Rule: Q[2, 10, 91]

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)
-14.484410852913760143 + 5.283925018842793331e-1044j 4.08e-488, 4.08e-488j
-12.730009000317201699 + 1.64962705734188429e-1042j 7.01e-487, 7.01e-487j
13.150304514059515383 + 6.1753748303753680513e-1042j 4.05e-487, 4.05e-487j
17.150914907635782433 + 1.58385152602407236e-1056j 9.21e-492, 9.21e-492j
13.581613900713963797 + 4.1131766770866542891e-1051j 2.18e-487, 2.18e-487j
-15.458606071057467092 - 8.7739111145931925187e-1064j 3.43e-489, 3.43e-489j
16.542729011090332806 + 9.0183075792245353098e-1064j 1.02e-490, 1.02e-490j
14.960814406119422394 - 1.5092727367108093318e-1060j 1.28e-488, 1.28e-488j
6.8516586047329975368 - 3.4646438564960238014e-1067j 8.23e-490, 8.23e-490j
-11.135466211122398452 + 5.2917462082138841151e-1068j 1.27e-486, 1.27e-486j
7.1896324669645155169 + 1.7338393232172021142e-1070j 2.37e-489, 2.37e-489j
12.319386497977646309 + 6.2626242703033297021e-1075j 9.39e-487, 9.39e-487j
-8.5706735030341366588 - 8.2838907760266973159e-1090j 8.51e-488, 8.51e-488j
-16.542729011090332806 + 3.3901991709872285591e-1095j 9.64e-491, 9.64e-491j
-15.983180435949673526 + 1.7163561411688281291e-1094j 6.57e-490, 6.57e-490j
-17.150914907635782433 - 5.2337395195351216553e-1096j 9.92e-492, 9.92e-492j
-13.581613900713963797 + 1.3595493989431246385e-1091j 2.22e-487, 2.22e-487j
15.983180435949673526 + 1.6713115275385403638e-1090j 6.59e-490, 6.59e-490j
14.484410852913760143 + 5.001684163546323151e-1120j 4.15e-488, 4.15e-488j
11.917339625343016033 + 1.555044592498881399e-1174j 1.17e-486, 1.17e-486j
11.135466211122398452 + 1.3678271671272056939e-1218j 1.24e-486, 1.24e-486j
-7.8740043315169555217 + 1.3735029444148074712e-1238j 1.83e-488, 1.83e-488j
-14.02560686531886512 + 1.7037320223148689068e-1237j 9.61e-488, 9.61e-488j
8.5706735030341366588 + 2.6701011180305150475e-1241j 8.69e-488, 8.69e-488j
-11.917339625343016033 - 6.295017790836009969e-1245j 1.1e-486, 1.1e-486j
-12.319386497977646309 + 2.6603502844789805335e-1250j 8.84e-487, 8.84e-487j
17.834266721435258456 - 2.7366335365759977067e-1259j 5.18e-493, 5.18e-493j
-18.662270651924032581 + 9.499797198146321568e-1271j 1.09e-494, 1.09e-494j
-13.150304514059515383 + 5.0162696883773557399e-1275j 4.05e-487, 4.05e-487j
-5.5262544485371449926 - 1.6858979380758476222e-1294j 5.73e-492, 5.73e-492j
14.02560686531886512 - 3.0333575629047948166e-1315j 1.02e-487, 1.02e-487j
-2.5303965688558160657 + 2.2630856778616811919e-1368j 3.72e-499, 3.72e-499j
18.662270651924032581 + 1.9740523182555492332e-1356j 1.1e-494, 1.1e-494j
-4.5649713045908546133 - 3.5444425792891152321e-1375j 7.92e-494, 7.92e-494j
10.378637600620378492 + 3.6829458802420640195e-1402j 1.02e-486, 1.02e-486j
10.754214950942261914 + 2.1528788859939205274e-1445j 1.17e-486, 1.17e-486j
-6.8516586047329975368 - 1.0240244230237405774e-1464j 8.4e-490, 8.4e-490j
4.5649713045908546133 - 3.4786862755173881594e-1468j 7.67e-494, 7.67e-494j
-2.8901633840314029187 - 1.1891036602444691662e-1470j 1.13e-495, 1.13e-495j
6.1836524196721823391 - 7.1648965354524413585e-1465j 7.78e-491, 7.78e-491j
15.458606071057467092 - 4.9271268883970574997e-1461j 3.18e-489, 3.18e-489j
