Rule: Q[3, 10, 92]

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)
10.084260548673563665 + 1.4816630972568493755e-1077j 2.52e-487, 2.52e-487j
8.8843224786380452995 + 7.1802231926291664229e-1082j 2.71e-486, 2.71e-486j
9.771946318462205891 - 1.543226168275847048e-1087j 5.09e-487, 5.09e-487j
12.76492059966650665 - 2.8460432424221259392e-1101j 8.58e-493, 8.58e-493j
6.0054305489496619708 - 1.8606551502889312009e-1093j 2.15e-487, 2.15e-487j
-10.742243158749625769 + 1.4766881587231149843e-1103j 2.87e-488, 2.87e-488j
-10.084260548673563665 - 7.7570464181035034168e-1102j 2.46e-487, 2.46e-487j
7.7842612712996253762 + 3.065549565557246484e-1107j 4.35e-486, 4.35e-486j
-12.76492059966650665 + 6.0712939379477183646e-1131j 8.57e-493, 8.57e-493j
6.7498112329375045676 - 2.8660837624155146e-1125j 1.37e-486, 1.37e-486j
11.461743318258994499 - 2.7654148011577559146e-1134j 1.16e-489, 1.16e-489j
-12.283772491503991738 + 1.1754020195187616649e-1141j 1.61e-491, 1.61e-491j
-8.324470754724349054 + 9.2798787718981816818e-1135j 4.31e-486, 4.31e-486j
13.348010381795830308 - 4.790596837469030766e-1146j 1.66e-494, 1.66e-494j
9.4685970670374011391 + 1.6908921750900582843e-1144j 1.08e-486, 1.08e-486j
5.282353368685460341 + 2.6087831412205126054e-1154j 1.61e-488, 1.61e-488j
3.0861978955818831873 - 4.8400763088845872584e-1168j 3.22e-493, 3.22e-493j
10.742243158749625769 + 2.2082863834553104701e-1160j 2.54e-488, 2.54e-488j
-2.6905491827044430304 - 9.1677846452472077953e-1175j 3.61e-494, 3.61e-494j
-4.1180864274630133413 + 2.1976439840536590035e-1172j 7.18e-491, 7.18e-491j
12.283772491503991738 + 3.8413860011823891488e-1167j 1.62e-491, 1.62e-491j
1.2247448713915890491 - 1.0954600324228524636e-1183j 1.06e-502, 1.06e-502j
-11.092544696219986248 - 1.3522632438563259246e-1167j 6.4e-489, 6.4e-489j
2.6905491827044430304 - 7.1308418364509751041e-1183j 3.74e-494, 3.74e-494j
-9.771946318462205891 - 5.9546248104789789713e-1174j 5.53e-487, 5.53e-487j
8.6016809918237152246 + 2.9420778194287029533e-1191j 3.99e-486, 3.99e-486j
2.2939038893319927253 - 1.598288176929832688e-1217j 1.12e-496, 1.12e-496j
-13.348010381795830308 - 1.6142964690082397937e-1215j 1.65e-494, 1.65e-494j
-6.7498112329375045676 - 1.2363145180797179642e-1206j 1.34e-486, 1.34e-486j
-0.81190435658534425804 + 2.0261941743832496649e-1226j 4.65e-505, 4.65e-505j
-10.407038084777186803 + 3.0196269940671160106e-1207j 8.8e-488, 8.8e-488j
-8.6016809918237152246 + 2.2881245415332276089e-1205j 3.75e-486, 3.75e-486j
-9.1730370883323747345 + 1.0668900611647215753e-1206j 1.78e-486, 1.78e-486j
11.092544696219986248 - 1.0683946881928342743e-1207j 6.4e-489, 6.4e-489j
-11.855610394913119354 - 3.1475625340560730359e-1216j 1.71e-490, 1.71e-490j
