Rule: Q[4, 10, 95]

Type

This rule is of Hermite (physicists') type.

Polynomials

One starts from the polynomial P1 and extends one by one with Pi until the final polynomial defining this rule is reached.
Note: Polynomials might be truncated due to size! The complete polynomials are included in the download.

Warning: This rule has negative weights!

Node locations in the complex plane

Plot of the node locations in the complex plane.

Magnitude of the Weights

Logarithmic magnitude of the weights
         plotted against the (real part) of the nodes.

Quadrature Rule Data

Nodes

Node (ball center) Error (ball radius)
-12.974126123534543037 + 1.3015794298021470317e-1025j 1.93e-492, 1.93e-492j
-13.554548612722150315 - 3.9320666513090030852e-1027j 3.35e-494, 3.35e-494j
-10.627714309970554057 - 4.3441964622880023755e-1019j 2.5e-487, 2.5e-487j
11.67715481333987218 - 1.6193080275687988232e-1025j 3.21e-489, 3.21e-489j
-11.309775193261211338 - 1.9065377034385662596e-1022j 1.72e-488, 1.72e-488j
4.5948761718501004767 + 5.2472976793082624745e-1026j 9.13e-490, 9.13e-490j
-11.67715481333987218 + 2.0894006966696932389e-1024j 3.23e-489, 3.23e-489j
-1.6506801238857845559 - 1.0405046601256855046e-1034j 4.63e-499, 4.63e-499j
-5.2928806546925314632 - 1.9464690254319020509e-1024j 2.61e-488, 2.61e-488j
3.911506869286660161 + 6.1353811933544902431e-1028j 1.99e-491, 1.99e-491j
-9.9958889621080766855 - 1.7409173844601404356e-1020j 1.65e-486, 1.65e-486j
10.306588475919474108 + 5.358312369980910085e-1028j 6.8e-487, 6.8e-487j
2.3166778458612639611 + 4.4750774095465040427e-1038j 8.11e-497, 8.11e-497j
8.5560640907112017789 + 1.4436052218840374065e-1027j 1.25e-485, 1.25e-485j
9.6941224938182246018 + 1.5886221061967767824e-1027j 3.11e-486, 3.11e-486j
12.974126123534543037 + 1.7091055160184952134e-1034j 1.88e-492, 1.88e-492j
12.069110679697883902 - 2.251789055413242759e-1032j 4.16e-490, 4.16e-490j
-10.961223607049599162 - 3.2486440004776367354e-1026j 7.16e-488, 7.16e-488j
-0.83117821903905907541 - 3.3503799723069118757e-1047j 1.85e-504, 1.85e-504j
5.0585485618956302122 + 1.9710336882837792173e-1031j 9.07e-489, 9.07e-489j
7.7562963053264187875 - 4.5493071598175349683e-1029j 1.19e-485, 1.19e-485j
12.495229992043379657 - 1.6978080193767264119e-1034j 3.74e-491, 3.74e-491j
13.554548612722150315 + 2.5076310613702568201e-1037j 3.58e-494, 3.58e-494j
-12.069110679697883902 - 1.89297513107486471e-1032j 4.06e-490, 4.06e-490j
-6.0069346946746797215 - 1.201105468900091127e-1027j 4.2e-487, 4.2e-487j
8.8317936401576615152 - 9.4549563930386004935e-1031j 1.06e-485, 1.06e-485j
1.2485313467948386889 + 3.493251077291159944e-1047j 5.32e-502, 5.32e-502j
-5.5289837441331091195 + 4.2326292214034569097e-1030j 7.44e-488, 7.44e-488j
6.7402648192882566106 - 1.8668393918897601189e-1034j 2.78e-486, 2.78e-486j
-1.0363502036603261655 + 1.1881290320488687683e-1051j 2.62e-503, 2.62e-503j
-6.4934252330097958844 - 5.3040853349549871131e-1033j 1.59e-486, 1.59e-486j
