) 3 / (x + 1) / (64 (7 x + 2) (7 x + 3) (7 x + 4) (7 x + 5) (7 x + 6) / 7 10 12 (2 x + 3) ), (3405384 + 82787382 x + 88020580991 x + 10158776432 x 13 11 9 8 + 1694304066 x + 36545408144 x + 149972633996 x + 186179723778 x 2 3 4 5 + 868231143 x + 5279170568 x + 20990968670 x + 58128300629 x 6 7 14 4 / + 116171268990 x + 170818429351 x + 128069340 x ) (x + 1) / (448 / 7 (7 x + 1) (7 x + 2) (7 x + 3) (7 x + 4) (7 x + 5) (7 x + 6) (2 x + 3) )], [ 4 3 2 3 (201 x + 1308 x + 3201 x + 3492 x + 1433) (x + 1) -----------------------------------------------------, - ( 7 32 (7 x + 6) (2 x + 3) 6 5 4 3 2 10521 x + 82803 x + 266256 x + 445902 x + 408243 x + 192845 x + 36670) 3 / 7 8 7 (x + 1) / (128 (7 x + 6) (7 x + 5) (2 x + 3) ), (104762 x + 945994 x / 6 5 4 3 2 + 3647091 x + 7821541 x + 10182824 x + 8226698 x + 4023823 x 3 / + 1088917 x + 124790) (x + 1) / (128 (7 x + 6) (7 x + 5) (7 x + 4) / 7 9 8 7 6 (2 x + 3) ), - (646212 x + 5728982 x + 21778624 x + 46409811 x 5 4 3 2 + 60840115 x + 50652308 x + 26638470 x + 8469721 x + 1459571 x 4 / + 101610) (x + 1) / (128 (7 x + 6) (7 x + 5) (7 x + 4) (7 x + 3) / 7 10 12 (2 x + 3) ), - 7 (107940 + 1681440 x + 20895574 x + 261366 x 11 9 8 2 3 + 3524472 x + 72338916 x + 163360771 x + 11539823 x + 46303958 x 4 5 6 7 3 / + 121291089 x + 218885772 x + 279326157 x + 254048082 x ) (x + 1) / / 7 (128 (7 x + 2) (7 x + 3) (7 x + 4) (7 x + 5) (7 x + 6) (2 x + 3) ), ( 10 12 13 2021700 + 48053248 x + 23771729562 x + 1475217618 x + 127060920 x 11 9 8 2 + 7686376180 x + 48641857628 x + 69473537945 x + 489229535 x 3 4 5 6 + 2864833054 x + 10869671221 x + 28408669108 x + 52869000547 x 7 4 / + 71173571430 x ) (x + 1) / (128 (7 x + 1) (7 x + 2) (7 x + 3) / 7 (7 x + 4) (7 x + 5) (7 x + 6) (2 x + 3) )], [ 2 3 7 (3 x + 5) (12 x + 39 x + 32) (x + 1) ----------------------------------------, 7 32 (7 x + 6) (2 x + 3) 5 4 3 2 3 (3150 x + 19773 x + 48138 x + 56415 x + 31618 x + 6788) (x + 1) - --------------------------------------------------------------------, ( 7 32 (7 x + 6) (7 x + 5) (2 x + 3) 7 6 5 4 3 2 117747 x + 874440 x + 2692473 x + 4443738 x + 4239073 x + 2337232 x 3 / + 690003 x + 84166) (x + 1) / (128 (7 x + 6) (7 x + 5) (7 x + 4) / 7 8 7 6 5 (2 x + 3) ), - (606424 x + 4336010 x + 12879405 x + 20611535 x 4 3 2 4 / + 19267276 x + 10629156 x + 3292769 x + 492055 x + 21762) (x + 1) / / 7 11 (128 (7 x + 6) (7 x + 5) (7 x + 4) (7 x + 3) (2 x + 3) ), - (2261742 x 10 9 8 7 6 + 24392788 x + 115903718 x + 320672576 x + 574692153 x + 701104054 x 5 4 3 2 + 594272021 x + 349819326 x + 139982617 x + 36196122 x + 5428449 x 3 / + 356394) (x + 1) / (64 (7 x + 2) (7 x + 3) (7 x + 4) (7 x + 5) / 7 10 (7 x + 6) (2 x + 3) ), (1661748 + 38590736 x + 7728940422 x 12 11 9 8 + 174759186 x + 1744701056 x + 20080204704 x + 34065050411 x 2 3 4 5 + 380924063 x + 2143681516 x + 7735231007 x + 18982019512 x 6 7 4 / + 32635050027 x + 39732446220 x ) (x + 1) / (128 (7 x + 1) (7 x + 2) / 7 (7 x + 3) (7 x + 4) (7 x + 5) (7 x + 6) (2 x + 3) )], [ 2 3 7 (23 x + 76 x + 63) (x + 1) ------------------------------, 7 32 (7 x + 6) (2 x + 3) 4 3 2 3 7 (273 x + 1274 x + 2114 x + 1463 x + 360) (x + 1) - ------------------------------------------------------, ( 7 32 (7 x + 6) (7 x + 5) (2 x + 3) 6 5 4 3 2 33075 x + 192115 x + 444114 x + 522686 x + 331255 x + 107453 x + 13950 3 / 7 7 ) (x + 