Rule: Q[4, 10, 95]

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)
17.068300009010710915 + 3.668214766210550025e-1383j 5.86e-490, 5.86e-490j
-17.068300009010710915 + 1.0382072428566899772e-1396j 6.2e-490, 6.2e-490j
13.7095595060638235 - 2.2170089599461986442e-1390j 4.3e-486, 4.3e-486j
-14.136321738188762839 + 1.140007435307905337e-1413j 2.25e-486, 2.25e-486j
-15.994437465700797211 + 2.1557001563235519266e-1415j 2.49e-488, 2.49e-488j
19.16902647995708569 + 4.1517313589265774392e-1415j 5.16e-494, 5.16e-494j
-18.348185123841620358 + 6.0992851261471589841e-1419j 2.76e-492, 2.76e-492j
18.348185123841620358 - 8.440996960336839376e-1411j 2.83e-492, 2.83e-492j
-10.241851373635692385 + 1.4935689140469983327e-1419j 1.07e-485, 1.07e-485j
-3.5742318177018439811 + 3.771217947908061311e-1433j 1.16e-495, 1.16e-495j
14.575717204443567835 + 4.1079293270926693128e-1422j 1.06e-486, 1.06e-486j
-14.575717204443567835 - 3.78600642997330625e-1451j 9.66e-487, 9.66e-487j
2.3344142183389772393 + 1.494882214996894481e-1469j 6.43e-499, 6.43e-499j
15.029857714186976957 + 7.8864887526997392691e-1455j 3.44e-487, 3.44e-487j
-15.501511085293680198 - 2.0031487919640512156e-1478j 1.03e-487, 1.03e-487j
-11.340217808225134005 + 5.462170463660679462e-1475j 1.96e-485, 1.96e-485j
5.5317060638607199116 - 5.2618564872578814048e-1475j 2.78e-491, 2.78e-491j
10.969059428776950035 - 3.5040540030817528336e-1490j 1.73e-485, 1.73e-485j
13.293772879741456144 - 1.429477034211005936e-1520j 8.14e-486, 8.14e-486j
-11.717044494415018929 - 2.8815076912653006806e-1535j 2.03e-485, 2.03e-485j
10.603080206406350703 + 1.5297695249345866867e-1533j 1.38e-485, 1.38e-485j
-12.88763046514705972 - 5.6745591087784876128e-1540j 1.21e-485, 1.21e-485j
-12.490042345991411212 - 2.4858486451996057163e-1540j 1.64e-485, 1.64e-485j
12.88763046514705972 + 1.412800179405172574e-1537j 1.16e-485, 1.16e-485j
2.9714439569518734479 + 2.202906931208682906e-1559j 1.24e-497, 1.24e-497j
15.994437465700797211 + 1.946564528855263993e-1549j 2.36e-488, 2.36e-488j
1.4656205133845524345 + 2.3887391780509174456e-1565j 3.66e-503, 3.66e-503j
-3.2762772292662860982 - 2.1418874881395425302e-1559j 1.14e-496, 1.14e-496j
-9.8849945532702096671 - 5.758351186729956204e-1548j 6.88e-486, 6.88e-486j
-17.670923719718808046 + 9.552349022293796694e-1554j 5.68e-491, 5.68e-491j
-13.7095595060638235 - 1.7785494460522781434e-1548j 4.81e-486, 4.81e-486j
-15.029857714186976957 + 3.7889425400678169295e-1549j 3.4e-487, 3.4e-487j
-16.513990706955514397 + 6.0811890692263293919e-1551j 4.79e-489, 4.79e-489j
-12.100101877617204931 - 4.8706049114988499074e-1547j 1.89e-485, 1.89e-485j
-3.8492600471106016812 + 1.4438190812588380384e-1556j 9.67e-495, 9.67e-495j
-4.3114957943342286437 + 1.9688597176155043007e-1555j 1.39e-493, 1.39e-493j
