| Coefficients of the powerseries, which approximates the function S(x,1) | ||||||||||||||||||||||||||||||||
| here: | logarithms of the (absolute values of the) coefficients | |||||||||||||||||||||||||||||||
| domain: | 1 | <= x <= | 3 | |||||||||||||||||||||||||||||
| -1 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 |
| 1 | 1.0625 | 1.125 | 1.1875 | 1.25 | 1.3125 | 1.375 | 1.4375 | 1.5 | 1.5625 | 1.625 | 1.6875 | 1.75 | 1.8125 | 1.875 | 1.9375 | 2 | 2.0625 | 2.125 | 2.1875 | 2.25 | 2.3125 | 2.375 | 2.4375 | 2.5 | 2.5625 | 2.625 | 2.6875 | 2.75 | 2.8125 | 2.875 | 2.9375 | |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 2 | -0.69314718 | -0.75201 | -0.80449 | -0.85173 | -0.89457 | -0.93369 | -0.96961 | -1.00277 | -1.03352 | -1.06215 | -1.08890 | -1.11399 | -1.13759 | -1.15984 | -1.18087 | -1.20081 | -1.21974 | -1.23775 | -1.254916 | -1.2713095 | -1.2869878 | -1.3020043 | -1.3164069 | -1.3302387 | -1.3435386 | -1.3563419 | -1.3686806 | -1.3805838 | -1.3920781 | -1.4031877 | -1.4139351 | -1.4243408 |
| 3 | 0 | -7.17977 | -6.03807 | -5.46758 | -5.12816 | -4.91319 | -4.77526 | -4.68925 | -4.64038 | -4.61933 | -4.61996 | -4.63814 | -4.67103 | -4.71674 | -4.77408 | -4.84241 | -4.92159 | -5.01196 | -5.1143699 | -5.2303345 | -5.3622253 | -5.513706 | -5.6905269 | -5.9021543 | -6.1655012 | -6.5151288 | -7.0408632 | -8.1629606 | -8.1467902 | -7.0721798 | -6.5777069 | -6.2566446 |
| 4 | 0 | -11.17389 | -9.52429 | -8.80619 | -8.53118 | -8.59217 | -9.09806 | -11.95408 | -8.85191 | -8.20865 | -7.89176 | -7.74045 | -7.70739 | -7.78243 | -7.98555 | -8.40110 | -9.48562 | -9.21677 | -8.1279462 | -7.5890726 | -7.2268626 | -6.95534 | -6.740004 | -6.563272 | -6.414848 | -6.288126 | -6.1785853 | -6.0829807 | -5.9988963 | -5.9244804 | -5.858281 | -5.799137 |
| 5 | 0 | -15.47065 | -13.40066 | -12.85038 | -15.04278 | -12.27089 | -12.33722 | -11.27942 | -9.81681 | -9.01251 | -8.47849 | -8.10615 | -7.84456 | -7.66445 | -7.54720 | -7.48032 | -7.45530 | -7.46639 | -7.509959 | -7.5841824 | -7.6890302 | -7.8265596 | -8.0017621 | -8.2245469 | -8.5146829 | -8.916558 | -9.5624215 | -11.503988 | -9.9921349 | -9.2442363 | -8.8577385 | -8.6093908 |
| 6 | 0 | -20.02489 | -17.76342 | -19.12193 | -16.41448 | -13.27600 | -11.75836 | -10.81545 | -10.23506 | -9.92579 | -9.84379 | -9.98080 | -10.38415 | -11.30690 | -12.50847 | -11.31730 | -11.50736 | -12.48142 | -10.447054 | -9.6531112 | -9.1396032 | -8.7652561 | -8.4772125 | -8.2489119 | -8.0647688 | -7.9147176 | -7.7918219 | -7.6910744 | -7.6087328 | -7.5419243 | -7.4883964 | -7.4463533 |
| 7 | 0 | -24.83050 | -23.24883 | -19.75832 | -16.28608 | -14.32588 | -13.12939 | -12.51442 | -12.46812 | -13.25668 | -15.26900 | -13.05249 | -11.34359 | -10.45722 | -9.90347 | -9.54417 | -9.31725 | -9.18913 | -9.140072 | -9.1584788 | -9.2384161 | -9.3788279 | -9.5841174 | -9.8668207 | -10.255535 | -10.822431 | -11.843571 | -12.922268 | -11.674332 | -11.435285 | -11.584597 | -12.398686 |
| 8 | 0 | -29.96162 | -27.65518 | -21.08845 | -18.04310 | -16.18945 | -15.25511 | -15.47326 | -19.29843 | -13.77155 | -12.24122 | -11.45325 | -11.07360 | -10.99088 | -11.17610 | -11.67716 | -12.74335 | -15.89667 | -13.730918 | -11.836941 | -10.924187 | -10.335071 | -9.9181208 | -9.610857 | -9.3807614 | -9.2085287 | -9.0816934 | -8.9917381 | -8.9326152 | -8.8999234 | -8.8904194 | -8.9017164 |
