Rule: Q[1, 94]

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.

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)
14.726385211953821997 - 1.5233748098968429169e-1069j 9.69e-489, 9.69e-489j
15.22670748514194014 + 8.1369999518575276039e-1071j 2.4e-489, 2.4e-489j
16.316080822742251883 + 4.0693495819048869833e-1071j 1.12e-490, 1.12e-490j
13.3397222642386006 + 1.3820898025390073604e-1071j 1.59e-487, 1.59e-487j
-17.613458051057314719 - 1.3246149764224478234e-1093j 5.43e-493, 5.43e-493j
9.3741879348923732137 + 1.57318298928330207e-1084j 1.86e-487, 1.86e-487j
17.613458051057314719 + 4.1105677353407052423e-1096j 5.42e-493, 5.42e-493j
-15.22670748514194014 + 1.9856907101860237422e-1100j 2.35e-489, 2.35e-489j
16.927069173894068608 - 3.0631409314064293551e-1097j 1.04e-491, 1.04e-491j
-3.8833856575152501183 - 1.9791297652656639508e-1111j 2.11e-496, 2.11e-496j
5.540156832966989726 + 4.1590904978093709711e-1108j 1.53e-492, 1.53e-492j
-16.927069173894068608 - 2.0957036190634118411e-1107j 9.89e-492, 9.89e-492j
-6.2143436932799702974 - 6.0598719838622459165e-1107j 3.29e-491, 3.29e-491j
-9.0099092168524540137 - 7.6859003255538885042e-1102j 1.04e-487, 1.04e-487j
-9.7427471922581067907 + 3.8582333198868628998e-1102j 2.9e-487, 2.9e-487j
4.211986825302162749 + 1.156721319262707272e-1116j 1.91e-495, 1.91e-495j
6.5544795200976155824 - 8.2225270638634845039e-1112j 1.18e-490, 1.18e-490j
-15.753865088167804083 - 1.8425137917287861509e-1108j 4.61e-490, 4.61e-490j
-2.9039815174901952033 + 5.8768775158892622865e-1122j 4.66e-499, 4.66e-499j
-4.8730696769462363631 - 2.1858004382856395099e-1115j 6.3e-494, 6.3e-494j
7.9394513345858440242 + 5.8285704755132191435e-1108j 7.11e-489, 7.11e-489j
1.9319918835967641427 - 1.6208731970652132257e-1145j 2.53e-502, 2.53e-502j
11.665377114924152361 + 7.2570749997272221918e-1127j 7.65e-487, 7.65e-487j
-9.3741879348923732137 - 3.0369449741454716234e-1147j 1.79e-487, 1.79e-487j
-1.9319918835967641427 - 1.6274813452759907346e-1161j 2.49e-502, 2.49e-502j
8.292838100144883984 + 7.0424069993130408255e-1145j 2.66e-488, 2.66e-488j
18.444995206594627938 - 2.6225705462665654358e-1152j 1.25e-494, 1.25e-494j
-2.255329529691504308 + 1.8938716954978443836e-1161j 3.88e-501, 3.88e-501j
-12.48312896506114805 - 2.9316249150267437593e-1146j 4.57e-487, 4.57e-487j
-10.115976611533334836 + 4.8338479259699623484e-1156j 4.57e-487, 4.57e-487j
12.069980901668103428 - 1.1212138621978139042e-1169j 6.16e-487, 6.16e-487j
7.241690341741019194 - 2.4936964943851573035e-1186j 1.24e-489, 1.24e-489j
2.9039815174901952033 - 3.4216251457407716747e-1196j 4.48e-499, 4.48e-499j
3.8833856575152501183 - 2.8984918209786861282e-1193j 2.06e-496, 2.06e-496j
1.2868243444556285651 + 1.0940002355715334533e-1201j 1.42e-504, 1.42e-504j
-12.069980901668103428 + 2.9345672060093290952e-1182j 6.11e-487, 6.11e-487j
-18.444995206594627938 - 6.7973012949130733204e-1195j 1.23e-494, 1.23e-494j
1.6091874075997044488 - 1.2327616373037018552e-1204j 2.18e-503, 2.18e-503j