-5.7622253194423724801 - 5.4334520804544112944e-1215j 9.86e-488, 9.86e-488j
-7.260238593597635359 - 1.3609413985281578564e-1216j 2.84e-486, 2.84e-486j
1.0172897667160791645 - 3.0059165109347990221e-1241j 7.28e-504, 7.28e-504j
-4.5776482477056425818 + 1.2127688921242146263e-1227j 7.44e-490, 7.44e-490j
-5.5212370197480455836 + 2.8192726429704136334e-1224j 4.35e-488, 4.35e-488j
-2.0759775802189017265 - 1.1246460290265570441e-1248j 5.82e-498, 5.82e-498j
-3.6704815520819829124 - 2.361831465187679799e-1242j 6.98e-492, 6.98e-492j
9.1730370883323747345 + 9.5909572908829089799e-1235j 1.88e-486, 1.88e-486j
2.0759775802189017265 + 1.4463522820767619125e-1258j 5.69e-498, 5.69e-498j
-3.2595330824338197843 + 8.1589469125667687785e-1254j 8.95e-493, 8.95e-493j
-1.0172897667160791645 + 1.1173448369765164702e-1265j 7.2e-504, 7.2e-504j
4.810588265852077174 + 1.5124379944193788484e-1246j 2.28e-489, 2.28e-489j
3.2595330824338197843 - 4.581240094506262776e-1255j 9.07e-493, 9.07e-493j
1.4344676577696694623 - 7.2081569195694940693e-1264j 1.74e-501, 1.74e-501j
-4.3467409652850942258 - 6.1647731979711826827e-1253j 2.44e-490, 2.44e-490j
5.0454881552006742228 + 6.755867623440768779e-1248j 6.05e-489, 6.05e-489j
-2.5296025834934300893 + 3.8540470678949503312e-1261j 9.48e-495, 9.48e-495j
-3.8922223103096910814 - 3.3025906845035981513e-1259j 2.2e-491, 2.2e-491j
-9.4685970670374011391 - 1.136309509432205154e-1251j 1.07e-486, 1.07e-486j
-6.0054305489496619708 - 1.0150754596408878263e-1260j 2.09e-487, 2.09e-487j
8.324470754724349054 + 4.6042491544837639169e-1275j 4.21e-486, 4.21e-486j
-6.4990548123726955686 - 1.8571524787360579896e-1291j 7.81e-487, 7.81e-487j
11.855610394913119354 - 4.1630659462849678374e-1291j 1.72e-490, 1.72e-490j
-11.461743318258994499 + 1.5564415333016260692e-1300j 1.18e-489, 1.18e-489j
2.5924866326706538145 + 6.0472691793231500605e-1329j 2.73e-494, 2.73e-494j
10.407038084777186803 - 4.5027164759713916557e-1333j 8.97e-488, 8.97e-488j
-1.8602834494799461889 - 5.1613555413180935303e-1380j 3.93e-499, 3.93e-499j
6.4990548123726955686 + 5.2397818627311788119e-1380j 7.52e-487, 7.52e-487j
-6.2509879386772345019 - 3.1931066666709187548e-1406j 4.27e-487, 4.27e-487j
-4.810588265852077174 + 6.6888075723415695203e-1417j 2.13e-489, 2.13e-489j
4.3467409652850942258 - 9.5611796712024607557e-1443j 2.38e-490, 2.38e-490j
7.260238593597635359 - 9.0055519775684394489e-1468j 2.98e-486, 2.98e-486j
-1.6463854426291250606 + 4.6836579430190289351e-1505j 2.31e-500, 2.31e-500j
4.1180864274630133413 + 9.8682544649977926159e-1493j 7.6e-491, 7.6e-491j
-5.282353368685460341 - 2.4532270064903029534e-1491j 1.6e-488, 1.6e-488j
0.81190435658534425804 - 1.9390803235272622796e-1519j 4.54e-505, 4.54e-505j