5.2928806546925314632 - 7.3353405273432957613e-1056j 2.71e-488, 2.71e-488j
-9.6941224938182246018 + 3.5023540065142900786e-1054j 3.13e-486, 3.13e-486j
6.4934252330097958844 + 1.7670063958459199401e-1068j 1.61e-486, 1.61e-486j
9.9958889621080766855 - 3.9112641517611756138e-1078j 1.63e-486, 1.63e-486j
-8.5560640907112017789 + 1.0422812525110048318e-1108j 1.28e-485, 1.28e-485j
-8.2852016174653621569 + 6.4936112503124010903e-1143j 1.41e-485, 1.41e-485j
1.0363502036603261655 - 3.1791119883460092979e-1178j 2.81e-503, 2.81e-503j
10.961223607049599162 - 1.8681588489856800337e-1163j 6.8e-488, 6.8e-488j
-6.2490384676551824808 + 1.2450195898470869888e-1159j 8.58e-487, 8.58e-487j
9.400116950819001587 - 1.3581082712920943836e-1170j 5.24e-486, 5.24e-486j
11.309775193261211338 - 7.7937792345168329686e-1180j 1.68e-488, 1.68e-488j
5.5289837441331091195 + 7.9400315388469329602e-1183j 7.06e-488, 7.06e-488j
-2.3166778458612639611 - 3.9667821186208111258e-1206j 7.81e-497, 7.81e-497j
-9.400116950819001587 - 5.5421643090843320739e-1194j 5.68e-486, 5.68e-486j
10.627714309970554057 + 1.7941806926838086621e-1222j 2.32e-487, 2.32e-487j
-3.2504166191195073219 + 1.9084133402247239697e-1235j 3.12e-493, 3.12e-493j
2.5273635558296938125 - 1.9028077820141893052e-1246j 7.95e-496, 7.95e-496j
0.64781779244031032889 - 1.2788098893908450561e-1254j 2.09e-505, 2.09e-505j
-6.7402648192882566106 - 6.9850730127386343551e-1246j 2.96e-486, 2.96e-486j
-3.911506869286660161 - 6.4267447474795608994e-1265j 1.83e-491, 1.83e-491j
-4.5948761718501004767 - 2.9402783038011640331e-1269j 8.97e-490, 8.97e-490j
3.2504166191195073219 + 6.7619810476925955642e-1286j 3.24e-493, 3.24e-493j
8.0187449123284393878 + 3.9419523789995901303e-1305j 1.33e-485, 1.33e-485j
0.83117821903905907541 - 4.1211057865483536183e-1352j 2.07e-504, 2.07e-504j
-8.0187449123284393878 + 1.4771895695661746493e-1355j 1.3e-485, 1.3e-485j
-12.495229992043379657 + 1.6093380323440222598e-1399j 3.78e-491, 3.78e-491j
2.8814997140645992587 + 1.3532012322008193492e-1431j 3.16e-494, 3.16e-494j
-9.112930895331825649 + 2.4914973191584928781e-1442j 8.36e-486, 8.36e-486j
1.8832199879620690267 + 4.5662575862893320567e-1482j 1.11e-498, 1.11e-498j
4.3654403151305761006 + 1.1576431074937963814e-1474j 2.62e-490, 2.62e-490j
-7.7562963053264187875 - 4.2063891801642167391e-1468j 1.29e-485, 1.29e-485j
-3.0486879132310133212 - 4.7904624633284473652e-1490j 9.54e-494, 9.54e-494j
5.7669617339887518723 + 4.4342460117897842477e-1485j 1.81e-487, 1.81e-487j
9.112930895331825649 + 1.5472021090644898576e-1483j 8.03e-486, 8.03e-486j
3.0486879132310133212 + 1.0366400552366648502e-1491j 1.04e-493, 1.04e-493j
-7.4975099154147885869 - 2.88087428401976676e-1482j 9.15e-486, 9.15e-486j
-0.64781779244031032889 + 4.5298124558532659401e-1507j 2.13e-505, 2.13e-505j
-6.9897466806094522435 + 7.4334451017994394732e-1487j 4.65e-486, 4.65e-486j
7.4975099154147885869 + 2.488649697863677627e-1492j 9.12e-486, 9.12e-486j