| 9 | 0 | -36.00825 | -28.70389 | -23.30202 | -20.21974 | -18.46484 | -18.33224 | -18.90504 | -14.91334 | -13.47294 | -12.91520 | -13.05751 | -14.22932 | -16.81249 | -12.99979 | -11.77332 | -11.09675 | -10.69806 | -10.479863 | -10.396904 | -10.427212 | -10.563153 | -10.809899 | -11.189983 | -11.760517 | -12.680191 | -14.740246 | -16.75382 | -13.017807 | -11.894431 | -11.201971 | -10.709118 |
| 10 | 0 | -40.10017 | -31.23127 | -25.81113 | -22.62702 | -21.21607 | -21.78667 | -17.27866 | -15.35070 | -14.82950 | -16.14460 | -16.07584 | -13.39624 | -12.40483 | -11.98698 | -11.94717 | -12.25941 | -13.06075 | -15.350414 | -15.084954 | -12.754425 | -11.753102 | -11.142021 | -10.734129 | -10.456107 | -10.271086 | -10.157938 | -10.103698 | -10.100252 | -10.142759 | -10.228899 | -10.358632 |
| 11 | 0 | -44.04566 | -34.13147 | -28.47287 | -25.23304 | -27.07472 | -21.19993 | -17.85617 | -16.80840 | -19.89624 | -15.78442 | -13.99085 | -13.46871 | -13.78225 | -15.75832 | -16.37738 | -13.28060 | -12.25653 | -11.724685 | -11.465983 | -11.404162 | -11.512704 | -11.797836 | -12.310235 | -13.222175 | -15.75721 | -17.090029 | -13.447886 | -12.306967 | -11.625792 | -11.154715 | -10.808889 |
| 12 | 0 | -48.66019 | -37.19736 | -31.23732 | -28.12190 | -26.30209 | -21.57198 | -19.09181 | -20.81611 | -17.39180 | -15.29578 | -15.13005 | -19.47080 | -15.62430 | -13.60142 | -12.88326 | -12.71710 | -13.00565 | -13.955285 | -16.100846 | -15.609414 | -13.152955 | -12.22461 | -11.687348 | -11.359974 | -11.173769 | -11.095826 | -11.109664 | -11.208843 | -11.39541 | -11.681781 | -12.098312 |
| 13 | 0 | -54.66357 | -40.35624 | -34.09159 | -31.94799 | -28.52790 | -22.60807 | -20.98900 | -22.37460 | -17.02620 | -16.81050 | -18.00318 | -15.20171 | -14.13392 | -14.14933 | -15.56384 | -16.21319 | -14.29864 | -13.035515 | -12.472109 | -12.258641 | -12.306974 | -12.616411 | -13.294611 | -15.060529 | -14.96229 | -15.59586 | -13.244152 | -12.360939 | -11.820367 | -11.456922 | -11.208054 |
| 14 | 0 | -57.33108 | -43.57776 | -37.04697 | -33.63413 | -28.50988 | -23.97952 | -24.27323 | -19.69730 | -18.15922 | -19.00889 | -16.10292 | -15.33657 | -16.90221 | -18.11272 | -14.49097 | -13.58434 | -13.41237 | -13.842941 | -15.636584 | -15.442769 | -14.824953 | -13.22677 | -12.517277 | -12.138612 | -11.964465 | -11.948083 | -12.07574 | -12.359847 | -12.855718 | -13.764084 | -16.642431 |
| 15 | 0 | -60.73655 | -46.84831 | -40.14996 | -35.31786 | -29.62232 | -25.64290 | -24.29232 | -20.06197 | -20.85745 | -17.69732 | -16.67660 | -17.97621 | -16.19757 | -14.71121 | -14.66924 | -16.49386 | -16.25418 | -14.70671 | -13.50617 | -13.05081 | -12.998077 | -13.310403 | -14.187969 | -16.044289 | -15.034726 | -14.973186 | -13.321261 | -12.591929 | -12.161683 | -11.902692 | -11.764513 |
| 16 | 0 | -64.51793 | -50.16188 | -43.56625 | -37.63897 | -31.05112 | -27.76030 | -24.95073 | -21.32738 | -21.42612 | -17.94861 | -18.81793 | -16.72816 | -15.69465 | -17.32187 | -17.38894 | -14.97662 | -14.10688 | -14.09506 | -15.000951 | -15.859361 | -16.852712 | -14.207772 | -13.255789 | -12.823174 | -12.676299 | -12.755923 | -13.073921 | -13.753944 | -15.862247 | -14.716852 | -14.827309 |