-17.834266721435258456 - 6.7320166107362808632e-1474j 5.76e-493, 5.76e-493j
9.2813466003863549195 + 3.0303352633017428201e-1465j 3.03e-487, 3.03e-487j
-1.6059705883815203646 - 1.5283983041975011789e-1492j 4.3e-503, 4.3e-503j
-5.8535833643675677966 - 1.69113101856589569e-1480j 2.02e-491, 2.02e-491j
-10.008244076231207046 + 1.7739728562725375003e-1475j 7.58e-487, 7.58e-487j
7.530369066264969706 + 4.2644446324637817856e-1475j 6.97e-489, 6.97e-489j
7.8740043315169555217 - 2.5964939064440645452e-1475j 1.74e-488, 1.74e-488j
-2.2219847823662942384 - 2.4516169890674753865e-1491j 1.49e-500, 1.49e-500j
3.0846786619611453577 + 1.073040329881032037e-1487j 9.37e-497, 9.37e-497j
-1.3003224368580819675 + 5.9367751483124343545e-1495j 2.43e-504, 2.43e-504j
-4.2551501203348463848 + 1.5711568199808729506e-1486j 1.82e-494, 1.82e-494j
-10.378637600620378492 + 6.6395933623183477219e-1476j 9.79e-487, 9.79e-487j
-6.1836524196721823391 - 1.7209679559195118746e-1482j 7.8e-491, 7.8e-491j
1.9137355618993510628 - 1.0762149568849906343e-1494j 7.9e-502, 7.9e-502j
-14.960814406119422394 - 6.5717261282544047056e-1481j 1.29e-488, 1.29e-488j
-3.665146847950937402 - 2.5712837461678691271e-1488j 1.1e-495, 1.1e-495j
5.8535833643675677966 + 3.1713027162736199871e-1484j 2.09e-491, 2.09e-491j
-8.9241337221987116514 + 3.5997745478138653514e-1478j 1.7e-487, 1.7e-487j
3.3826596802941071269 + 1.8429491931467003694e-1490j 2.66e-496, 2.66e-496j
-9.2813466003863549195 - 6.2249731572958776018e-1480j 3.03e-487, 3.03e-487j
-7.1896324669645155169 + 6.5852807340033483803e-1488j 2.73e-489, 2.73e-489j
-1.9137355618993510628 + 7.0789477892950444066e-1502j 8.23e-502, 8.23e-502j
2.8871489830997686416 + 5.3554832849013177599e-1494j 1.24e-495, 1.24e-495j
10.008244076231207046 + 2.9750900252762385276e-1484j 7.56e-487, 7.56e-487j
5.5262544485371449926 - 1.1176120642122893222e-1506j 5.27e-492, 5.27e-492j
8.9241337221987116514 + 1.4548176919307367832e-1500j 1.72e-487, 1.72e-487j
-2.8871489830997686416 - 2.5990926951864855481e-1522j 1.06e-495, 1.06e-495j
6.5163489637609677259 - 1.5642433796051611251e-1512j 2.47e-490, 2.47e-490j
-4.8811705983160063598 - 1.1729952778863255677e-1520j 3.24e-493, 3.24e-493j
1.6059705883815203646 + 1.473333091386232453e-1530j 4e-503, 4e-503j
11.522955882442944103 - 8.8653312890131657591e-1513j 1.35e-486, 1.35e-486j
2.5303965688558160657 + 4.1398347067968337758e-1535j 3.45e-499, 3.45e-499j
-9.6426059433311385644 - 5.7250258080077936834e-1523j 4.87e-487, 4.87e-487j
-6.5163489637609677259 + 8.2463007375253133677e-1527j 2.47e-490, 2.47e-490j
4.8811705983160063598 + 7.5899941583609549004e-1529j 3.28e-493, 3.28e-493j
3.665146847950937402 - 3.4637640153236308133e-1531j 1.05e-495, 1.05e-495j
2.8901633840314029187 - 3.892465904205076146e-1531j 1.17e-495, 1.17e-495j
-1 - 5.3898399252674527691e-1542j 1.66e-505, 1.66e-505j
-5.2019365924015129919 - 1.0622469336812880754e-1528j 1.37e-492, 1.37e-492j
0.23704314987094039888 - 7.6381165503226866935e-1545j 7.8e-509, 7.8e-509j
0.71305252548315913708 - 1.6393921966422704459e-1542j 1.27e-506, 1.27e-506j
9.6426059433311385644 - 2.0832438064526622234e-1521j 4.81e-487, 4.81e-487j
5.2019365924015129919 - 8.994666831779020469e-1529j 1.36e-492, 1.36e-492j