6.0069346946746797215 - 8.3920167734416571053e-1495j 3.98e-487, 3.98e-487j
-3.6874392033376396139 + 4.4555970327423819434e-1499j 4.68e-492, 4.68e-492j
-1.2485313467948386889 - 2.1138383812793510489e-1509j 5.82e-502, 5.82e-502j
-2.7218378818623558384 + 1.2189138073961823173e-1502j 6.6e-495, 6.6e-495j
6.2490384676551824808 + 2.1161220502577872086e-1494j 8.17e-487, 8.17e-487j
-1.8832199879620690267 - 4.9670481834064156296e-1506j 1.14e-498, 1.14e-498j
8.2852016174653621569 + 1.090600361670444295e-1493j 1.41e-485, 1.41e-485j
-1.5963386725041329846 - 4.5232525382752592567e-1507j 2.92e-499, 2.92e-499j
-2.5273635558296938125 - 9.9114868579430239078e-1503j 8.21e-496, 8.21e-496j
6.9897466806094522435 - 6.7095275061164130715e-1494j 4.96e-486, 4.96e-486j
4.1376128113821015791 - 3.6985945144924058215e-1499j 7.11e-491, 7.11e-491j
0.52464762327529031788 - 1.5667364785190406618e-1513j 4.1e-506, 4.1e-506j
-5.7669617339887518723 + 8.1926107908952863095e-1494j 1.69e-487, 1.69e-487j
1.5963386725041329846 - 9.0737835262501539948e-1507j 2.81e-499, 2.81e-499j
-4.3654403151305761006 + 2.3309016195441910453e-1497j 2.63e-490, 2.63e-490j
4.8259015771121197079 - 1.1304816347673255306e-1497j 2.98e-489, 2.98e-489j
1.6506801238857845559 - 2.5486494065346021256e-1506j 4.82e-499, 4.82e-499j
2.1011281718764573197 + 4.4394293507339869899e-1505j 9.05e-498, 9.05e-498j
-10.306588475919474108 - 1.7797631880580903651e-1492j 6.62e-487, 6.62e-487j
-2.8814997140645992587 - 7.7841206901215458061e-1507j 2.99e-494, 2.99e-494j
-4.8259015771121197079 - 3.0787292290941720893e-1501j 2.98e-489, 2.98e-489j
-8.8317936401576615152 - 2.548630845601354845e-1497j 1.09e-485, 1.09e-485j
2.1777939096240404351e-1594 - 4.9740215752221684518e-1594j 5.92e-1592, 5.92e-1592j
-4.1376128113821015791 + 1.1231884475886667953e-1509j 7.13e-491, 7.13e-491j
-1.4699739520834862226 - 1.4475695748541355524e-1520j 2.39e-500, 2.39e-500j
-3.4662476258618589097 - 9.0985954207039921283e-1512j 1.2e-492, 1.2e-492j
3.6874392033376396139 - 9.4623077809969825026e-1512j 4.76e-492, 4.76e-492j
2.7218378818623558384 + 2.4769864254854349115e-1515j 7.11e-495, 7.11e-495j
7.2420825582025547284 + 3.957322031761328023e-1505j 7.05e-486, 7.05e-486j
-5.0585485618956302122 - 3.9801690891996518553e-1508j 9.18e-489, 9.18e-489j
-0.37575546188304297337 + 9.1113672313343029317e-1528j 2.48e-507, 2.48e-507j
-7.2420825582025547284 + 1.6705772021477768747e-1504j 6.85e-486, 6.85e-486j
1.4699739520834862226 - 2.966944228002790263e-1522j 2.44e-500, 2.44e-500j
0.37575546188304297337 + 8.8816162072028370842e-1530j 2.36e-507, 2.36e-507j
3.4662476258618589097 + 5.5723965839751753684e-1515j 1.24e-492, 1.24e-492j
-0.18980675578014987883 - 2.0504028617548304646e-1530j 9.8e-509, 9.8e-509j
-0.52464762327529031788 + 7.7232802958805763518e-1528j 3.88e-506, 3.88e-506j
-2.1011281718764573197 - 3.5200139277027579212e-1521j 8.81e-498, 8.81e-498j
0.18980675578014987883 - 1.96376987707520205e-1530j 8.99e-509, 8.99e-509j

