Rule: Q[6, 9, 74]

Type

This rule is of Hermite (probabilists') 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)
16.197115320682037987 - 4.0835291254979900961e-1165j 3.35e-495, 3.35e-495j
14.287129291930341299 + 9.4316640005048344956e-1190j 2.04e-492, 2.04e-492j
-15.492591017901869507 - 3.4763343356089375248e-1208j 4.61e-494, 4.61e-494j
-14.287129291930341299 + 1.3368044188910265483e-1205j 2.15e-492, 2.15e-492j
-14.865006018695329294 - 9.9653594254450014293e-1207j 3.69e-493, 3.69e-493j
-12.26158458860294186 - 1.6933599026123975425e-1204j 1.24e-490, 1.24e-490j
14.865006018695329294 - 5.8094271535695924326e-1203j 3.82e-493, 3.82e-493j
13.230032961121944239 + 1.8618054496191683583e-1210j 2.46e-491, 2.46e-491j
-4.0045269466496493244 + 6.8841046170350922505e-1228j 1.51e-496, 1.51e-496j
8.8626247485097925339 + 7.5982970452282554586e-1220j 2.27e-490, 2.27e-490j
-1.8891758777537106755 - 4.235740737355483146e-1248j 4.54e-502, 4.54e-502j
12.736876088749533156 + 8.167179365876040607e-1236j 6.31e-491, 6.31e-491j
17.049927993225963778 + 2.6159610154225941233e-1243j 8.96e-497, 8.96e-497j
-2.9904240353730319061 + 1.3335990058473309182e-1254j 6.75e-499, 6.75e-499j
-4.9704733407469194846 - 1.2282685194139629911e-1249j 2.84e-494, 2.84e-494j
-13.74493965200479781 - 2.1870133768998029644e-1247j 8.1e-492, 8.1e-492j
-2.6798017558109127176 - 3.3217147368136815669e-1255j 1.49e-499, 1.49e-499j
-11.353847009615271547 + 3.9251191498230617463e-1244j 2.98e-490, 2.98e-490j
-2.4440098084964929991 - 1.0196600503136967976e-1263j 4e-500, 4e-500j
11.801300920138525246 + 2.5026982529136795138e-1252j 2.37e-490, 2.37e-490j
13.74493965200479781 + 1.695394225762290656e-1266j 8.37e-492, 8.37e-492j
-12.736876088749533156 - 3.8488329388792062651e-1275j 6.31e-491, 6.31e-491j
-13.230032961121944239 - 1.2058541129160032874e-1277j 2.57e-491, 2.57e-491j
-6.9584855463172786228 - 1.6574491368285790171e-1277j 9.53e-492, 9.53e-492j
-6.5930306973939955418 + 7.5224104790564557419e-1278j 4.15e-492, 4.15e-492j
15.492591017901869507 + 7.6495430791670387453e-1276j 5.1e-494, 5.1e-494j
0.94473204276587668564 - 1.1448239925120441431e-1295j 8.13e-506, 8.13e-506j
5.2520541810335630885 + 7.168178648303141831e-1284j 1.02e-493, 1.02e-493j
-10.073008765100116585 + 3.331806978207596465e-1278j 4.74e-490, 4.74e-490j
-17.049927993225963778 - 2.3921717032078923302e-1287j 8.94e-497, 8.94e-497j
7.3293068982506138368 + 1.1900887085689893488e-1279j 2.07e-491, 2.07e-491j
6.9584855463172786228 + 8.0989314803804397603e-1292j 9.72e-492, 9.72e-492j
3.6639594221247682646 - 1.3825062784445250955e-1319j 2.35e-497, 2.35e-497j
12.26158458860294186 + 1.5770065795978202478e-1312j 1.2e-490, 1.2e-490j
5.8849966733128800446 + 1.327529010405719982e-1325j 6.71e-493, 6.71e-493j