-10.878265011202223208 + 6.3358311685670229147e-1186j 6.15e-487, 6.15e-487j
-5.8762892257006734839 - 5.4591469812745231375e-1201j 8.43e-492, 8.43e-492j
2.5792940587805195072 + 8.9577015048774852059e-1209j 3.88e-500, 3.88e-500j
-14.726385211953821997 - 6.0113967233566122766e-1195j 9.73e-489, 9.73e-489j
13.786195069589500367 - 1.0631128258192633732e-1211j 7.61e-488, 7.61e-488j
2.255329529691504308 - 2.4031711881803415084e-1263j 4.04e-501, 4.04e-501j
-8.6495633569895287066 + 1.177473858383839349e-1248j 5.27e-488, 5.27e-488j
-2.5792940587805195072 - 7.5476571467234936648e-1288j 3.92e-500, 3.92e-500j
10.878265011202223208 - 9.6912946625300044219e-1294j 6.37e-487, 6.37e-487j
-14.247482456113389943 + 3.0019322469061217102e-1329j 2.97e-488, 2.97e-488j
10.115976611533334836 - 1.4920417516375278506e-1363j 4.41e-487, 4.41e-487j
6.8968672709856590444 - 2.8260087389777406782e-1391j 4.12e-490, 4.12e-490j
-7.5891467659459332791 - 3.8601229629776572338e-1392j 3.32e-489, 3.32e-489j
-0.96481253589804791572 + 3.7500614338398474651e-1433j 1.01e-505, 1.01e-505j
14.247482456113389943 - 5.9472828701614009849e-1419j 3.1e-488, 3.1e-488j
6.2143436932799702974 + 1.9495483446076198145e-1444j 3.18e-491, 3.18e-491j
10.494315881397543963 + 4.5226803474104601016e-1456j 5.44e-487, 5.44e-487j
-12.905926425229825824 - 6.9187968126810437195e-1472j 2.91e-487, 2.91e-487j
15.753865088167804083 + 5.1161636916543138344e-1481j 4.54e-490, 4.54e-490j
12.48312896506114805 + 1.1507640837880225993e-1512j 4.51e-487, 4.51e-487j
4.5418415419278368881 + 6.7487584481069184962e-1550j 1.09e-494, 1.09e-494j
0.96481253589804791572 + 1.3307129948057436969e-1561j 9.83e-506, 9.83e-506j
5.8762892257006734839 - 1.0153126289072006835e-1546j 8.34e-492, 8.34e-492j
11.268397448784670318 - 3.5188094131101990105e-1541j 6.01e-487, 6.01e-487j
-0.64306308314118281987 - 4.0799312458388398268e-1571j 4.72e-507, 4.72e-507j
-10.494315881397543963 - 9.0417196209968346751e-1551j 5.24e-487, 5.24e-487j
3.5559235354798363118 - 1.4657986075161014847e-1562j 3.16e-497, 3.16e-497j
-5.540156832966989726 + 1.49798558002838418e-1557j 1.51e-492, 1.51e-492j
-7.9394513345858440242 - 2.9958895319119504544e-1554j 7.09e-489, 7.09e-489j
-3.5559235354798363118 + 8.1021195310370385641e-1562j 3.17e-497, 3.17e-497j
-5.2057971719548570456 - 4.001557921006558779e-1558j 3.48e-493, 3.48e-493j
-13.3397222642386006 - 1.502510694618712939e-1552j 1.6e-487, 1.6e-487j
7.5891467659459332791 - 3.1285368090727750982e-1553j 3.21e-489, 3.21e-489j
-4.211986825302162749 + 2.2580904936006142785e-1561j 1.91e-495, 1.91e-495j
-16.316080822742251883 - 1.5289003127249901512e-1556j 1.09e-490, 1.09e-490j
-7.241690341741019194 + 1.2796859810228422275e-1555j 1.24e-489, 1.24e-489j
12.905926425229825824 + 9.4700359636379290396e-1551j 2.96e-487, 2.96e-487j
4.8730696769462363631 + 1.3480885214128814903e-1561j 6.37e-494, 6.37e-494j
5.2057971719548570456 - 2.2855179448522221009e-1560j 3.31e-493, 3.31e-493j