Weights

Weight (ball center) Error (ball radius)
2.2937948669756501311e-74 + 1.6512793249129812076e-1071j 9.45e-133, 1.48e-376j
6.1313843255399130248e-81 - 5.8339120174738566938e-1075j 6.59e-135, 1.03e-378j
1.6333104276939093644e-50 + 8.2167802196964118543e-1059j 1.36e-124, 2.13e-368j
1.2907266803605370765e-60 + 1.7170890570440002682e-1064j 2.52e-132, 3.94e-376j
5.666304399229816951e-57 + 2.7610741732554885153e-1062j 1.95e-127, 3.05e-371j
8.7977994399199798854e-11 - 2.8329342225650963866e-1035j 2.45e-91, 3.83e-335j
1.2907266803605370765e-60 - 3.1326711636694750931e-1064j 5.89e-129, 9.22e-373j
0.011591975473270120642 + 2.5436011060527379872e-1028j 8.33e-47, 1.3e-290j
9.0424379545514824049e-14 - 1.1939441566986517067e-1036j 1.75e-97, 2.73e-341j
2.8792038716721140624e-08 + 2.605343841325216552e-1034j 1.76e-85, 2.75e-329j
6.9729995920227635676e-45 + 9.4174368664565609821e-1056j 3.67e-123, 5.74e-367j
1.310209636064868732e-47 + 1.5376357856994277768e-1057j 4.65e-129, 7.27e-373j
0.00056351668130195259335 - 2.4742166826145007191e-1031j 1.54e-65, 2.4e-309j
2.4823538886208305427e-33 + 1.0279829257613929087e-1049j 1.67e-121, 2.62e-365j
2.5820153946936373177e-42 + 1.1410407291290356956e-1054j 1.22e-126, 1.91e-370j
2.2937948669756501311e-74 - 9.674270069212100575e-1072j 4.7e-141, 7.34e-385j
1.2593623731471992544e-64 - 1.2936729994831087756e-1066j 2.59e-137, 4.06e-381j
1.2698735378158198432e-53 - 1.7318789571176470383e-1060j 5.75e-132, 8.99e-376j
0.056324842571258699784 - 3.1633176240557337482e-1028j 1.87e-54, 2.92e-298j
1.0151845542437929919e-12 + 5.5271771433549038595e-1037j 8.97e-103, 1.4e-346j
1.0967948753461758532e-27 - 1.6210431902667396701e-1046j 4.34e-120, 6.8e-364j
3.9455960524823815749e-69 + 5.4521997057852268855e-1069j 2.66e-139, 4.16e-383j
6.1313843255399130248e-81 + 3.504461395473529277e-1075j 2.58e-144, 4.04e-388j
1.2593623731471992544e-64 + 2.3090040143035670817e-1066j 7.42e-139, 1.16e-382j
2.9020535419117982361e-17 - 1.6583333511291002457e-1039j 1.04e-114, 1.63e-358j
2.0930183629607940074e-35 - 7.1782057996770959541e-1051j 5.29e-126, 8.27e-370j
0.025512519510877440091 - 4.9414782969980910531e-1029j 2.05e-58, 3.21e-302j
7.0791031766395647284e-15 - 1.4818860924434852624e-1037j 1.58e-111, 2.48e-355j
2.6037147800109269791e-21 - 9.1698451150141023972e-1043j 1.55e-117, 2.43e-361j
0.040359274714879318886 + 1.7158617277791044796e-1028j 1.87e-54, 2.92e-298j
6.757456956747726586e-20 - 2.6441651193091503168e-1041j 2.28e-118, 3.56e-362j
9.0424379545514824049e-14 - 8.0977228668399014906e-1038j 4.71e-109, 7.37e-353j
2.5820153946936373177e-42 - 2.4096336320894459842e-1054j 1.88e-132, 2.94e-376j
6.757456956747726586e-20 + 6.7301251903824366733e-1042j 1.52e-116, 2.37e-360j
6.9729995920227635676e-45 - 4.5824668652820150914e-1056j 1.17e-131, 1.83e-375j
2.4823538886208305427e-33 - 2.4680945567084751045e-1049j 1.06e-129, 1.66e-373j