| 17 | 0 | -68.44652 | -53.51682 | -53.30105 | -40.80323 | -32.65932 | -31.31058 | -24.71473 | -24.48562 | -19.86871 | -23.61254 | -18.12214 | -16.86608 | -17.97024 | -16.65754 | -15.13699 | -15.30236 | -17.33745 | -17.178549 | -14.700499 | -13.827614 | -13.621678 | -13.910735 | -15.023886 | -15.480313 | -15.411198 | -14.827725 | -13.509121 | -12.908468 | -12.593794 | -12.462811 | -12.479528 |
| 18 | 0 | -72.45742 | -56.91525 | -49.08475 | -42.54458 | -34.40313 | -30.62111 | -25.34185 | -23.79407 | -20.56266 | -22.72524 | -17.96921 | -18.65189 | -16.95248 | -16.08362 | -19.08750 | -18.70614 | -15.14598 | -14.564092 | -14.968553 | -17.372663 | -15.872936 | -15.254644 | -13.925208 | -13.435177 | -13.333481 | -13.558821 | -14.237544 | -18.290708 | -14.862395 | -15.168039 | -14.993717 |
| 19 | 0 | -76.52288 | -60.36406 | -51.18291 | -43.64126 | -36.27723 | -31.78165 | -26.41572 | -24.28566 | -23.49334 | -19.51890 | -20.43078 | -18.04994 | -17.22661 | -17.75052 | -16.57112 | -15.50008 | -16.32565 | -16.447749 | -16.552289 | -14.637253 | -14.20365 | -14.439703 | -15.832074 | -15.519879 | -15.911446 | -14.853731 | -13.758562 | -13.286825 | -13.112065 | -13.161642 | -13.441698 |
| 20 | 0 | -80.62839 | -63.87843 | -53.59243 | -45.29789 | -38.31601 | -33.67540 | -28.09362 | -23.83376 | -22.89438 | -20.39864 | -20.84704 | -18.16380 | -18.50897 | -16.88437 | -16.64332 | -17.27900 | -17.11152 | -15.240404 | -15.169839 | -17.11788 | -15.977793 | -16.617604 | -14.541822 | -13.989959 | -13.955222 | -14.409193 | -16.229835 | -15.236215 | -15.243486 | -15.792356 | -14.056484 |
| 21 | 0 | -84.76547 | -67.49239 | -56.14584 | -47.15352 | -40.66584 | -35.54131 | -30.08117 | -24.52938 | -22.47408 | -21.40915 | -19.16851 | -19.39220 | -17.74869 | -18.09754 | -18.01437 | -16.35189 | -16.02298 | -17.856421 | -17.055278 | -15.555043 | -14.764518 | -14.913942 | -16.646426 | -15.693332 | -16.520941 | -14.965437 | -14.052248 | -13.725647 | -13.740212 | -14.095957 | -15.104367 |
| 22 | 0 | -88.92877 | -71.29871 | -58.79485 | -49.12157 | -45.27662 | -35.36417 | -29.71009 | -26.82656 | -22.51087 | -22.45114 | -22.38380 | -19.22514 | -19.01021 | -19.36705 | -16.84500 | -18.12324 | -17.39527 | -16.227777 | -15.524043 | -16.524902 | -16.308071 | -18.479555 | -15.118116 | -14.498825 | -14.558694 | -15.417024 | -16.054472 | -15.341816 | -17.457571 | -14.724892 | -13.929133 |
| 23 | 0 | -93.11479 | -75.75816 | -61.52473 | -51.16765 | -44.25847 | -36.11147 | -30.62260 | -26.36235 | -25.00145 | -21.19050 | -21.23784 | -19.29325 | -19.59042 | -17.63953 | -18.83067 | -18.87977 | -16.34791 | -17.387536 | -16.825174 | -16.79391 | -15.322934 | -15.34621 | -17.521466 | -15.913637 | -17.312052 | -15.128768 | -14.385567 | -14.23819 | -14.549664 | -15.754032 | -15.618282 |
| 24 | 0 | -97.32117 | -78.86097 | -64.33972 | -53.27595 | -45.32003 | -37.13911 | -33.06000 | -27.19643 | -24.03341 | -23.36812 | -20.39959 | -20.09660 | -18.57329 | -19.20587 | -18.33071 | -17.19619 | -17.72058 | -18.302571 | -16.020609 | -16.438122 | -16.767335 | -17.177063 | -15.664246 | -14.970373 | -15.16201 | -17.095325 | -15.731371 | -15.936409 | -15.819721 | -14.545573 | -14.120505 |