12.730009000317201699 - 1.0727124271948586168e-1521j 7.12e-487, 7.12e-487j
-1.0758921385584782599e-1616 - 1.6594913722610991706e-1616j 2.04e-1614, 2.04e-1614j
1 + 5.2461685038379924697e-1551j 1.85e-505, 1.85e-505j
-0.71305252548315913708 - 5.3568154239575058918e-1552j 1.28e-506, 1.28e-506j
-3.3826596802941071269 + 3.2318235418703334997e-1542j 2.62e-496, 2.62e-496j
1.3003224368580819675 - 4.1303720798609282078e-1551j 2.48e-504, 2.48e-504j
-11.522955882442944103 - 2.357013041361008025e-1531j 1.33e-486, 1.33e-486j
-10.754214950942261914 + 1.9088597753673487973e-1530j 1.11e-486, 1.11e-486j
-8.2207064132334614882 - 1.1738166512580533015e-1533j 3.93e-488, 3.93e-488j
8.2207064132334614882 - 4.6698987037246788447e-1533j 4.19e-488, 4.19e-488j
-7.530369066264969706 + 6.5148451092486285065e-1535j 6.98e-489, 6.98e-489j
-3.0846786619611453577 - 1.3857712102110175209e-1542j 9.06e-497, 9.06e-497j
3.9544879426500450264 - 8.0347656968396111688e-1541j 4.56e-495, 4.56e-495j
0.45861927664843302606 - 7.2246204843993574626e-1554j 1.01e-507, 1.01e-507j
4.2551501203348463848 - 1.9474342471094462603e-1540j 1.88e-494, 1.88e-494j
-3.9544879426500450264 + 9.635940999417245206e-1543j 4.57e-495, 4.57e-495j
-0.45861927664843302606 - 6.5253614022659335252e-1553j 9.88e-508, 9.88e-508j
-0.23704314987094039888 - 3.0181781364404027489e-1554j 8.1e-509, 8.1e-509j
2.2219847823662942384 + 1.5673507338893306371e-1546j 1.58e-500, 1.58e-500j

Weights

Weight (ball center) Error (ball radius)
5.1665546156867879446e-47 - 3.0685847364657617267e-1084j 4.2e-126, 8.8e-369j
1.0711204997529927575e-36 + 1.2136764373722522694e-1077j 2.06e-120, 4.31e-363j
4.7696101602947914014e-39 - 2.1137131893426436449e-1079j 2.38e-123, 4.98e-366j
3.404733385762562102e-65 + 6.7639847498623463309e-1095j 1.41e-135, 2.96e-378j
1.5370851021555116479e-41 - 3.0001723208641088843e-1081j 4.03e-125, 8.44e-368j
2.6134795601249698609e-53 - 9.2873326241643084848e-1088j 3.62e-132, 7.59e-375j
8.7114850262930671003e-61 - 1.7594094609681102884e-1092j 3.38e-134, 7.08e-377j
4.8381090688899503142e-50 + 1.8278236418913407307e-1086j 6.11e-130, 1.28e-372j
8.5908308921293664164e-12 + 2.898994234322502868e-1065j 2.29e-100, 4.79e-343j
1.8179851891237490611e-28 + 3.4234654637800057644e-1074j 3.31e-121, 6.94e-364j
8.0727489325793715519e-13 - 6.4679690677585375666e-1066j 2.3e-102, 4.83e-345j
1.7937822433821071174e-34 - 1.1466881138606115475e-1077j 6.85e-123, 1.43e-365j
1.5710318667500031503e-17 - 2.1785405474821109227e-1068j 5.61e-112, 1.18e-354j
8.7114850262930671003e-61 - 7.9080276152659502057e-1092j 3.84e-138, 8.05e-381j
7.2563816674441316244e-57 + 1.0510777283722313462e-1089j 2.16e-136, 4.53e-379j
3.404733385762562102e-65 + 3.3961413979760553377e-1094j 1.93e-140, 4.03e-383j
1.5370851021555116479e-41 - 5.1943101642239259929e-1081j 1.84e-130, 3.86e-373j
7.2563816674441316244e-57 + 2.5920379478291967259e-1090j 8.86e-138, 1.86e-380j
5.1665546156867879446e-47 - 1.0578253859855218481e-1084j 1.68e-133, 3.52e-376j
2.2960289357498939303e-32 + 1.1307599573240039093e-1076j 2.95e-127, 6.17e-370j
1.8179851891237490611e-28 + 1.0371346006342519119e-1074j 8.02e-126, 1.68e-368j
4.7400853236740955945e-15 - 5.7779597794777045575e-1067j 7.17e-117, 1.5e-359j