-13.786195069589500367 + 7.6012124591866361526e-1556j 8.23e-488, 8.23e-488j
-1.6091874075997044488 - 7.3189109919496111302e-1571j 2.24e-503, 2.24e-503j
-6.8968672709856590444 - 2.6368622931761980028e-1558j 4.21e-490, 4.21e-490j
8.6495633569895287066 + 2.4792812315504582558e-1555j 5.32e-488, 5.32e-488j
0.64306308314118281987 - 1.5241056360636536827e-1575j 5.15e-507, 5.15e-507j
-11.665377114924152361 - 9.7487632221508515965e-1555j 7.87e-487, 7.87e-487j
-4.5418415419278368881 - 3.8052436888995813922e-1563j 1.08e-494, 1.08e-494j
-8.292838100144883984 + 6.15753532851332164e-1557j 2.71e-488, 2.71e-488j
9.7427471922581067907 + 2.5015903273799717839e-1553j 2.98e-487, 2.98e-487j
0.32148802070571970618 + 2.5029520588485332859e-1581j 1.22e-508, 1.22e-508j
7.1039494655348853593e-1642 - 7.4929602872344134059e-1643j 6.79e-1640, 6.79e-1640j
-3.2294906903657862144 - 7.7844341188666665607e-1572j 4.05e-498, 4.05e-498j
-0.32148802070571970618 - 2.3573804603273160284e-1581j 1.22e-508, 1.22e-508j
-11.268397448784670318 - 2.7721539487891122433e-1560j 6.08e-487, 6.08e-487j
3.2294906903657862144 - 4.7317179995612353563e-1572j 3.95e-498, 3.95e-498j
9.0099092168524540137 - 6.7492790195237648912e-1560j 1.04e-487, 1.04e-487j
-6.5544795200976155824 + 7.2618029774169486925e-1565j 1.19e-490, 1.19e-490j
-1.2868243444556285651 - 2.7551456803510780613e-1578j 1.41e-504, 1.41e-504j

Weights

Weight (ball center) Error (ball radius)
1.5781896481861856048e-48 - 2.3309244179582433251e-1115j 7.34e-136, 3.8e-378j
9.2168164951538673819e-52 + 4.5696529300358075982e-1117j 2.43e-137, 1.26e-379j
3.6249653405618984403e-59 + 5.6732025481835433926e-1121j 7.96e-141, 4.12e-383j
4.0107729924378820857e-40 - 3.6999489003569879521e-1110j 1.66e-133, 8.59e-376j
1.2698222441807732408e-68 - 1.0150652617965920664e-1126j 6.94e-149, 3.59e-391j
1.2103610981302244894e-20 - 7.8076570237031501626e-1102j 1.1e-121, 5.69e-364j
1.2698222441807732408e-68 + 7.3753523245842603346e-1126j 4.22e-145, 2.19e-387j
9.2168164951538673819e-52 - 2.9631656052848141343e-1118j 4.16e-144, 2.16e-386j
1.550567224513162167e-63 - 3.0734437814284148343e-1123j 5.64e-143, 2.92e-385j
6.9513976320109699348e-05 - 1.3495807760395638011e-1094j 1.42e-93, 7.36e-336j
2.8924699100740719426e-08 + 6.0786666602758602449e-1096j 1.78e-105, 9.22e-348j
1.550567224513162167e-63 + 3.6274793674384580987e-1124j 6.6e-148, 3.42e-390j
5.5640327696894640234e-10 + 3.363138968563600023e-1097j 5.86e-112, 3.04e-354j
3.4060258107589913481e-19 + 7.280370974819274013e-1102j 7.41e-126, 3.84e-368j
3.6159278623816397153e-22 + 2.2968387856589734947e-1103j 8.5e-129, 4.4e-371j
1.8450497294197409431e-05 + 1.3118086497270274965e-1094j 8.94e-100, 4.63e-342j
6.3834259625762909294e-11 - 3.2828436771635684735e-1097j 1.39e-114, 7.19e-357j
2.7744195103676275875e-55 + 5.0479109883361542994e-1120j 3.39e-146, 1.76e-388j
0.0019128291467162905769 + 7.506222640406640446e-1094j 5.02e-89, 2.6e-331j
9.2350042719617003878e-07 + 1.4710315864235803345e-1095j 7.44e-106, 3.85e-348j