1) / (64 (7 x + 6) (7 x + 5) (7 x + 4) (2 x + 3) ), - (256221 x / 6 5 4 3 2 + 1363719 x + 2842266 x + 2926490 x + 1507505 x + 302579 x - 25224 x 4 / - 13140) (x + 1) / (128 (7 x + 6) (7 x + 5) (7 x + 4) (7 x + 3) / 7 10 9 8 7 (2 x + 3) ), - (2122484 x + 18653712 x + 71516725 x + 157873884 x 6 5 4 3 2 + 222639445 x + 209760558 x + 133686939 x + 56849594 x + 15407307 x 3 / + 2396412 x + 161820) (x + 1) / (64 (7 x + 6) (7 x + 5) (7 x + 4) / 7 11 10 (7 x + 3) (7 x + 2) (2 x + 3) ), (59799306 x + 499086266 x 9 8 7 6 + 1826157382 x + 3870789741 x + 5284636336 x + 4877883445 x 5 4 3 2 + 3101260280 x + 1354057577 x + 396024776 x + 73386727 x + 7677696 x 4 / + 338580) (x + 1) / (64 (7 x + 1) (7 x + 2) (7 x + 3) (7 x + 4) / 3 7 35 (3 x + 5) (x + 1) (7 x + 5) (7 x + 6) (2 x + 3) )], [-----------------------, 7 64 (7 x + 6) (2 x + 3) 3 2 3 7 (84 x + 255 x + 233 x + 67) (x + 1) - ----------------------------------------, 7 32 (7 x + 6) (7 x + 5) (2 x + 3) 4 3 2 3 7 (3 x + 2) (441 x + 1547 x + 1862 x + 927 x + 161) (x + 1) ---------------------------------------------------------------, - 7 64 (7 x + 6) (7 x + 5) (7 x + 4) (2 x + 3) 6 5 4 3 2 (20580 x + 63651 x + 54159 x - 12183 x - 40868 x - 20659 x - 3342) 4 / 7 (x + 1) / (64 (7 x + 6) (7 x + 5) (7 x + 4) (7 x + 3) (2 x + 3) ), - ( / 9 8 7 6 5 1793547 x + 12472509 x + 37479561 x + 64164849 x + 69075349 x 4 3 2 3 + 48480297 x + 22152269 x + 6340021 x + 1028054 x + 71664) (x + 1) / 7 / (128 (7 x + 6) (7 x + 5) (7 x + 4) (7 x + 3) (7 x + 2) (2 x + 3) ), ( / 10 9 8 7 6 20437312 x + 136837792 x + 397905382 x + 663951176 x + 704368385 x 5 4 3 2 + 495657743 x + 233540274 x + 72383837 x + 14020571 x + 1516628 x 4 / + 68532) (x + 1) / (64 (7 x + 1) (7 x + 2) (7 x + 3) (7 x + 4) / 3 7 7 (x + 1) (7 x + 5) (7 x + 6) (2 x + 3) )], [-----------------------, 7 32 (7 x + 6) (2 x + 3) 3 2 3 7 (3 x + 2) (x + 1) 7 (3 x + 2) (7 x + 8 x + 2) (x + 1) - -----------------------, -------------------------------------, 7 7 64 (7 x + 6) (2 x + 3) 64 (7 x + 6) (7 x + 4) (2 x + 3) 2 4 7 (3 x + 2) (x + 1) ---------------------------------, - 7 64 (7 x + 6) (7 x + 4) (2 x + 3) 6 5 4 3 2 (2940 x + 11844 x + 19794 x + 17422 x + 8437 x + 2106 x + 208) 3 / 7 (x + 1) / (64 (7 x + 2) (7 x + 4) (7 x + 6) (2 x + 3) ), (3 x + 2) / 5 4 3 2 4 / (5439 x + 16737 x + 20367 x + 12087 x + 3442 x + 368) (x + 1) / (128 / 7 901 x + 773 (7 x + 2) (7 x + 4) (7 x + 6) (2 x + 3) )]], [-------------, 128 (7 x + 6) 3 2 28 x + 105 x + 121 x + 44 ---------------------------, 128 (7 x + 6) (7 x + 5) 5 4 3 2 294 x + 924 x + 857 x - 5 x - 360 x - 128 7 6 - ---------------------------------------------, (2058 x + 8330 x 128 (7 x + 6) (7 x + 5) (7 x + 4) 5 4 3 2 + 14812 x + 17113 x + 15690 x + 10731 x + 4358 x + 744)/(128 (7 x + 6) 8 7 6 5 (7 x + 5) (7 x + 4) (7 x + 3)), (10290 x + 46648 x + 96866 x + 134911 x 4 3 2 + 149960 x + 128295 x + 73118 x + 23596 x + 3216)/(128 (7 x + 6) 11 10 (7 x + 5) (7 x + 4) (7 x + 3) (7 x + 2)), - (2016840 x + 13628076 x 9 8 7 6 5 + 41367172 x + 74545856 x + 88380866 x + 71174067 x + 37322069 x 4 3 2 + 9747079 x - 1731379 x - 2473206 x - 838144 x - 104448)/(896 (7 x + 1) (7 x + 2) (7 x + 3) (7 x + 4) (7 x + 5) (7 x + 6))], TooHardToCompute] The error in using 30 terms is 0.69740864592368445622844669396421242598308459108989591560195294583442415149\ -117 71845684 10