3.4545339663727975662e-44 + 1.3185573165333571077e-1082j 1.52e-134, 3.19e-377j
1.5710318667500031503e-17 - 9.7390842970154611304e-1069j 9.83e-120, 2.06e-362j
2.2960289357498939303e-32 + 4.8655457429622001593e-1076j 3.08e-130, 6.44e-373j
1.7937822433821071174e-34 - 6.873709721153995683e-1077j 4.54e-131, 9.51e-374j
2.5246746897879077174e-70 - 1.0986469169125709902e-1097j 1.64e-148, 3.44e-391j
9.0001619372940517856e-77 + 2.4203139881176910414e-1100j 2.08e-151, 4.35e-394j
4.7696101602947914014e-39 + 2.278466342301342098e-1079j 4.06e-133, 8.51e-376j
3.0367589415464666146e-08 + 1.3118363793555094798e-1062j 9.48e-112, 1.99e-354j
3.4545339663727975662e-44 + 5.4140395850108078186e-1083j 5.7e-137, 1.19e-379j
0.0050268435911451899184 - 5.4059182677378100359e-1058j 8.17e-90, 1.71e-332j
9.0001619372940517856e-77 + 3.6047051002933202913e-1101j 5.89e-152, 1.23e-394j
3.7314819514012112827e-06 - 6.4065858277661026778e-1061j 1.14e-107, 2.39e-350j
6.0569684666723257835e-25 + 7.4370688927812309085e-1073j 4.86e-130, 1.02e-372j
1.1614946339370949585e-26 - 9.0928163657192197842e-1074j 1.46e-130, 3.07e-373j
8.5908308921293664164e-12 + 5.3935330942788091771e-1065j 6.03e-121, 1.26e-363j
3.7314819514012112827e-06 - 4.2849676250020799148e-1061j 2.18e-111, 4.56e-354j
-0.050319020616795130283 - 5.2720238607956744533e-1056j 3.2e-98, 6.7e-341j
6.5776684500033306152e-10 + 5.1510317594981486384e-1064j 1.46e-118, 3.06e-361j
2.6134795601249698609e-53 - 2.5351461184432253091e-1088j 2.08e-142, 4.35e-385j
2.5246746897879077174e-70 - 6.2645839268418004615e-1097j 3.26e-152, 6.83e-395j
2.8211532485711600391e-20 - 2.6769352223444721438e-1070j 1.52e-128, 3.18e-371j
0.033734927012504188804 + 8.2990666235755159252e-1058j 2.17e-87, 4.55e-330j
4.7568446259679283999e-09 - 3.476710219060089978e-1063j 1.43e-118, 3e-361j
2.6070856788270454406e-23 - 1.5259487835751046081e-1071j 1.08e-132, 2.26e-375j
6.6296248220077617613e-14 + 1.377780192230309151e-1066j 5.23e-124, 1.09e-366j
4.7400853236740955945e-15 - 2.7919744797632107911e-1067j 3.06e-125, 6.41e-368j
0.010413661667575315059 + 5.1082636641992225662e-1058j 1.92e-98, 4.02e-341j
0.0011673556184981900802 + 4.7674531979056187542e-1058j 4.86e-108, 1.02e-350j
0.052030842786173085528 - 1.2501876108564775471e-1057j 6.97e-88, 1.46e-330j
1.4274654192584687226e-05 + 2.3092884487364422284e-1060j 2.11e-113, 4.42e-356j
6.0569684666723257835e-25 + 2.1207373380117350622e-1072j 1.63e-134, 3.42e-377j
6.5776684500033306152e-10 + 8.9705747881614300401e-1064j 3.51e-122, 7.36e-365j
0.019700415527933845833 - 5.1718516974066535991e-1058j 4.19e-101, 8.79e-344j
4.8381090688899503142e-50 + 6.0137470256347859826e-1086j 3.13e-145, 6.55e-388j
0.00013725758634835675697 + 2.8212462835578225888e-1059j 2.13e-112, 4.46e-355j
4.7568446259679283999e-09 - 2.061037395657389353e-1063j 1.03e-123, 2.16e-366j
7.2086199816454473799e-19 + 3.8854638817638518002e-1069j 1.34e-131, 2.81e-374j
0.00037072569446640540043 - 7.2975968345162634226e-1059j 2.04e-115, 4.28e-358j
2.8211532485711600391e-20 - 6.526014253547772879e-1070j 1.11e-132, 2.33e-375j
8.0727489325793715519e-13 - 1.2454505026891148511e-1065j 2.92e-127, 6.12e-370j
0.019700415527933845833 - 6.1054406123367655676e-1058j 2.77e-104, 5.8e-347j
