Digital Library of Mathematical Functions
The Gamma Function -- Tables

Tables

These tables show Axiom's compliance with published standard values. In all cases shown here Axiom conforms to the accuracy of the published tables.

The Gamma Function

This table was constructed from the published values in the Handbook of Mathematical Functions, by Milton Abramowitz and Irene A. Stegun, by Dover (1965), pp 267-270. The first column is the point where the Gamma function is evaluated. The second column is the value reported in the Handbook. The third column is the actual value computed by Axiom at the given point. The fourth column is the difference of Axiom's value and the Handbook value.
point Handbook Value Axiom Computed Value Difference
1.000 1.0000000000 1. 0.
1.005 0.9971385354 0.9971385352483757 -1.51E-10
1.010 0.9943258512 0.99432585118631189 -2.03E-11
1.015 0.9915612888 0.99156128884131323 4.14E-11
1.020 0.9888442033 0.9888442032538789 -4.31E-11
1.025 0.9861739633 0.98617396313592742 -1.54E-10
1.030 0.9835499506 0.98354995053928918 -7.59E-11
1.035 0.9809715606 0.98097156056367696 -4.60E-11
1.040 0.9784382009 0.9784382009247683 3.00E-11
1.045 0.9759492919 0.97594929183099266 -6.55E-11
1.050 0.9735042656 0.97350426556841785 -2.72E-11
1.055 0.9711025663 0.97110256624499502 -6.77E-11
1.060 0.9687436495 0.96874364951272707 -2.36E-12
1.065 0.9664269823 0.96642698229777113 -1.37E-11
1.070 0.9641520425 0.96415204253821729 4.61E-11
1.075 0.9619183189 0.96191831892929192 2.31E-11
1.080 0.9597253107 0.95972531067573963 -3.00E-11
1.085 0.9575725273 0.95757252725116249 -3.68E-11
1.090 0.9554594882 0.95545948816407866 -4.24E-11
1.095 0.9533857227 0.95338572273049704 2.34E-11
1.100 0.9513507699 0.95135076987625944 -2.49E-11
1.105 0.9493541778 0.94935417782771081 2.11E-11
1.110 0.9473955040 0.94739550404472173 5.80E-11
1.115 0.9454743149 0.94547431492209555 1.12E-11
1.120 0.9435901856 0.94359018561564112 1.06E-11
1.125 0.9417426997 0.94174269984970138 1.39E-10
1.130 0.9399314497 0.93993144972988807 1.67E-11
1.135 0.9381560356 0.93815603556085947 -5.14E-11
1.140 0.9364160657 0.93641606566898694 -2.97E-11
1.145 0.9347111562 0.93471115622975964 2.05E-11
1.150 0.9330409311 0.93304093109978414 6.51E-12
1.155 0.9314050217 0.93140502165323868 -3.93E-11
1.160 0.9298030666 0.92980306664109957 4.51E-11
1.165 0.9282347120 0.92823471196190366 -2.59E-11
1.170 0.9266996106 0.92669961062266581 2.10E-11
1.175 0.9251974225 0.92519742251686099 1.24E-11
1.180 0.9237278143 0.92372781430006712 -1.17E-11
1.185 0.9222904591 0.92229045925047382 1.49E-10
1.190 0.9208850371 0.92088503713299241 2.60E-11
1.195 0.9195112341 0.91951123406686597 -2.98E-11
1.200 0.9181687424 0.91816874239667101 -1.67E-11
1.205 0.9168572606 0.91685726056661909 -3.28E-11
1.210 0.9155764930 0.91557649299805532 8.85E-12
1.215 0.9143261400 0.91432614997006778 9.98E-9
1.220 0.9131059475 0.91310594750311536 1.37E-11
1.225 0.9119156071 0.91191560725927312 1.49E-10
1.230 0.9107548564 0.91075485637655895 -1.50E-11
1.235 0.9096234274 0.90962342744425173 4.03E-11