8.0521510735262690706 + 6.7803832059129271196e-1500j 4.51e-486, 4.51e-486j
-1.4344676577696694623 - 5.7757230394639975248e-1540j 1.53e-501, 1.53e-501j
5.7622253194423724801 + 1.2541249436289592856e-1523j 9.71e-488, 9.71e-488j
-7.520405027495181383 - 2.403135117907107181e-1532j 3.79e-486, 3.79e-486j
1.8602834494799461889 + 1.6704299837080217432e-1549j 3.6e-499, 3.6e-499j
4.5776482477056425818 + 1.4176101647701622757e-1537j 7.66e-490, 7.66e-490j
-2.5924866326706538145 - 7.3003456531154095475e-1544j 2.6e-494, 2.6e-494j
-0.40515420497453451728 - 2.9492207290430117239e-1557j 1.56e-507, 1.56e-507j
-7.0034618137247146872 - 1.7755740038005674758e-1535j 2.04e-486, 2.04e-486j
7.520405027495181383 - 1.7602327796742970652e-1540j 3.7e-486, 3.7e-486j
3.8922223103096910814 + 3.6311391806688268842e-1558j 2.38e-491, 2.38e-491j
-7.7842612712996253762 - 7.7636961843754989507e-1553j 4.43e-486, 4.43e-486j
-0.20255323945411544562 + 7.9792921486844206738e-1575j 7.2e-509, 7.2e-509j
-3.0861978955818831873 - 1.0045772016907336545e-1560j 3.19e-493, 3.19e-493j
-5.0454881552006742228 - 4.9998514671716042662e-1556j 6.2e-489, 6.2e-489j
0.60808265691331281929 + 1.4003040754650244914e-1572j 2.84e-506, 2.84e-506j
2.5296025834934300893 + 6.8905876015570712727e-1561j 9.04e-495, 9.04e-495j
0.40515420497453451728 - 6.3981093212653891334e-1574j 1.37e-507, 1.37e-507j
-1.2247448713915890491 + 1.0493824030346043313e-1569j 1.07e-502, 1.07e-502j
6.2509879386772345019 - 2.5292936156825976227e-1551j 4.19e-487, 4.19e-487j
2.9059310212658523636 + 8.7009864933472313441e-1566j 8.96e-494, 8.96e-494j
-1.230761805191825703e-1643 + 6.2702785847365792304e-1645j 1.29e-1641, 1.29e-1641j
5.5212370197480455836 + 1.6203373525766767423e-1557j 4.19e-488, 4.19e-488j
-2.2939038893319927253 + 5.4098442738058190213e-1574j 1.11e-496, 1.11e-496j
-3.4564690254692822479 + 2.7270849432948060005e-1569j 2.39e-492, 2.39e-492j
3.6704815520819829124 - 3.6917818563868069349e-1569j 6.97e-492, 6.97e-492j
0.20255323945411544562 - 5.9730535526135631186e-1638j 7.2e-509, 7.2e-509j
3.4564690254692822479 + 3.2962658344423249644e-1569j 2.33e-492, 2.33e-492j
-8.8843224786380452995 + 5.8410544238288774314e-1562j 2.7e-486, 2.7e-486j
-0.60808265691331281929 - 5.7963552233428892159e-1583j 2.82e-506, 2.82e-506j
-8.0521510735262690706 + 2.015833748865549865e-1563j 4.49e-486, 4.49e-486j
7.0034618137247146872 + 4.2428680743266046709e-1562j 2.17e-486, 2.17e-486j
1.6463854426291250606 - 4.0150991274398779001e-1581j 2.67e-500, 2.67e-500j
-2.9059310212658523636 + 1.091763406067939583e-1575j 8.93e-494, 8.93e-494j

Weights

Weight (ball center) Error (ball radius)
1.2258446717421757214e-45 - 1.674195314895060378e-1121j 2.87e-130, 2.75e-370j
8.4673203628954465816e-36 - 6.1247694376037790953e-1116j 3.41e-125, 3.27e-365j