15.501511085293680198 + 4.2921430790238775865e-1549j 1.01e-487, 1.01e-487j
-19.16902647995708569 - 1.22024856408168601e-1556j 5.09e-494, 5.09e-494j
12.100101877617204931 - 1.7587972961235497355e-1545j 1.79e-485, 1.79e-485j
16.513990706955514397 - 2.6909371899784193281e-1559j 5.17e-489, 5.17e-489j
-9.5321739214236911177 - 1.6638797513787877795e-1558j 4.08e-486, 4.08e-486j
-5.2148265317863309166 - 2.0015378622554552671e-1563j 6.8e-492, 6.8e-492j
3.5742318177018439811 - 1.4844535614979821972e-1566j 1.2e-495, 1.2e-495j
-6.4981361996553802747 - 8.9698175097321594465e-1562j 1.33e-489, 1.33e-489j
12.490042345991411212 + 3.2337176330472506847e-1555j 1.63e-485, 1.63e-485j
-2.0788570993716443757 - 6.8486823940457718045e-1576j 3.29e-500, 3.29e-500j
-7.4852636058883645016 + 6.8454308675149173828e-1564j 3.64e-488, 3.64e-488j
-13.293772879741456144 + 2.1319422901442444028e-1563j 8.06e-486, 8.06e-486j
1.1754635101141524304 - 1.5870961108648962578e-1579j 2.91e-504, 2.91e-504j
-7.8191637970934173099 - 4.929118480074731884e-1565j 1.01e-487, 1.01e-487j
4.9020144030373826358 - 6.1056906336372428486e-1567j 1.77e-492, 1.77e-492j
-5.851468153705238871 + 3.0518627669207280606e-1566j 1.01e-490, 1.01e-490j
-7.1538679821557160971 - 3.5210731095976801738e-1564j 1.37e-488, 1.37e-488j
0.74196378430272585765 + 8.9186967233263872394e-1582j 5.73e-506, 5.73e-506j
2.6632752479080548124 - 4.07845493192149858e-1574j 1.62e-498, 1.62e-498j
-8.4950885134984188332 + 2.1884959125125057828e-1562j 5.53e-487, 5.53e-487j
-9.1830900307781282227 + 2.3673830607460892503e-1562j 2.28e-486, 2.28e-486j
7.8191637970934173099 - 8.4575868472455825698e-1560j 1.01e-487, 1.01e-487j
17.670923719718808046 - 6.4668737669275627168e-1574j 5.38e-491, 5.38e-491j
6.8248554610296684699 - 7.7430067582634948044e-1568j 4.22e-489, 4.22e-489j
-6.8248554610296684699 - 2.5265674023713389434e-1574j 4.11e-489, 4.11e-489j
14.136321738188762839 + 5.9278135404021061638e-1570j 2.26e-486, 2.26e-486j
-0.91615270801568555349 - 5.9275133413960318146e-1606j 2.76e-505, 2.76e-505j
5.851468153705238871 + 8.6701982210105178112e-1586j 1.01e-490, 1.01e-490j
-5.5317060638607199116 - 4.4935007475897318645e-1606j 2.75e-491, 2.75e-491j
8.837474952749142716 + 3.0521452510531803256e-1598j 1.19e-486, 1.19e-486j
4.0750559756043516922 + 2.4854071763908020011e-1641j 4.95e-494, 4.95e-494j
-8.837474952749142716 - 2.4388690781883950747e-1632j 1.24e-486, 1.24e-486j
-4.0750559756043516922 + 9.6069303096116639338e-1650j 4.22e-494, 4.22e-494j
8.4950885134984188332 + 3.1048946632165147594e-1640j 5.91e-487, 5.91e-487j
0.53139847033076593316 - 8.572635697845801491e-1692j 3.47e-507, 3.47e-507j
3.8492600471106016812 - 1.6228976497309817585e-1679j 1e-494, 1e-494j
-2.3344142183389772393 - 2.143657412361580916e-1683j 6.9e-499, 6.9e-499j
9.8849945532702096671 - 2.130675531380312032e-1669j 6.86e-486, 6.86e-486j