-8.0857505888462073737 + 8.5705264719448074955e-1336j 8.93e-491, 8.93e-491j
4.668354695422966135 - 1.1930281631607418858e-1352j 5.75e-495, 5.75e-495j
2.9904240353730319061 + 1.960006902617533454e-1367j 6.54e-499, 6.54e-499j
9.6627998909683316431 + 5.1166869343162234197e-1358j 4.16e-490, 4.16e-490j
-16.197115320682037987 - 8.1600738645625137168e-1375j 3.34e-495, 3.34e-495j
-8.4714978071669830571 - 1.107835071628446628e-1368j 1.38e-490, 1.38e-490j
-6.2341567119338226859 + 3.1875707735046451629e-1371j 1.63e-492, 1.63e-492j
-8.8626247485097925339 + 6.8213969860586321981e-1368j 2.16e-490, 2.16e-490j
3.3242574335521189524 + 1.2954689100467809996e-1381j 3.91e-498, 3.91e-498j
-9.6627998909683316431 + 5.9276536090693403533e-1372j 3.98e-490, 3.98e-490j
7.7050760261587912506 - 4.0800547361535830633e-1379j 4.24e-491, 4.24e-491j
-11.801300920138525246 - 6.3345803595790719458e-1383j 2.22e-490, 2.22e-490j
5.5533529315903281928 + 1.4933985060551005267e-1393j 2.55e-493, 2.55e-493j
-9.259550588012963481 - 8.8673140706082889824e-1391j 3.12e-490, 3.12e-490j
4.3418637687749014379 + 2.0014861994742704497e-1414j 9.99e-496, 9.99e-496j
-7.7050760261587912506 + 3.1922187386337809541e-1407j 4.53e-491, 4.53e-491j
-2.2047283888037813158 + 3.6637803438643518007e-1430j 5.9e-501, 5.9e-501j
-5.8849966733128800446 + 3.1248557592358845544e-1419j 6.52e-493, 6.52e-493j
2.6798017558109127176 - 3.1694420435433931524e-1452j 1.52e-499, 1.52e-499j
1.4101631878200285279 - 7.7386149624618664573e-1456j 1.61e-502, 1.61e-502j
10.073008765100116585 - 1.1275996053689978112e-1442j 4.45e-490, 4.45e-490j
11.353847009615271547 - 6.6621915479604615162e-1474j 3.11e-490, 3.11e-490j
-0.94473204276587668564 - 5.585548381872601307e-1501j 7.39e-506, 7.39e-506j
1.4889715091683343655 - 9.6776029629710986583e-1497j 1.47e-502, 1.47e-502j
2.4440098084964929991 - 1.6848826526989102986e-1494j 4.06e-500, 4.06e-500j
6.5930306973939955418 - 1.9082983468346671089e-1486j 3.73e-492, 3.73e-492j
-3.6639594221247682646 + 9.2366349646203405803e-1492j 2.44e-497, 2.44e-497j
-1.3498952853218839149 + 3.4153081725789712326e-1497j 5.8e-503, 5.8e-503j
1.3498952853218839149 - 2.0218748485359253016e-1497j 5.75e-503, 5.75e-503j
6.2341567119338226859 - 7.0029976307619941974e-1487j 1.6e-492, 1.6e-492j
2.2047283888037813158 + 6.822866413461834886e-1495j 5.71e-501, 5.71e-501j
-10.490941228305770131 - 4.394357637050621337e-1483j 4.37e-490, 4.37e-490j
-0.61670659019259415219 - 5.1410569847461389628e-1508j 2.46e-507, 2.46e-507j
-7.3293068982506138368 - 9.7311496083132608945e-1491j 2.03e-491, 2.03e-491j
8.4714978071669830571 - 6.4943282909955511227e-1491j 1.35e-490, 1.35e-490j
4.0045269466496493244 - 6.6070581793144217079e-1524j 1.55e-496, 1.55e-496j
-4.3418637687749014379 + 4.5618656394111552341e-1523j 1.03e-495, 1.03e-495j