5.8646636182772424032e-43 + 5.729814957618346799e-1121j 5.63e-129, 5.39e-369j
5.0250295934383499774e-72 - 2.2196228079779072311e-1136j 1.65e-142, 1.58e-382j
2.9959466709202567606e-17 + 7.7524800639926421015e-1107j 8.78e-110, 8.42e-350j
1.4790840799466030501e-51 - 1.8665336062876046943e-1126j 3.63e-138, 3.47e-378j
1.2258446717421757214e-45 - 2.6185232962722182033e-1123j 1.71e-135, 1.64e-375j
7.2451115300085621456e-28 - 1.5321968125150405926e-1112j 7.81e-122, 7.49e-362j
5.0250295934383499774e-72 + 3.3651958312485942316e-1137j 1.13e-146, 1.08e-386j
2.3263662844329242197e-21 - 3.9454825838341497213e-1109j 1.8e-116, 1.72e-356j
1.8951972455297898697e-58 + 4.5370904512004164101e-1129j 4.66e-139, 4.47e-379j
7.4773273543076519175e-67 - 1.6847008038419214549e-1134j 4.01e-145, 3.85e-385j
1.2446057141712728296e-31 - 9.935502722404612283e-1116j 7.59e-130, 7.27e-370j
1.5945618851930601179e-78 + 8.0401201985919029781e-1140j 5.8e-147, 5.56e-387j
1.9548900781037107382e-40 + 1.564921624182213962e-1119j 2.58e-130, 2.47e-370j
1.0221636898067861202e-13 - 9.4258877250697668134e-1105j 6.71e-111, 6.43e-351j
6.9795482480075191472e-06 - 1.2666358731053741076e-1098j 1.42e-92, 1.36e-332j
1.4790840799466030501e-51 + 3.3269097835032734356e-1125j 2.37e-136, 2.27e-376j
0.00010833946859919088625 - 1.0828895209765370493e-1097j 5.69e-91, 5.45e-331j
5.5354822275160836714e-09 + 5.29739550221649959e-1102j 2.81e-107, 2.7e-347j
7.4773273543076519175e-67 + 1.2782678516957082851e-1133j 4.38e-143, 4.2e-383j
0.026257919811995209565 - 2.1973010216691727667e-1097j 4.17e-63, 3.99e-303j
7.3950348542424013021e-55 + 3.3529923850888256761e-1128j 7.65e-144, 7.33e-384j
0.00010833946859919088625 - 1.9727158156696525829e-1097j 1.54e-91, 1.47e-331j
5.8646636182772424032e-43 + 7.1077698833918292024e-1122j 2.86e-139, 2.74e-379j
1.1623543511497201756e-33 + 3.435577612691321042e-1115j 1.71e-129, 1.64e-369j
0.00064330394928592436375 + 1.0976277697826756223e-1097j 1.41e-87, 1.35e-327j
1.5945618851930601179e-78 - 1.4005522489629131718e-1140j 1.62e-153, 1.55e-393j
2.3263662844329242197e-21 - 6.0316604454302366603e-1110j 7.13e-129, 6.83e-369j
0.059680292610012625074 - 2.7372979669509662844e-1097j 5.55e-71, 5.32e-311j
1.703032580872223166e-48 + 7.8658752309792126312e-1125j 2.13e-141, 2.04e-381j
1.1623543511497201756e-33 + 7.6411632003045658233e-1117j 2.48e-136, 2.38e-376j
4.7126184427346409557e-38 + 3.1152438427930376929e-1119j 2.37e-138, 2.27e-378j
7.3950348542424013021e-55 - 4.4142636380523202569e-1127j 6.1e-144, 5.85e-384j
2.0921564284425257015e-62 + 3.5859635065707779396e-1132j 2.31e-148, 2.22e-388j
5.192694274782159921e-16 - 9.2440268513167614228e-1107j 1.13e-126, 1.09e-366j