0.052078956023558409219 + 4.080634524064426915e-1056j 1.07e-113, 2.25e-356j
2.6070856788270454406e-23 - 5.6683733300618164172e-1072j 1.79e-136, 3.76e-379j
3.0367589415464666146e-08 + 8.0230154423964934727e-1063j 1.32e-125, 2.76e-368j
7.2086199816454473799e-19 + 1.665939024907837205e-1069j 5.74e-134, 1.2e-376j
0.052078956023558409219 + 5.2470248140320876072e-1056j 5.35e-113, 1.12e-355j
8.0163165702973567943e-11 - 1.2454484744961172805e-1064j 9.92e-128, 2.08e-370j
8.5229017630943886391e-07 + 1.7688891201136814286e-1061j 1.53e-123, 3.21e-366j
0.033734927012504188804 + 7.2211507014106961687e-1058j 9.38e-111, 1.97e-353j
2.2929677753863579916e-30 - 1.1095761835956853577e-1075j 1.84e-140, 3.85e-383j
0.0050268435911451899184 - 4.3385269854895714597e-1058j 9.76e-117, 2.04e-359j
9.3533058899268386322e-22 + 1.0301158161491544252e-1070j 1.01e-136, 2.12e-379j
8.0163165702973567943e-11 - 2.2408969632904983738e-1064j 9.78e-129, 2.05e-371j
8.5229017630943886391e-07 + 1.1491351519097955663e-1061j 7.96e-126, 1.67e-368j
0.00013725758634835675697 + 2.0473018343297719827e-1059j 1.93e-122, 4.04e-365j
-0.050319020616795130283 - 4.0989840151698084913e-1056j 3.92e-117, 8.21e-360j
0.071551037643828285933 + 2.0905310015409909636e-1057j 1.3e-113, 2.73e-356j
1.7124709065404457815e-07 - 4.8497099978488110413e-1062j 1.57e-126, 3.29e-369j
0.086871131586818289342 - 8.8319062363585335683e-1057j 1.25e-114, 2.61e-357j
0.085039126872327196084 - 3.629940052881178818e-1057j 4.49e-115, 9.41e-358j
9.3533058899268386322e-22 + 4.0295772988622689396e-1071j 1e-136, 2.1e-379j
1.7124709065404457815e-07 - 3.0579112991688052218e-1062j 5.66e-127, 1.19e-369j
1.0711204997529927575e-36 + 1.3561348019541516752e-1078j 7.42e-145, 1.55e-387j
0.097799174602855868164 + 9.4081715871794320923e-1057j 4.91e-115, 1.03e-357j
0.071551037643828285933 + 1.9172763401324383549e-1057j 6.94e-116, 1.45e-358j
0.085039126872327196084 - 3.8608126312243155071e-1057j 1.35e-115, 2.84e-358j
0.00037072569446640540043 - 9.805470865486155588e-1059j 6.27e-124, 1.31e-366j
0.052030842786173085528 - 1.1170950254169148929e-1057j 2.09e-118, 4.38e-361j
2.2929677753863579916e-30 - 4.0687562818385194833e-1075j 3.96e-144, 8.29e-387j
1.1614946339370949585e-26 - 2.7704132351801036025e-1073j 2.89e-142, 6.05e-385j
2.9379799662824115502e-16 + 1.1531387114159626981e-1067j 5.91e-137, 1.24e-379j
2.9379799662824115502e-16 + 5.364016188743345729e-1068j 5.09e-137, 1.07e-379j
6.6296248220077617613e-14 + 2.7487038569817627435e-1066j 1.48e-135, 3.09e-378j
0.0011673556184981900802 + 6.238314218276792428e-1058j 1.3e-126, 2.72e-369j
4.7328355753910239464e-05 - 5.8027174253948074838e-1060j 4.18e-130, 8.72e-373j
0.083230757803192074108 + 6.5539730679846411012e-1057j 7.7e-126, 1.75e-368j
1.4274654192584687226e-05 + 1.5888567323561602644e-1060j 1.06e-130, 2.22e-373j
4.7328355753910239464e-05 - 8.2072150887092999018e-1060j 5.79e-130, 1.28e-372j
0.083230757803192074108 + 6.8190521845527100319e-1057j 4.52e-127, 1.09e-369j
0.086871131586818289342 - 9.0147420230222542753e-1057j 4.42e-127, 1.18e-369j
0.010413661667575315059 + 4.2121037053243856328e-1058j 2.16e-128, 3.61e-371j

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