2.3364487035018196402e-31 + 3.2940911523979914187e-1048j 9.74e-129, 1.52e-372j
0.040359274714879318886 + 7.9882203365880534438e-1029j 1.44e-63, 2.25e-307j
1.2698735378158198432e-53 + 9.074611629761909744e-1061j 4.23e-137, 6.62e-381j
1.5066518290215346209e-18 + 2.0912706497981169329e-1040j 7.77e-120, 1.21e-363j
6.9069806793857750002e-40 - 2.4213148655524710948e-1053j 4.87e-131, 7.62e-375j
5.666304399229816951e-57 - 1.4801224329190743656e-1062j 1.16e-138, 1.81e-382j
7.0791031766395647284e-15 + 1.268304647251167515e-1038j 5.19e-116, 8.11e-360j
0.00056351668130195259335 - 3.0123124673899894484e-1030j 1.68e-95, 2.63e-339j
6.9069806793857750002e-40 + 5.2629945868524251168e-1053j 1.91e-135, 2.98e-379j
1.6333104276939093644e-50 - 4.2049262243935119046e-1059j 7.18e-136, 1.12e-379j
3.0748312886174625053e-06 + 4.9520454349726205165e-1032j 1.76e-106, 2.75e-350j
0.00019532460713004521411 + 5.1562426710103524558e-1032j 4.68e-98, 7.32e-342j
0.058076425559295496599 + 4.55084086645575158e-1028j 1.04e-75, 1.62e-319j
2.6037147800109269791e-21 + 3.2593484152616870258e-1042j 2.7e-125, 4.22e-369j
2.8792038716721140624e-08 - 9.4459899506504220303e-1034j 3.49e-112, 5.46e-356j
8.7977994399199798854e-11 + 2.4790542353485453092e-1035j 3.83e-116, 5.98e-360j
3.0748312886174625053e-06 - 6.2701573640880634887e-1033j 3.74e-107, 5.85e-351j
1.771819015537691436e-29 + 1.5322795378944065035e-1047j 1.57e-129, 2.46e-373j
0.056324842571258699784 - 1.7347365760386848691e-1028j 5.23e-81, 8.18e-325j
1.771819015537691436e-29 - 3.9905387908521326653e-1047j 9.34e-132, 1.46e-375j
3.9455960524823815749e-69 - 9.5197578786179118489e-1069j 8.59e-150, 1.34e-393j
2.105220622166904315e-05 - 2.5509019025811691081e-1032j 1.78e-106, 2.78e-350j
1.3759603074354895853e-37 - 9.9746277261373399185e-1052j 8.4e-136, 1.31e-379j
0.0035699911556732969827 - 4.1075202691264930897e-1030j 2.56e-98, 4e-342j
6.8265053988423326012e-10 + 8.1572454073061725236e-1035j 3.58e-116, 5.6e-360j
1.0967948753461758532e-27 + 4.4252808104914496088e-1046j 1.7e-131, 2.66e-375j
9.7458958300749138341e-06 - 1.9671750071240010795e-1031j 2.19e-111, 3.42e-355j
4.8533313026301474546e-16 - 2.005838425961037756e-1039j 1.61e-123, 2.52e-367j
1.3759603074354895853e-37 + 4.4498868866084047613e-1052j 2.28e-135, 3.56e-379j
9.7458958300749138341e-06 + 1.6357463765406897711e-1032j 8.62e-110, 1.35e-353j
5.6054812559874011304e-26 - 4.5287903057620099846e-1045j 2.62e-131, 4.1e-375j
0.058076425559295496599 + 7.2219196194041808839e-1028j 3.87e-95, 6.06e-339j
8.5653018237927105515e-23 - 3.85167675616566488e-1043j 1.65e-129, 2.58e-373j
5.6054812559874011304e-26 + 1.5737275306747896813e-1045j 1.45e-131, 2.27e-375j
2.9020535419117982361e-17 + 3.1170753830187889192e-1040j 7.09e-126, 1.11e-369j
1.5639861668813058752e-07 + 3.3786851555482430215e-1033j 7.98e-120, 1.25e-363j
0.025512519510877440091 - 1.2736788065673873762e-1028j 3.28e-102, 5.12e-346j