1.8691101638085165064e-24 - 1.0113294164389549822e-1111j 4.06e-133, 3.89e-373j
0.041362712495176856695 + 2.7206102268644724869e-1097j 3.09e-78, 2.96e-318j
1.0380734103033403063e-10 + 2.6970178369159593057e-1103j 1.04e-120, 9.92e-361j
7.8060610088339769333e-15 + 4.9844618710803573188e-1106j 1.13e-125, 1.08e-365j
0.001642198553942867843 - 6.4217377766367669974e-1098j 5.46e-100, 5.23e-340j
1.7397453000446917278e-07 + 1.0509145211616166684e-1100j 3.92e-115, 3.75e-355j
4.7126184427346409557e-38 - 1.053161122316387225e-1117j 1.12e-140, 1.07e-380j
0.001642198553942867843 - 1.0142629444189110236e-1097j 1.21e-100, 1.16e-340j
2.5227635098265545901e-06 + 2.0385633158017117277e-1099j 1.44e-112, 1.38e-352j
0.041362712495176856695 + 2.1811892325431497015e-1097j 6.38e-85, 6.12e-325j
1.1753350422071737042e-11 - 1.8794026332987703886e-1103j 6.63e-125, 6.35e-365j
2.5227635098265545901e-06 + 4.2621923259399675614e-1099j 8.72e-114, 8.36e-354j
0.015196727871725513801 + 1.7455231337912663204e-1097j 1.79e-93, 1.71e-333j
8.0763328956859346501e-10 - 1.2027127904143131992e-1102j 1.67e-120, 1.6e-360j
1.1703006438986184959e-12 + 4.2838945233963470308e-1104j 4.32e-126, 4.14e-366j
0.0003112973227944945527 - 2.3455040463738482628e-1097j 2.13e-108, 2.04e-348j
3.3314866868526035273e-08 - 2.3378854630478623839e-1101j 1.02e-117, 9.75e-358j
1.9548900781037107382e-40 - 1.6121351820910796787e-1120j 1.36e-143, 1.3e-383j
2.9959466709202567606e-17 + 1.6226601514897385799e-1107j 7.94e-131, 7.61e-371j
1.2446057141712728296e-31 - 2.3628562300357140503e-1114j 6.71e-142, 6.43e-382j
6.3779370200057494948e-20 + 4.1635741323978695613e-1109j 1.81e-133, 1.73e-373j
2.0921564284425257015e-62 - 3.1715921804850817303e-1131j 1.04e-155, 9.96e-396j
1.8951972455297898697e-58 - 4.2947298917337128772e-1130j 7.24e-153, 6.93e-393j
-0.00013426751337785002791 + 5.2463614893893702657e-1097j 9.69e-115, 9.29e-355j
1.703032580872223166e-48 - 2.3719017169605425369e-1123j 3.35e-149, 3.21e-389j
0.0038066199777038835954 + 7.5932937851610247803e-1098j 2.39e-110, 2.29e-350j
6.3779370200057494948e-20 + 2.4226697107574711301e-1108j 2e-137, 1.92e-377j
1.4919364985748438304e-18 - 2.6837551395478591316e-1108j 1.63e-133, 1.56e-373j
1.1753350422071737042e-11 - 5.9075618005001614936e-1104j 8.34e-128, 7.99e-368j
8.0763328956859346501e-10 - 3.3451797154146104577e-1102j 1.07e-129, 1.03e-369j
1.8691101638085165064e-24 - 8.7351731297767660832e-1111j 7.03e-141, 6.73e-381j
0.0079892670216821052178 - 9.7013024295132181908e-1098j 9.1e-113, 8.72e-353j
5.5354822275160836714e-09 + 1.3833550678205481572e-1101j 3.56e-129, 3.41e-369j
1.0221636898067861202e-13 - 2.5560685415561552288e-1105j 1.35e-131, 1.3e-371j
0.059680292610012625074 - 3.2643980712553216184e-1097j 3.66e-109, 3.51e-349j