1.240 0.9085210583 0.90852105834198582 4.21E-11
1.245 0.9074474922 0.90744749215126341 -5.77E-11
1.250 0.9064024771 0.90640247705547716 -3.68E-11
1.255 0.9053857663 0.90538576624240463 -5.23E-11
1.260 0.9043971178 0.90439711780910215 2.01E-11
1.265 0.9034362946 0.90343629466913566 5.78E-11
1.270 0.9025030645 0.90250306446208062 -5.13E-11
1.275 0.9015971994 0.90159719946523187 5.66E-11
1.280 0.9007184765 0.90071847650745973 5.78E-13
1.285 0.8998666769 0.89986667689491762 5.55E-12
1.290 0.8990415863 0.89904158628967101 -3.93E-12
1.295 0.8982429947 0.89824299468914737 -1.72E-11
1.300 0.8974706963 0.89747069630804477 2.65E-12
1.305 0.8967244895 0.89672448951215833 2.37E-11
1.310 0.8960041767 0.89600417674396082 4.53E-11
1.315 0.8953095644 0.89530956444995535 5.43E-11
1.320 0.8946404630 0.89464046300975775 1.28E-11
1.325 0.8939966866 0.89399668666686083 7.95E-11
1.330 0.8933780535 0.89337805346103716 -3.97E-11
1.335 0.8927843850 0.89278438516233538 1.51E-10
1.340 0.8922155072 0.89221550720663356 1.43E-11
1.345 0.8916712485 0.89167124863270442 1.24E-10
1.350 0.8911514420 0.89115144202666452 3.78E-11
1.355 0.8906559235 0.89065592343803057 -5.12E-11
1.360 0.8901845324 0.8901845323574008 -5.70E-11
1.365 0.8897371116 0.88973711163470881 3.11E-11
1.370 0.8893135074 0.88931350742948501 4.09E-11
1.375 0.8889135692 0.88891356915622532 -5.89E-11
1.380 0.8885371494 0.88853714943101736 2.03E-11
1.385 0.8881841041 0.88818410401940351 -9.53E-11
1.390 0.8878542918 0.88785429178544073 -1.00E-11
1.395 0.8875475748 0.88754757464193323 -1.49E-10
1.400 0.8872638175 0.88726381750180738 -7.13E-12
1.405 0.8870028884 0.88700288823059736 -1.66E-10
1.410 0.8867646576 0.88676465760002188 3.66E-12
1.415 0.8865489993 0.88654899924499497 -4.45E-11
1.420 0.8863557896 0.88635578960951567 -1.60E-12
1.425 0.8861849081 0.88618490791840432 -1.81E-10
1.430 0.8860362361 0.88603623612466142 2.35E-11
1.435 0.8859096587 0.88590965887072826 1.59E-10
1.440 0.8858050635 0.88580506344804788 -5.45E-11
1.445 0.8857223397 0.88572233975753722 5.12E-11
1.450 0.8856613803 0.88566138027095553 -3.63E-11
1.455 0.8856220700 0.88562207999314335 9.99E-9
1.460 0.8856043364 0.88560433642511449 3.29E-11
1.465 0.8856080495 0.88560804952797856 4.00E-11
1.470 0.8856331217 0.88563312168767672 -2.25E-11
1.475 0.8856794575 0.88567945767984679 1.68E-10
1.480 0.8857469646 0.88574696463853297 3.58E-11
1.485 0.8858355520 0.88583555202000774 1.39E-11
1.490 0.8859451316 0.885945131572484 -2.22E-11
1.495 0.8860756174 0.88607561730422169 -9.20E-11
1.500 0.8862269255 0.88622692545275816 -5.14E-11
1.505 0.8863989744 0.88639897445482596 5.62E-11
1.510 0.8865916850 0.88659168491694862 -8.75E-11
1.515 0.8868049797 0.88680497958669369 -1.15E-10
1.520 0.8870387833 0.88703878332457031 3.78E-11
1.525 0.8872930231 0.88729302307655866 -3.89E-11
1.530 0.8875676278 0.88756762784725507 5.05E-11
1.535 0.8878625287 0.88786252867361892 -2.97E-11
1.540 0.8881776586 0.88817765859552456 -1.03E-11
1.545 0.8885129527 0.88851295264558472 -4.41E-11
1.550 0.8888683478 0.88886834780261559 2.74E-12