6.093953999034865477e-05 - 9.7819853006884687329e-1031j 7.58e-115, 1.19e-358j
1.5066518290215346209e-18 - 4.683688302129288691e-1041j 4.21e-127, 6.58e-371j
0.0035699911556732969827 - 2.1289274337591589748e-1029j 6.3e-110, 9.85e-354j
2.3364487035018196402e-31 - 1.319820186479818559e-1048j 1.18e-134, 1.85e-378j
-0.0060115103999762883325 - 3.7290161425391174711e-1028j 2.34e-107, 3.66e-351j
0.00019532460713004521411 + 1.5826311872909133361e-1030j 2.07e-114, 3.23e-358j
8.5653018237927105515e-23 + 1.1762268157217380394e-1043j 1.04e-130, 1.62e-374j
4.7031999469177542217e-09 - 1.7006009160540052803e-1034j 1.54e-121, 2.41e-365j
0.048917690285893349521 - 6.7147761883822135341e-1028j 1.66e-106, 2.6e-350j
4.8533313026301474546e-16 + 1.3950524614195783899e-1038j 1.25e-129, 1.96e-373j
-0.0060115103999762883325 - 1.0263159212804627e-1028j 2.18e-111, 3.41e-355j
6.8265053988423326012e-10 - 8.0392744837064434808e-1035j 8.32e-126, 1.3e-369j
1.004997124126907887e-11 - 4.8023003305623531137e-1036j 8.05e-124, 1.26e-367j
0.011591975473270120642 + 6.5873056911631207425e-1029j 5.27e-112, 8.24e-356j
0.0014794953732747135014 + 9.4570067603242680927e-1031j 8.24e-115, 1.29e-358j
1.310209636064868732e-47 - 3.0795149329640674983e-1057j 1.25e-147, 1.95e-391j
2.105220622166904315e-05 + 5.4588141180010126736e-1031j 5.11e-120, 8e-364j
1.004997124126907887e-11 - 8.3416613141100088099e-1036j 2e-128, 3.12e-372j
2.0930183629607940074e-35 + 1.6630479961273599638e-1050j 8.12e-142, 1.27e-385j
0.10709541828447808221 + 4.9094940450814200134e-1028j 4.41e-115, 6.9e-359j
4.7031999469177542217e-09 + 2.7177257524771222003e-1034j 5.19e-126, 8.11e-370j
0.015564594539684325367 + 1.9498679275591114497e-1028j 6.22e-117, 9.72e-361j
7.4858221699321845411e-07 - 1.257900142495841525e-1032j 1.13e-123, 1.76e-367j
1.5639861668813058752e-07 - 6.7875895225279477024e-1034j 3.52e-126, 5.51e-370j
6.093953999034865477e-05 + 1.1196637663552157692e-1032j 8.77e-123, 1.37e-366j
2.3889768522599651826e-24 - 1.4111892775887040842e-1044j 9.6e-137, 1.5e-380j
1.0151845542437929919e-12 + 3.6079189045947635435e-1036j 3.18e-130, 4.98e-374j
0.087069623813001759961 + 7.700602360849095904e-1028j 1.56e-120, 2.44e-364j
2.3889768522599651826e-24 + 4.3117849282287443028e-1044j 1.92e-137, 3e-381j
0.015564594539684325367 + 6.1294077314835314795e-1029j 5.8e-121, 9.12e-365j
0.087069623813001759961 + 5.9125265713199495984e-1028j 5.32e-121, 8.38e-365j
7.4858221699321845411e-07 + 2.1564794231400708055e-1033j 2.99e-126, 4.64e-370j
0.10314277524100196353 - 5.6023982474909163606e-1028j 1.32e-121, 2.06e-365j
0.048917690285893349521 - 9.7342297484240629954e-1028j 1.82e-121, 2.82e-365j
0.0014794953732747135014 + 6.9789442174280258835e-1030j 3.78e-124, 5.55e-368j
0.10314277524100196353 - 4.9056930443011733425e-1028j 6.82e-122, 1.12e-365j

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All rules of Hermite (physicists') type can be downloaded here packed into a single file.