5.2148265317863309166 + 1.1991007136470001481e-1693j 7.17e-492, 7.17e-492j
7.1538679821557160971 + 8.8877258685469014379e-1687j 1.3e-488, 1.3e-488j
3.2762772292662860982 + 7.9437431241593020533e-1705j 1.16e-496, 1.16e-496j
11.717044494415018929 - 4.1199230791337965752e-1692j 2e-485, 2e-485j
-2.2575638007960074228 - 3.0443674825148898369e-1737j 4.47e-499, 4.47e-499j
10.241851373635692385 - 3.8618386380124920391e-1722j 1.11e-485, 1.11e-485j
-1.7656899636852069692 - 4.3675448760415026106e-1776j 7.31e-502, 7.31e-502j
0.91615270801568555349 - 3.3537570589028524525e-1780j 2.66e-505, 2.66e-505j
-4.9020144030373826358 - 9.9773043356437851865e-1768j 1.71e-492, 1.71e-492j
-1.4656205133845524345 + 1.7987295787734103831e-1777j 3.96e-503, 3.96e-503j
-2.9714439569518734479 + 3.6766010784324571704e-1772j 1.31e-497, 1.31e-497j
9.1830900307781282227 + 2.8317096233896150454e-1758j 2.37e-486, 2.37e-486j
1.7656899636852069692 + 5.4734889760475521498e-1797j 7e-502, 7e-502j
6.1736648993879386897 + 1.4546585060272142188e-1779j 3.85e-490, 3.85e-490j
-1.1754635101141524304 + 3.3570689406627062562e-1808j 2.82e-504, 2.82e-504j
-0.74196378430272585765 + 3.1048221898498875808e-1810j 5.55e-506, 5.55e-506j
-10.969059428776950035 - 8.3206648439047966245e-1788j 1.75e-485, 1.75e-485j
-2.6632752479080548124 + 1.5586789555041920961e-1803j 1.78e-498, 1.78e-498j
2.2575638007960074228 + 4.0870100035951251818e-1804j 4.26e-499, 4.26e-499j
11.340217808225134005 - 2.1134893319500293936e-1789j 2.06e-485, 2.06e-485j
4.3114957943342286437 - 1.5544598181886855776e-1814j 1.36e-493, 1.36e-493j
-8.1557154978935541228 - 1.6021882375836648566e-1809j 2.54e-487, 2.54e-487j
-0.26842728825432580984 - 6.78026286178392439e-1831j 1.39e-508, 1.39e-508j
6.4981361996553802747 + 1.238933803742540071e-1807j 1.29e-489, 1.29e-489j
8.1557154978935541228 - 1.9815210961533291008e-1827j 2.66e-487, 2.66e-487j
2.8089100467071452948e-1922 - 1.2216565492263132022e-1922j 3.34e-1920, 3.34e-1920j
-0.53139847033076593316 + 5.4802095237622644862e-1880j 3.37e-507, 3.37e-507j
-6.1736648993879386897 + 4.7805700048033881056e-1863j 3.74e-490, 3.74e-490j
2.0788570993716443757 - 1.1802584328490391589e-1872j 3.28e-500, 3.28e-500j
-4.5967832661217101006 + 2.4462414690816058233e-1866j 4.77e-493, 4.77e-493j
9.5321739214236911177 - 5.6491961653388230201e-1857j 4.14e-486, 4.14e-486j
-10.603080206406350703 + 3.7356089271182394537e-1872j 1.45e-485, 1.45e-485j
0.26842728825432580984 - 2.0654906676782318885e-1892j 1.1e-508, 1.1e-508j
4.5967832661217101006 - 6.2387205410674149663e-1877j 4.6e-493, 4.6e-493j
7.4852636058883645016 + 1.3013832882077959869e-1869j 3.88e-488, 3.88e-488j

Weights

Weight (ball center) Error (ball radius)
1.2593623731471992544e-64 + 2.417066600223685879e-1444j 1.7e-127, 6e-368j
1.2593623731471992544e-64 - 2.6841976536279802963e-1445j 6.98e-128, 2.46e-368j