-3.3242574335521189524 - 1.2123332817325378428e-1525j 3.98e-498, 3.98e-498j
-5.2520541810335630885 + 5.1030723411738473847e-1520j 9.74e-494, 9.74e-494j
-1.4889715091683343655 - 1.1652842816903822375e-1531j 1.51e-502, 1.51e-502j
8.0857505888462073737 + 5.1013959989684635108e-1518j 8.79e-491, 8.79e-491j
4.9704733407469194846 + 5.2426079478821941964e-1535j 2.79e-494, 2.79e-494j
-5.5533529315903281928 - 1.2130158007678413101e-1538j 2.58e-493, 2.58e-493j
-0.30328462253494373749 - 1.114183495402703296e-1588j 8.35e-509, 8.35e-509j
-4.668354695422966135 + 3.9612445661937700704e-1543j 5.83e-495, 5.83e-495j
1.8891758777537106755 - 1.1512687539656471121e-1556j 4.63e-502, 4.63e-502j
0.61670659019259415219 - 1.5491236145386063703e-1562j 2.09e-507, 2.09e-507j
10.917516096886354349 + 1.9801339023476107314e-1543j 3.8e-490, 3.8e-490j
-10.917516096886354349 - 9.6202242495231231637e-1563j 3.95e-490, 3.95e-490j
-1.4101631878200285279 - 2.8264399907072882243e-1600j 1.74e-502, 1.74e-502j
9.259550588012963481 - 9.0131251715087592601e-1587j 3.05e-490, 3.05e-490j
0.30328462253494373749 - 2.616242074170220137e-1641j 8.35e-509, 8.35e-509j
10.490941228305770131 - 8.4739683129190368562e-1623j 4.28e-490, 4.28e-490j
6.5696390932831755668e-1683 - 3.0623660022105890065e-1683j 6.45e-1681, 6.45e-1681j

Weights

Weight (ball center) Error (ball radius)
3.2622282848042650042e-58 + 1.1387116223431174928e-1221j 7.68e-150, 6.92e-396j
1.0549517536720691133e-45 - 3.1430774040661744443e-1216j 4.5e-145, 4.06e-391j
1.9974551320934293385e-53 - 1.4387174564729317182e-1221j 1.2e-149, 1.08e-395j
1.0549517536720691133e-45 - 1.9692906960101613664e-1217j 5.09e-147, 4.59e-393j
2.4897630094445312868e-49 + 2.218222178007028635e-1219j 2.66e-148, 2.4e-394j
4.2000918575990628927e-34 - 4.1513655677950321556e-1211j 1.69e-142, 1.53e-388j
2.4897630094445312868e-49 + 5.1724499144470166978e-1218j 6.34e-150, 5.72e-396j
1.9706709858829179463e-39 - 4.8849094229459466856e-1213j 1.64e-146, 1.48e-392j
4.4656406043684145932e-05 - 9.6945672159938147234e-1193j 1.7e-107, 1.53e-353j
1.3812618675763132047e-18 - 1.1609582704403703772e-1201j 8.48e-135, 7.64e-381j
0.022506517297301976735 + 8.2289347622733404482e-1190j 6.26e-83, 5.64e-329j
1.1431423578483073615e-36 + 1.33923853260842178e-1211j 1.34e-145, 1.21e-391j
2.9528870424905322539e-64 + 1.0237064739910762579e-1225j 9.95e-157, 8.97e-403j
0.0014937052301362825954 + 3.1547468605128870599e-1191j 8.16e-100, 7.36e-346j
4.9440680478770157205e-07 + 5.9945244600735866344e-1194j 5.16e-117, 4.65e-363j
1.9902041357172744534e-42 + 1.1588195764356221349e-1215j 8.21e-150, 7.4e-396j
0.0031111793335847433718 - 1.2428573614951687222e-1190j 1.68e-97, 1.51e-343j
1.7929233013789515974e-29 - 1.5861761807546407202e-1208j 8.67e-145, 7.81e-391j
0.0041071345702078428853 + 3.0497683282865840362e-1190j 4.3e-95, 3.88e-341j