1.555 0.8892437830 0.88924378298210571 -1.06E-11
1.560 0.8896391990 0.88963919900923583 -3.65E-12
1.565 0.8900545387 0.89005453859597561 -1.04E-10
1.570 0.8904897463 0.89048974631869759 2.61E-11
1.575 0.8909447686 0.89094476859629979 8.93E-12
1.580 0.8914195537 0.89141955366882042 -2.38E-11
1.585 0.8919140515 0.8919140515765388 8.47E-11
1.590 0.8924282141 0.8924282141395512 3.07E-11
1.595 0.8929619949 0.89296199493781103 4.74E-11
1.600 0.8935153493 0.89351534928506793 -2.24E-11
1.605 0.8940882342 0.89408823423580575 3.63E-11
1.610 0.8946806085 0.89468060852796683 2.74E-11
1.615 0.8952924327 0.89529243259029823 -9.74E-11
1.620 0.8959236685 0.89592366851824745 2.86E-11
1.625 0.8965742800 0.89657428005659789 6.46E-11
1.630 0.8972442326 0.89724423258250552 -7.80E-12
1.635 0.8979334930 0.89793349308892934 9.89E-11
1.640 0.8986420302 0.89864203016845012 -2.68E-11
1.645 0.8993698138 0.89936981399746452 2.04E-10
1.650 0.9001168163 0.9001168163207548 1.21E-11
1.655 0.9008830104 0.90088301043641827 2.24E-11
1.660 0.9016683712 0.90166837118115595 -1.49E-11
1.665 0.9024728748 0.90247287490643413 1.16E-10
1.670 0.9032964995 0.9032964995021503 -1.09E-11
1.675 0.9041392243 0.90413922432675797 3.24E-11
1.680 0.9050010302 0.90500103023115419 4.40E-11
1.685 0.9058818996 0.90588189953639731 -7.63E-11
1.690 0.9067818160 0.90678181602099839 9.93E-12
1.695 0.9077007650 0.90770076490852225 -9.63E-11
1.700 0.9086387329 0.90863873285549646 -5.97E-11
1.705 0.9095957079 0.90959570793962097 4.25E-11
1.710 0.9105716796 0.9105716796482709 5.89E-11
1.715 0.9115666390 0.91156663886729161 -1.31E-10
1.720 0.9125805779 0.91258057787007674 -1.93E-11
1.725 0.9136134904 0.91361349029479011 -1.16E-10
1.730 0.9146653712 0.91466537118231861 -2.63E-11
1.735 0.9157362171 0.9157362168940244 -2.15E-10
1.740 0.9168260252 0.91682602514979106 -5.47E-11
1.745 0.9179347950 0.91793479500653363 8.97E-12
1.750 0.9190625268 0.91906252684888312 3.95E-11
1.755 0.9202092224 0.92020922238011904 -3.48E-11
1.760 0.9213748846 0.92137488461334993 4.68E-12
1.765 0.9225595178 0.92255951786293755 4.88E-11
1.770 0.9237631277 0.9237631277361581 2.96E-11
1.775 0.9249857211 0.92498572112510025 2.89E-11
1.780 0.9262273062 0.92622730619879157 8.37E-12
1.785 0.9274878926 0.92748789239555507 -1.97E-10
1.790 0.9287674904 0.92876749040057904 -3.84E-12
1.795 0.9300661123 0.93006611219852275 -1.13E-10
1.800 0.9313837710 0.93138377097715253 -2.97E-11
1.805 0.9327204811 0.93272048117993289 8.20E-11
1.810 0.9340762585 0.93407625848467779 -2.05E-11
1.815 0.9354511198 0.93545111979719375 8.27E-12
1.820 0.9368450832 0.93684508324512517 4.80E-11
1.825 0.9382581682 0.93825816817200214 -2.82E-11
1.830 0.9396903951 0.93969039513148056 1.86E-11
1.835 0.9411417859 0.94114178588178177 -2.64E-11
1.840 0.9426123634 0.94261236338031951 -2.35E-11
1.845 0.9441021519 0.94410215177851575 -1.22E-10
1.850 0.9456111764 0.94561117639912362 -2.02E-12
1.855 0.9471394637 0.94713946380190617 9.43E-11
1.860 0.9486870417 0.94868704167359708 -2.86E-11
1.865 0.9502539389 0.95025393889348797 -1.33E-11
1.870 0.9518401855 0.95184018551169203 9.61E-12