2.5820153946936373177e-42 + 4.2266324159768404289e-1431j 5.48e-118, 1.93e-358j
6.9729995920227635676e-45 - 8.5611462713887797934e-1435j 1.07e-119, 3.79e-360j
5.666304399229816951e-57 - 2.9720906538639311009e-1441j 4.07e-125, 1.44e-365j
6.1313843255399130248e-81 - 4.6152086775621156183e-1453j 1.17e-134, 4.14e-375j
2.2937948669756501311e-74 - 2.0747809509984641645e-1450j 2.02e-132, 7.13e-373j
2.2937948669756501311e-74 + 1.436070366192808806e-1449j 1.87e-132, 6.6e-373j
2.3889768522599651826e-24 - 1.9597609826327401253e-1423j 4.41e-108, 1.56e-348j
0.00019532460713004521411 + 1.6284020562379717415e-1409j 1.04e-63, 3.66e-304j
1.310209636064868732e-47 - 9.5569187485329410355e-1435j 6.4e-123, 2.26e-363j
1.310209636064868732e-47 + 2.9285726308603033272e-1436j 5.18e-122, 1.83e-362j
0.011591975473270120642 + 5.5312657804942663878e-1407j 4.26e-49, 1.5e-289j
1.6333104276939093644e-50 + 1.7740217279592613176e-1436j 2e-124, 7.06e-365j
1.2698735378158198432e-53 + 1.7915508645271103304e-1439j 1.27e-124, 4.48e-365j
1.771819015537691436e-29 + 2.3958315072681770485e-1426j 2.05e-113, 7.22e-354j
2.8792038716721140624e-08 - 9.6626300275897677317e-1413j 3.87e-87, 1.36e-327j
1.0967948753461758532e-27 - 2.2028070214526802634e-1424j 2.9e-114, 1.02e-354j
6.9069806793857750002e-40 - 2.815778852648849697e-1430j 1.41e-120, 4.96e-361j
2.3364487035018196402e-31 - 2.130704703234531188e-1427j 1.33e-115, 4.68e-356j
5.6054812559874011304e-26 + 1.787099754944292309e-1423j 1.88e-113, 6.64e-354j
1.3759603074354895853e-37 + 7.789266095791935577e-1431j 8.22e-120, 2.9e-360j
2.0930183629607940074e-35 - 1.2256679683035117218e-1429j 1.44e-118, 5.06e-359j
1.3759603074354895853e-37 + 2.5195910718754205432e-1429j 3.01e-121, 1.06e-361j
0.0014794953732747135014 + 1.3668713117597743654e-1408j 1.65e-70, 5.82e-311j
5.666304399229816951e-57 + 3.8572555945904003131e-1440j 1.58e-130, 5.57e-371j
0.040359274714879318886 + 4.2631548903168644429e-1407j 2e-46, 7.05e-287j
0.00056351668130195259335 - 3.4337567515265775016e-1409j 4.44e-75, 1.57e-315j
8.5653018237927105515e-23 + 1.5538006525815373856e-1422j 1.15e-112, 4.04e-353j
3.9455960524823815749e-69 + 1.149826224203668079e-1447j 1.28e-135, 4.53e-376j
2.5820153946936373177e-42 + 2.0887630764286451901e-1433j 2.35e-123, 8.3e-364j
1.6333104276939093644e-50 - 8.1569519766408400616e-1438j 4.43e-127, 1.56e-367j
1.2907266803605370765e-60 + 3.5052951012460288087e-1443j 4.64e-132, 1.64e-372j
2.4823538886208305427e-33 + 1.7087543470684803537e-1428j 2.27e-119, 8e-360j
6.093953999034865477e-05 - 9.1186109599359146022e-1410j 1.28e-87, 4.52e-328j
9.7458958300749138341e-06 - 1.5355757070229835318e-1410j 7.42e-92, 2.62e-332j
1.2698735378158198432e-53 - 2.917121430719713987e-1438j 2.95e-135, 1.04e-375j
6.1313843255399130248e-81 + 7.656280949810268431e-1454j 1.82e-143, 6.43e-384j