1.0578701581398278733e-29 + 1.8999822366275622899e-1113j 8.34e-143, 7.99e-383j
0.015196727871725513801 + 1.2765383505417293365e-1097j 1.13e-113, 1.08e-353j
5.192694274782159921e-16 - 4.0261189999420052272e-1106j 6.65e-136, 6.37e-376j
4.0502733671719102702e-26 + 1.1586050722439482497e-1112j 2.44e-142, 2.34e-382j
0.0038066199777038835954 + 1.1420312889651760572e-1097j 3.87e-119, 3.71e-359j
1.0380734103033403063e-10 + 8.0109297359219503881e-1103j 1.24e-131, 1.18e-371j
-0.00013426751337785002791 + 2.9473430665181354285e-1097j 2.19e-122, 2.1e-362j
0.097044710293510735742 - 3.779455778240161303e-1097j 5.62e-115, 5.38e-355j
7.1907788683785936683e-23 + 8.1213109932203403839e-1111j 5.49e-140, 5.26e-380j
4.0502733671719102702e-26 + 1.1884463795252652714e-1111j 1.86e-142, 1.78e-382j
3.3314866868526035273e-08 - 5.7465088869332507683e-1101j 9.47e-131, 9.08e-371j
7.2451115300085621456e-28 - 1.2140680915402615289e-1113j 6.94e-144, 6.65e-384j
0.10968601623439407994 + 4.1363288142613674196e-1097j 4.23e-119, 4.05e-359j
6.9795482480075191472e-06 - 6.3221262424901736942e-1099j 1.94e-127, 1.86e-367j
1.1703006438986184959e-12 + 1.2530897756604806039e-1104j 3.29e-133, 3.15e-373j
0.079231216321168947286 + 3.7568509942567865773e-1097j 3.84e-120, 3.68e-360j
0.0003112973227944945527 - 4.1138870295467285958e-1097j 1.26e-125, 1.21e-365j
0.097044710293510735742 - 4.1259043432926938765e-1097j 1.99e-120, 1.9e-360j
0.026257919811995209565 - 1.6831693299433994648e-1097j 6.77e-122, 6.49e-362j
1.4919364985748438304e-18 - 1.4024310341806279637e-1107j 1.74e-139, 1.66e-379j
2.3614666066564058179e-05 + 3.2705746692866135771e-1098j 2.35e-128, 2.26e-368j
0.11427911165563427536 - 4.3239800519304594574e-1097j 2.7e-123, 2.59e-363j
7.8060610088339769333e-15 + 1.9916649013787531288e-1105j 3.56e-137, 3.41e-377j
0.00064330394928592436375 + 6.6106073859656414479e-1098j 1.53e-127, 1.47e-367j
7.5902638992426153931e-07 - 4.820239116015427697e-1100j 4.47e-131, 4.28e-371j
1.7397453000446917278e-07 + 2.4377841564133375717e-1100j 3.21e-132, 3.08e-372j
0.10968601623439407994 + 4.3216382896193434538e-1097j 1.2e-125, 1.15e-365j
7.5902638992426153931e-07 - 1.0587023845501294631e-1099j 1.72e-131, 1.64e-371j
8.4673203628954465816e-36 - 5.2101912574287337137e-1118j 1.95e-151, 1.87e-391j
0.079231216321168947286 + 3.2931322066913158476e-1097j 2.16e-128, 2.07e-368j
1.0578701581398278733e-29 + 1.1562047869137571121e-1114j 4.38e-148, 4.2e-388j
7.1907788683785936683e-23 + 6.051179832962918268e-1110j 2.81e-144, 2.68e-384j
0.0079892670216821052178 - 1.3906376249274850504e-1097j 9.31e-131, 8.81e-371j
2.3614666066564058179e-05 + 1.7053489263134430778e-1098j 6.26e-132, 6.08e-372j

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