1.03582560890496879e-31 + 5.6333673906670795305e-1209j 3.98e-146, 3.58e-392j
1.9902041357172744534e-42 + 1.4149654898002339117e-1214j 1.65e-149, 1.49e-395j
1.1431423578483073615e-36 + 1.6016060991629430077e-1212j 3e-148, 2.71e-394j
1.9706709858829179463e-39 - 4.9253595482896276533e-1214j 2.31e-149, 2.08e-395j
4.4944265453018531502e-12 + 5.4832502699593327759e-1198j 5.23e-133, 4.72e-379j
5.262768379137519016e-11 - 3.2300781236928185859e-1197j 2.34e-131, 2.11e-377j
1.9974551320934293385e-53 - 6.4713926148332944136e-1220j 2.67e-157, 2.41e-403j
0.086245252656514812061 + 2.0101972150568142832e-1189j 6.03e-98, 5.44e-344j
1.1645758276031099852e-07 - 4.0782039600488477484e-1194j 1.25e-129, 1.13e-375j
1.5306784782608098091e-23 + 3.8758024516422542529e-1205j 1.56e-144, 1.41e-390j
2.9528870424905322539e-64 - 2.6258871976734248853e-1227j 8.83e-163, 7.96e-409j
3.2219717833678278337e-13 - 2.3662407523437561045e-1198j 4.58e-139, 4.13e-385j
4.4944265453018531502e-12 + 1.3743158650794054114e-1197j 8.15e-138, 7.35e-384j
0.00016527621650741039256 + 4.4395810373132874184e-1192j 5.21e-123, 4.69e-369j
4.2000918575990628927e-34 - 3.0019449713508894098e-1210j 1.66e-151, 1.49e-397j
4.1191815879776589835e-09 - 2.1693888850197864576e-1195j 2.49e-134, 2.25e-380j
9.7129984891864646044e-16 - 1.9998258209816174553e-1200j 1.23e-142, 1.11e-388j
2.3400177436338621917e-06 - 2.6511433606439034961e-1193j 2.51e-129, 2.26e-375j
0.0014937052301362825954 + 4.5834212549374276784e-1191j 3.88e-120, 3.5e-366j
8.6122838603460731999e-22 - 1.6223713925430135491e-1203j 2.45e-147, 2.21e-393j
3.2622282848042650042e-58 + 4.1122767700528487237e-1224j 2.52e-163, 2.27e-409j
4.039372457753783118e-17 + 2.7096772569261673551e-1201j 2.17e-144, 1.95e-390j
5.1467035540274674843e-10 + 1.8394793986340820001e-1196j 1.33e-137, 1.2e-383j
1.3812618675763132047e-18 - 3.3978953754985616401e-1202j 6.04e-146, 5.44e-392j
0.00053721483010523563683 - 1.3419815014422186068e-1191j 1.26e-127, 1.13e-373j
8.6122838603460731999e-22 - 4.0994281443907984736e-1204j 1.12e-148, 1.01e-394j
1.9364254818974287769e-14 + 3.8756896345810735858e-1199j 2.22e-146, 2e-392j
1.03582560890496879e-31 + 8.8445136633631361709e-1210j 5.67e-154, 5.11e-400j
2.5536093016241924955e-08 + 1.0557440354320764921e-1194j 3.29e-139, 2.97e-385j
3.8451481163502808037e-20 + 3.9116767358469799547e-1203j 1.26e-147, 1.13e-393j
1.0731724941403313163e-05 + 6.2880529165114898167e-1193j 2.06e-135, 1.86e-381j
1.9364254818974287769e-14 + 1.3769661614975311169e-1199j 2.52e-144, 2.27e-390j
0.010074094068969395386 - 4.7649170581481413367e-1190j 1.18e-124, 1.06e-370j
4.1191815879776589835e-09 - 1.0130822441572422034e-1195j 2.47e-140, 2.23e-386j
0.0031111793335847433718 - 1.7356492647935998433e-1190j 5.77e-130, 5.2e-376j