2.4823538886208305427e-33 + 2.7393413624790102612e-1427j 9.19e-128, 3.24e-368j
1.2907266803605370765e-60 - 3.765092416926442792e-1442j 1.45e-138, 5.11e-379j
2.6037147800109269791e-21 - 1.1437103716388358337e-1421j 3.39e-117, 1.2e-357j
1.5639861668813058752e-07 + 1.7501132239491066908e-1412j 4.05e-102, 1.43e-342j
0.00019532460713004521411 + 2.7767829117655181396e-1409j 3.2e-94, 1.13e-334j
8.7977994399199798854e-11 + 5.0729555328543946991e-1415j 4.46e-109, 1.57e-349j
2.0930183629607940074e-35 - 2.632261421279415087e-1428j 2.71e-129, 9.55e-370j
0.015564594539684325367 + 3.2507363188896346708e-1407j 1.92e-79, 6.76e-320j
9.0424379545514824049e-14 - 4.8270569935086999729e-1417j 2.83e-113, 1e-353j
6.9069806793857750002e-40 - 4.3375148314836625916e-1432j 2.16e-126, 7.63e-367j
0.056324842571258699784 - 8.2125247221672707032e-1407j 1.54e-68, 5.45e-309j
7.0791031766395647284e-15 + 9.3922400762896914048e-1418j 1.2e-114, 4.24e-355j
7.4858221699321845411e-07 - 1.6064628711711803759e-1411j 5.62e-109, 1.98e-349j
4.7031999469177542217e-09 + 9.6460514537856777986e-1414j 4.28e-108, 1.51e-348j
1.0151845542437929919e-12 + 2.3697619560274559684e-1416j 1.27e-112, 4.48e-353j
0.048917690285893349521 - 2.7014272934068753358e-1406j 5.95e-74, 2.1e-314j
0.0035699911556732969827 - 4.3910616116213631385e-1408j 1.43e-93, 5.05e-334j
2.9020535419117982361e-17 + 3.0484685224562610932e-1419j 1.61e-117, 5.66e-358j
6.757456956747726586e-20 + 7.8501718537546177788e-1421j 4.63e-119, 1.63e-359j
7.0791031766395647284e-15 + 3.4323184204991076788e-1417j 2.06e-126, 7.27e-367j
3.9455960524823815749e-69 - 9.1373842836037792844e-1447j 2.63e-150, 9.29e-391j
1.004997124126907887e-11 - 3.3294232061463021231e-1415j 4.25e-123, 1.5e-363j
1.004997124126907887e-11 - 1.1163938555130020217e-1415j 2.44e-114, 8.62e-355j
6.9729995920227635676e-45 + 5.5828347577571306179e-1433j 1.58e-139, 5.56e-380j
0.058076425559295496599 + 1.7064094482035126002e-1406j 1.34e-84, 4.73e-325j
4.7031999469177542217e-09 + 2.4009716677037750006e-1413j 3.72e-119, 1.31e-359j
2.8792038716721140624e-08 - 4.1071035634779260768e-1413j 7.24e-112, 2.55e-352j
1.5066518290215346209e-18 - 2.3345190820250695157e-1419j 2.25e-130, 7.95e-371j
2.105220622166904315e-05 + 8.6301815974144923847e-1410j 4.41e-112, 1.56e-352j
1.5066518290215346209e-18 - 5.0453399738918512867e-1420j 1.08e-121, 3.8e-362j
2.105220622166904315e-05 + 4.6755100464104175623e-1410j 1.05e-107, 3.7e-348j
2.9020535419117982361e-17 + 1.2979325167271462552e-1418j 1.74e-129, 6.13e-370j
0.087069623813001759961 + 2.2093387032880566105e-1406j 1.61e-91, 5.67e-332j
6.093953999034865477e-05 - 1.623720176135659412e-1409j 1.06e-111, 3.73e-352j
0.011591975473270120642 + 3.9217766755151552648e-1407j 3e-103, 1.06e-343j
8.5653018237927105515e-23 + 9.5838881071414325712e-1422j 1.51e-133, 5.31e-374j