2.8797849856229697382e-15 - 2.7721435179710094657e-1099j 7.21e-122, 3.74e-364j
0.019937246110455258849 - 3.4504009023623821837e-1093j 2.47e-78, 1.28e-320j
4.5087698733560791213e-31 - 1.1137245740731785272e-1106j 3.34e-135, 1.73e-377j
1.2103610981302244894e-20 - 1.3504141795123521771e-1102j 1.15e-128, 5.98e-371j
0.019937246110455258849 - 2.5775493728263351712e-1093j 2.47e-80, 1.28e-322j
1.6507592706642157163e-16 + 7.1052539525520345295e-1100j 1.27e-123, 6.59e-366j
5.0910680309123675737e-75 - 3.9065761547076961342e-1129j 1.9e-152, 9.85e-395j
0.010149485842885909959 + 1.800941051653703168e-1093j 5.93e-86, 3.07e-328j
2.4216823517371680279e-35 - 5.3133366131226636468e-1110j 7.41e-141, 3.84e-383j
9.0039651906413041377e-24 - 3.566751902283904747e-1104j 2.9e-132, 1.5e-374j
3.7787665212995209659e-33 + 1.3440550094295240962e-1107j 6.14e-137, 3.18e-379j
5.6554309308958149584e-13 - 3.4388046212620028061e-1098j 3.97e-121, 2.06e-363j
0.0019128291467162905769 + 1.1682774783618613383e-1093j 7.06e-98, 3.66e-340j
6.9513976320109699348e-05 - 2.4577753158944571068e-1094j 4.55e-105, 2.36e-347j
0.056159183207386805835 - 5.4809925350454851586e-1093j 1.26e-77, 6.51e-320j
3.7787665212995209659e-33 + 6.7450778896336046802e-1109j 2.17e-140, 1.13e-382j
5.0910680309123675737e-75 + 6.2591577601825893012e-1130j 1.56e-157, 8.08e-400j
0.035255985064556877661 + 4.4620745970939254781e-1093j 4.6e-86, 2.38e-328j
3.1050945316418084439e-27 - 6.415147399294527202e-1106j 4.36e-137, 2.26e-379j
4.2693792817480123206e-09 - 9.4799150267748631205e-1097j 1.27e-120, 6.57e-363j
0.0046477428408772141121 - 1.7661360387731198211e-1093j 4.57e-99, 2.37e-341j
1.5781896481861856048e-48 + 1.2480080425278833096e-1116j 7.08e-148, 3.67e-390j
9.6970583363191837993e-43 - 6.0851793213607452103e-1112j 8.64e-145, 4.47e-387j
0.010149485842885909959 + 2.5336374638512390544e-1093j 1.43e-97, 7.41e-340j
8.1193885986440671119e-18 - 3.6128416387728523983e-1101j 3.4e-131, 1.76e-373j
0.0046477428408772141121 - 1.1939088967304477706e-1093j 1.43e-102, 7.42e-345j
3.1050945316418084439e-27 - 6.2874045152899060553e-1105j 2.9e-138, 1.5e-380j
1.5621318517404466484e-45 - 3.9945668596840910123e-1115j 1.16e-147, 6e-390j
9.0039651906413041377e-24 - 2.5818282143327397094e-1103j 1.32e-136, 6.84e-379j
6.4259202019201344589e-12 + 1.0970040572091504326e-1097j 1.57e-126, 8.15e-369j
4.3342373331693764805e-14 + 2.7733472895193731346e-1099j 1.95e-131, 1.01e-373j
0.080621459381274027785 + 5.5335942061931781437e-1093j 9.75e-96, 5.05e-338j
1.5621318517404466484e-45 + 1.1894776112267619818e-1113j 7.18e-147, 3.72e-389j
5.5640327696894640234e-10 + 9.2290076478107139013e-1097j 2.04e-125, 1.06e-367j
1.8506648471592910192e-25 + 4.1975824188511772408e-1104j 9.34e-138, 4.84e-380j
1.158030842443424335e-37 + 3.6150731313468089904e-1111j 1.46e-147, 7.57e-390j
2.7744195103676275875e-55 - 6.1388990930584975606e-1119j 1.34e-151, 6.92e-394j
2.4216823517371680279e-35 - 1.5940645167696079107e-1108j 2.7e-143, 1.4e-385j