1.875 0.9534458127 0.95344581274503493 5.77E-11
1.880 0.9550708530 0.95507085297311556 -2.73E-11
1.885 0.9567153398 0.95671533973453671 -6.02E-11
1.890 0.9583793077 0.95837930772329927 1.97E-11
1.895 0.9600627927 0.960062792785362 8.60E-11
1.900 0.9617658319 0.96176583191536336 2.60E-11
1.905 0.9634884632 0.96348846325350124 5.75E-11
1.910 0.9652307261 0.96523072608257054 -3.05E-11
1.915 0.9669926608 0.96699266080453206 5.78E-13
1.920 0.9687743090 0.96877430902013406 1.66E-11
1.925 0.9705757134 0.97057571340334281 -3.67E-12
1.930 0.9723969178 0.9723969177808085 -5.87E-12
1.935 0.9742379672 0.97423796710926569 -8.59E-11
1.940 0.9760989075 0.97609890747347727 -2.67E-11
1.945 0.9779797861 0.97797978608432246 -2.76E-11
1.950 0.9798806513 0.9798806512770295 -3.65E-11
1.955 0.9818015524 0.98180155250954815 1.02E-10
1.960 0.9837425404 0.98374254036106346 -5.01E-11
1.965 0.9857036664 0.985703666530647 1.27E-10
1.970 0.9876849838 0.98768498383604675 4.68E-11
1.975 0.9896865462 0.98968654618919183 -1.77E-11
1.980 0.9917084087 0.99170840868869103 -3.22E-12
1.985 0.9937506274 0.9937506274792185 6.46E-11
1.990 0.9958132598 0.99581325984380575 4.71E-11
1.995 0.9978963643 0.99789636418011041 -1.27E-10

The Psi Function

This table was constructed from the published values in the Handbook of Mathematical Functions, by Milton Abramowitz and Irene A. Stegun, by Dover (1965), pp 267-270. Axiom implements the polygamma function which allows for multiple derivatives. The Psi function is a special case of the polygamma function for zero derivatives. For the purpose of this table it is defined as: 
   Psi(x) == polygamma(0,x)
The first column is the point where the Gamma function is evaluated. The second column is the value reported in the Handbook. The third column is the actual value computed by Axiom at the given point. The fourth column is the difference of Axiom's value and the Handbook value.
point Handbook Value Axiom Computed Value Difference
1.000 -0.5772156649 -0.57721566490153275 -1.53E-12
1.005 -0.5690209113 -0.56902091134438304 -4.43E-11
1.010 -0.5608854579 -0.56088545786867472 3.13E-11
1.015 -0.5528085156 -0.55280851559434629 5.65E-12
1.020 -0.5447893105 -0.54478931045617984 4.38E-11
1.025 -0.5368270828 -0.53682708284938863 -4.93E-11
1.030 -0.5289210873 -0.5289210872854303 1.45E-11
1.035 -0.5210705921 -0.52107059205771 4.22E-11
1.040 -0.5132748789 -0.51327487891683021 -1.68E-11
1.045 -0.5055332428 -0.50553324275508449 4.49E-11
1.050 -0.4978449913 -0.49784499129987031 1.29E-13
1.055 -0.4902094448 -0.49020944481574569 -1.57E-11
1.060 -0.4826259358 -0.48262593581482538 -1.48E-11
1.065 -0.4750938088 -0.47509380877526647 2.47E-11
1.070 -0.4676124199 -0.46761241986755342 3.24E-11
1.075 -0.4601811367 -0.4601811366883593 1.16E-11
1.080 -0.4527993380 -0.45279933800171246 -1.71E-12
1.085 -0.4454664135 -0.44546641348725191 1.27E-11
1.090 -0.4381817635 -0.43818176349533489 4.66E-12
1.095 -0.4309447988 -0.43094479880878706 -8.78E-12
1.100 -0.4237549404 -0.42375494041107653 -1.10E-11