1.5639861668813058752e-07 + 3.8985759859432224879e-1412j 9.34e-119, 3.3e-359j
1.0151845542437929919e-12 + 7.5409015328794723317e-1416j 3.41e-126, 1.2e-366j
0.00056351668130195259335 - 5.5900599462298601577e-1409j 7.4e-111, 2.61e-351j
2.3364487035018196402e-31 - 2.7182281985267753582e-1426j 1.41e-137, 4.98e-378j
-0.0060115103999762883325 - 5.8869002161452218617e-1407j 3.34e-107, 1.18e-347j
2.3889768522599651826e-24 - 1.3533248015922015444e-1422j 1.94e-134, 6.86e-375j
0.025512519510877440091 - 2.3339548703852385683e-1407j 3.69e-106, 1.3e-346j
0.058076425559295496599 + 1.950782791741190574e-1406j 1.17e-101, 4.12e-342j
7.4858221699321845411e-07 - 7.6027793492801333551e-1412j 5.54e-118, 1.95e-358j
0.040359274714879318886 + 3.4397484653687274433e-1407j 3.61e-105, 1.27e-345j
0.0014794953732747135014 + 8.7993519598464257076e-1409j 8.42e-112, 2.97e-352j
6.757456956747726586e-20 + 3.9695680319831897067e-1420j 1.04e-132, 3.65e-373j
0.025512519510877440091 - 3.0239532107925910938e-1407j 1.75e-109, 6.19e-350j
6.8265053988423326012e-10 - 5.9019085833354008037e-1414j 2.8e-125, 9.89e-366j
0.056324842571258699784 - 6.9155513415133670804e-1407j 4.96e-107, 1.75e-347j
0.048917690285893349521 - 2.4240595329559492391e-1406j 1.3e-106, 4.59e-347j
1.0967948753461758532e-27 - 2.4467526823418623404e-1425j 2e-135, 7.05e-376j
0.0035699911556732969827 - 2.9626282080724576714e-1408j 2.2e-112, 7.75e-353j
-0.0060115103999762883325 - 8.2076590954009482794e-1407j 1.29e-112, 4.56e-353j
1.771819015537691436e-29 + 2.5323209135815598497e-1425j 1.62e-137, 5.73e-378j
9.7458958300749138341e-06 - 2.9443353779399700011e-1410j 1.6e-120, 5.66e-361j
4.8533313026301474546e-16 - 1.7383811490504134608e-1418j 8.35e-129, 2.94e-369j
0.10314277524100196353 - 1.6131821584154207934e-1406j 4.9e-111, 1.73e-351j
8.7977994399199798854e-11 + 1.4213934216748179934e-1414j 8.72e-127, 3.08e-367j
4.8533313026301474546e-16 - 6.8430085624618707124e-1418j 3.58e-131, 1.26e-371j
0.10709541828447808221 + 1.5386504201224620503e-1406j 4.1e-113, 1.44e-353j
0.087069623813001759961 + 2.0444706708287140437e-1406j 6.43e-113, 2.26e-353j
6.8265053988423326012e-10 - 2.2370735203338133856e-1414j 1.62e-125, 5.68e-366j
0.015564594539684325367 + 4.4126812816940148067e-1407j 5.95e-117, 2.09e-357j
3.0748312886174625053e-06 + 3.4328262787689561362e-1411j 5.36e-122, 1.89e-362j
2.6037147800109269791e-21 - 6.3621284418694756769e-1421j 1.78e-134, 6.26e-375j
5.6054812559874011304e-26 + 2.2839250212483465681e-1424j 1.39e-136, 4.84e-377j
0.10314277524100196353 - 1.6776087367814441446e-1406j 1.29e-117, 4.54e-358j
3.0748312886174625053e-06 + 6.8956459391131250423e-1411j 5.41e-124, 1.85e-364j
9.0424379545514824049e-14 - 1.6435014526115013691e-1416j 4.89e-130, 1.73e-370j

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