4.3724546033877052863e-06 - 6.6254512738162042503e-1095j 4.01e-123, 2.08e-365j
0.080621459381274027785 + 6.3962544614925703683e-1093j 5.45e-105, 2.82e-347j
4.2693792817480123206e-09 - 2.4406062375308942828e-1096j 7.97e-127, 4.13e-369j
4.1988215770937830633e-29 + 8.6889425366814351306e-1106j 3.88e-140, 2.01e-382j
0.10435025952136268969 - 6.440307324529253908e-1093j 6.01e-107, 3.11e-349j
1.8506648471592910192e-25 + 5.0323644881152303588e-1105j 1.99e-143, 1.03e-385j
0.00023422105916897280882 + 4.3604843387156883018e-1094j 2.15e-120, 1.12e-362j
2.8924699100740719426e-08 + 2.5114167577056231649e-1096j 4.86e-132, 2.52e-374j
2.8797849856229697382e-15 - 7.0310557170340215096e-1100j 1.39e-138, 7.19e-381j
0.00023422105916897280882 + 2.5252860015360694601e-1094j 4.76e-126, 2.47e-368j
1.7348918193098009211e-07 - 6.2615086669973041256e-1096j 2.56e-131, 1.32e-373j
4.0107729924378820857e-40 - 2.0929217572109602605e-1112j 2.27e-152, 1.18e-394j
4.3342373331693764805e-14 + 1.0096713195404619645e-1098j 1.36e-135, 7.05e-378j
1.8450497294197409431e-05 + 6.8227722862757064927e-1095j 1.09e-129, 5.62e-372j
3.6249653405618984403e-59 - 5.6606547450447450023e-1122j 9.25e-161, 4.79e-403j
5.6554309308958149584e-13 - 1.0187080270148826389e-1098j 3.75e-138, 1.94e-380j
1.158030842443424335e-37 + 2.1747400006627154944e-1109j 1.61e-148, 8.33e-391j
9.2350042719617003878e-07 + 3.164027906800332821e-1095j 3.27e-131, 1.69e-373j
1.7348918193098009211e-07 - 1.4274923867516102628e-1095j 6.59e-132, 3.41e-374j
9.6970583363191837993e-43 + 1.0121682453842587846e-1113j 3.27e-154, 1.69e-396j
0.035255985064556877661 + 3.5016035242822349202e-1093j 1.77e-126, 9.16e-369j
6.4259202019201344589e-12 + 3.4923740707052590591e-1098j 2.99e-139, 1.55e-381j
8.1193885986440671119e-18 - 1.6973969253295684338e-1100j 9.51e-142, 4.9e-384j
0.10435025952136268969 - 7.0925423678065077596e-1093j 7.03e-127, 3.64e-369j
4.5087698733560791213e-31 - 7.4870471989985722818e-1108j 1.12e-149, 5.77e-392j
4.3724546033877052863e-06 - 3.2601327632085965841e-1095j 1.41e-135, 7.29e-378j
1.6507592706642157163e-16 + 1.6558873299986610077e-1100j 3.43e-142, 1.75e-384j
3.6159278623816397153e-22 + 1.4616451740131005133e-1102j 3.05e-145, 1.53e-387j
0.12180661602010472193 + 7.4736061102701209744e-1093j 5.08e-131, 2.65e-373j
0.1282493807360890884 - 7.4839335655821983796e-1093j 1.52e-131, 7.89e-374j
0.00070681369798608654168 - 4.4732278534611373276e-1094j 6.32e-135, 3.36e-377j
0.12180661602010472193 + 7.1219277069343352922e-1093j 4.86e-132, 2.47e-374j
4.1988215770937830633e-29 + 7.3416551588378177317e-1107j 6.03e-149, 3.13e-391j
0.00070681369798608654168 - 7.330294256935841127e-1094j 2.75e-135, 1.36e-377j
3.4060258107589913481e-19 + 3.7781169371710703125e-1101j 6.83e-144, 3.31e-386j
6.3834259625762909294e-11 - 1.1196676731922872516e-1097j 5.11e-140, 3.03e-382j
0.056159183207386805835 - 4.5167545847967139595e-1093j 1.81e-134, 6.7e-377j

Download

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