1.105 -0.4166116193 -0.41661161926071655 3.92E-11
1.110 -0.4095142761 -0.40951427607169383 2.83E-11
1.115 -0.4024623611 -0.40246236109974648 2.53E-13
1.120 -0.3954553339 -0.39545533393429283 -3.42E-11
1.125 -0.3884926633 -0.38849266329585463 4.14E-12
1.130 -0.3815738268 -0.38157382683879215 -3.87E-11
1.135 -0.3746983110 -0.37469831095919082 4.08E-11
1.140 -0.3678656106 -0.36786561060774969 -7.74E-12
1.145 -0.3610752291 -0.361075229107509 -7.50E-12
1.150 -0.3543266780 -0.35432667797627904 2.37E-11
1.155 -0.3476194768 -0.34761947675362337 4.63E-11
1.160 -0.3409531528 -0.34095315283226135 -3.22E-11
1.165 -0.3343272413 -0.3343272412937619 6.23E-12
1.170 -0.3277412847 -0.3277412847483927 -4.83E-11
1.175 -0.3211948332 -0.3211948331790081 2.09E-11
1.180 -0.3146874438 -0.31468744378886082 1.11E-11
1.185 -0.3082186809 -0.30821868085320625 4.67E-11
1.190 -0.3017881156 -0.30178811557461016 2.53E-11
1.195 -0.2953953259 -0.2953953259418296 -4.18E-11
1.200 -0.2890398966 -0.28903989659218843 7.81E-12
1.205 -0.2827214187 -0.28272141867731704 2.26E-11
1.210 -0.2764394897 -0.2764394897321919 -3.21E-11
1.215 -0.2701937135 -0.27019371354735244 -4.73E-11
1.220 -0.2639837000 -0.26398370004422023 -4.42E-11
1.225 -0.2578090652 -0.25780906515343338 4.65E-11
1.230 -0.2516694307 -0.25166943069609982 3.90E-12
1.235 -0.2455644243 -0.24556442426789726 3.21E-11
1.240 -0.2394936791 -0.23949367912593666 -2.59E-11
1.245 -0.2334568341 -0.23345683407831253 2.16E-11
1.250 -0.2274535334 -0.22745353337626528 2.37E-11
1.255 -0.2214834266 -0.22148342660888165 -8.88E-12
1.260 -0.2155461686 -0.21554616860026521 -2.65E-13
1.265 -0.2096414193 -0.20964141930911384 -9.11E-12
1.270 -0.2037688437 -0.20376884373062343 -3.06E-11
1.275 -0.1979281118 -0.19792811180067393 -6.73E-13
1.280 -0.1921188983 -0.19211889830222173 -2.22E-12
1.285 -0.1863408828 -0.18634088277384209 2.61E-11
1.290 -0.1805937494 -0.1805937494203691 -2.03E-11
1.295 -0.1748771870 -0.17487718702556942 -2.55E-11
1.300 -0.1691908889 -0.16919088886679934 3.32E-11
1.305 -0.1635345526 -0.163534552631597 -3.15E-11
1.310 -0.1579078803 -0.15790788033614178 -3.61E-11
1.315 -0.1523105782 -0.15231057824555994 -4.55E-11
1.320 -0.1467423568 -0.1467423567959959 4.00E-12
1.325 -0.1412029305 -0.14120293051842803 -1.84E-11
1.330 -0.1356920180 -0.13569201796416941 3.58E-11
1.335 -0.1302093416 -0.13020934163201769 -3.20E-11
1.340 -0.1247546279 -0.12475462789700376 2.99E-12
1.345 -0.1193276069 -0.11932760694070754 -4.07E-11
1.350 -0.1139280127 -0.11392801268308839 1.69E-11
1.355 -0.1085555827 -0.10855558271580501 -1.58E-11
1.360 -0.1032100582 -0.10321005823697738 -3.69E-11
1.365 -0.0978911840 -0.097891183987354968 1.26E-11
1.370 -0.0925987082 -0.092598708187860979 1.21E-11
1.375 -0.0873323825 -0.087332382478473081 2.15E-11
1.380 -0.0820919619 -0.082091961858406615 4.15E-11
1.385 -0.0768772046 -0.076877204627574525 -2.75E-11
1.390 -0.0716878723 -0.071687872329281643 -2.92E-11
1.395 -0.0665237297 -0.066523729694132228 5.86E-12
1.400 -0.0613845446 -0.061384544585116108 1.48E-11
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