-0.27874348221448757952 + 3.9416322771528794896e-1188j 7.28e-122, 6.56e-368j
1.5306784782608098091e-23 + 1.6625741308145124717e-1204j 1.9e-155, 1.72e-401j
1.7929233013789515974e-29 - 9.0229732070244437389e-1208j 3.61e-158, 3.25e-404j
0.086245252656514812061 + 1.7886227626564966104e-1189j 1.69e-124, 1.52e-370j
0.14605170802291631437 - 1.6923568144648312479e-1188j 1.54e-124, 1.38e-370j
0.0041071345702078428853 + 4.1336927846750351726e-1190j 9.66e-131, 8.71e-377j
5.262768379137519016e-11 - 7.6648587529365202819e-1197j 1.24e-145, 1.12e-391j
0.00016527621650741039256 + 2.8015584244794296904e-1192j 4.35e-138, 3.92e-384j
0.22166791087003174412 - 2.0605121172754141186e-1188j 5.2e-127, 4.69e-373j
0.22166791087003174412 - 2.4351917658337744341e-1188j 1.16e-125, 1.05e-371j
5.1467035540274674843e-10 + 4.1415270713784512862e-1196j 1.43e-144, 1.29e-390j
0.010074094068969395386 - 6.2664975904103989516e-1190j 2.06e-131, 1.86e-377j
2.1238243484364641847e-25 - 3.2728913771726084275e-1206j 1.5e-155, 1.35e-401j
0.10558965057450030294 - 1.5122859407312148943e-1189j 6.1e-128, 5.5e-374j
3.2219717833678278337e-13 - 8.9190653291295070697e-1199j 1.56e-147, 1.41e-393j
4.039372457753783118e-17 + 8.6522507534843826404e-1201j 1.14e-152, 1.02e-398j
4.4656406043684145932e-05 - 1.6062723748734050449e-1192j 2.01e-139, 1.81e-385j
1.0731724941403313163e-05 + 3.6295109300351344811e-1193j 2.23e-142, 2.01e-388j
0.00053721483010523563683 - 8.8493454700699585048e-1192j 2.34e-139, 2.11e-385j
1.1645758276031099852e-07 - 2.0810219099215455174e-1194j 8.02e-145, 7.23e-391j
0.14605170802291631437 - 1.4074016285802968103e-1188j 3.53e-135, 3.18e-381j
9.7129984891864646044e-16 - 5.9868473257912564041e-1200j 1.1e-152, 9.92e-399j
4.9440680478770157205e-07 + 1.1302545161633944061e-1193j 4.17e-144, 3.76e-390j
2.5536093016241924955e-08 + 5.1663663175002467312e-1195j 1.06e-145, 9.53e-392j
0.11705929078300033969 + 1.5349892922291423238e-1189j 1.78e-137, 1.6e-383j
2.3400177436338621917e-06 - 1.464831473459132671e-1193j 5.76e-144, 5.19e-390j
0.022506517297301976735 + 1.0401980729444985886e-1189j 2.8e-139, 2.52e-385j
0.10558965057450030294 - 1.632005098557859301e-1189j 7.58e-139, 6.83e-385j
2.2562617113828556699e-27 + 1.2534466333145043316e-1206j 1.2e-161, 1.08e-407j
2.2562617113828556699e-27 + 2.4406364852995066081e-1207j 2.64e-160, 2.38e-406j
-0.27874348221448757952 + 3.3102632970484014229e-1188j 6.16e-140, 5.57e-386j
3.8451481163502808037e-20 + 1.4353487375527612551e-1202j 1.42e-157, 1.28e-403j
0.11705929078300033969 + 1.5935703425662606698e-1189j 2.12e-142, 1.93e-388j
2.1238243484364641847e-25 - 1.5307473753627187515e-1205j 1.01e-160, 9.07e-407j
0.12015235704037053095 - 1.58834910195714579e-1189j 2.24e-142, 2.04e-388j

Download

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