| 25 | 0 | -101.54639 | -81.12941 | -67.26783 | -55.44023 | -46.72254 | -38.34515 | -32.37057 | -27.75609 | -26.18173 | -22.58350 | -21.62071 | -20.29666 | -21.44536 | -19.22165 | -18.20769 | -18.08444 | -17.17867 | -16.920666 | -17.315841 | -19.403878 | -15.899486 | -15.746517 | -18.595517 | -16.151422 | -18.694492 | -15.3283 | -14.761319 | -14.858838 | -15.816494 | -16.036332 | -15.369816 |
| 26 | 0 | -105.78958 | -83.94318 | -70.39900 | -57.66140 | -48.28372 | -39.71669 | -32.49510 | -27.35604 | -24.32914 | -23.12017 | -21.52229 | -20.29490 | -21.45539 | -18.89632 | -18.80469 | -17.54835 | -19.78103 | -17.884251 | -16.701158 | -16.541958 | -17.360546 | -17.01431 | -16.189106 | -15.411343 | -15.78886 | -17.189192 | -15.87664 | -17.458287 | -15.363437 | -14.668951 | -14.56434 |
| 27 | 0 | -110.05046 | -86.92945 | -74.20071 | -59.94880 | -49.95407 | -41.31205 | -33.15583 | -28.15728 | -25.36989 | -22.78910 | -21.86576 | -20.75062 | -19.45125 | -19.35293 | -18.23273 | -19.01423 | -19.67852 | -17.050167 | -18.587999 | -17.579364 | -16.523257 | -16.122913 | -20.880573 | -16.394408 | -18.958612 | -15.55708 | -15.189405 | -15.679784 | -17.154874 | -15.673635 | -16.115768 |
| 28 | 0 | -114.32935 | -90.00320 | -76.60569 | -62.32692 | -51.72185 | -43.46029 | -34.22391 | -30.26396 | -25.61499 | -24.17104 | -21.92501 | -21.29910 | -20.44587 | -19.15345 | -19.50258 | -19.01537 | -18.00274 | -17.826378 | -17.745517 | -16.764249 | -18.189009 | -17.059078 | -16.701253 | -15.827186 | -16.479439 | -16.622122 | -16.23301 | -17.044009 | -15.324128 | -15.009559 | -15.342629 |
| 29 | 0 | -118.62727 | -93.13071 | -78.22378 | -64.86039 | -53.60026 | -45.02787 | -36.25602 | -29.03273 | -26.08978 | -23.91496 | -22.30130 | -21.19597 | -21.71456 | -22.16462 | -20.00414 | -19.03508 | -18.48562 | -17.539768 | -18.835429 | -17.474602 | -17.249485 | -16.48207 | -19.810873 | -16.63693 | -18.138256 | -15.812839 | -15.690952 | -17.131502 | -16.158984 | -16.041295 | -17.374655 |
| 30 | 0 | -122.94617 | -96.29507 | -80.38421 | -67.79627 | -55.64433 | -45.03070 | -36.32488 | -29.76279 | -26.38298 | -24.02094 | -25.85246 | -21.35578 | -20.44996 | -20.82231 | -19.51139 | -19.17979 | -18.04473 | -18.540004 | -20.980034 | -17.085695 | -19.970767 | -17.187953 | -17.209947 | -16.222439 | -17.329299 | -16.560853 | -16.790644 | -16.40774 | -15.499213 | -15.596369 | -17.22914 |
| 31 | 0 | -127.28931 | -99.48650 | -82.72034 | -71.05589 | -58.07250 | -45.77102 | -36.27988 | -31.29373 | -26.35067 | -24.46405 | -22.51707 | -22.26552 | -20.70384 | -19.80244 | -19.55073 | -18.69035 | -18.65511 | -18.545291 | -18.11524 | -17.673895 | -18.237238 | -16.829744 | -19.394029 | -16.876294 | -17.899425 | -16.096595 | -16.313352 | -17.43623 | -16.174622 | -17.180664 | -16.023624 |
| 32 | 0 | -131.66211 | -102.69886 | -85.14808 | -71.53064 | -61.27430 | -46.73832 | -36.80847 | -30.34574 | -27.84597 | -24.53147 | -23.46087 | -22.01558 | -21.40010 | -20.27369 | -19.41318 | -19.19505 | -18.76513 | -21.491483 | -18.467053 | -17.514058 | -19.31825 | -17.360492 | -17.726709 | -16.60101 | -18.776251 | -16.666076 | -17.72247 | -16.279039 | -15.854619 | -16.677788 | -16.572802 |