Rule: Q[8, 13, 70]

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)
-11.476077127420471114 + 2.2796649203983986344e-1297j 2.92e-490, 2.92e-490j
-12.892632278272556755 - 1.0597233950075577644e-1330j 4.53e-491, 4.53e-491j
-13.935455503992532208 - 5.2174964996994506462e-1356j 5.28e-492, 5.28e-492j
-18.116546304162365 + 8.8340792084170284998e-1376j 4.64e-498, 4.64e-498j
18.116546304162365 - 4.2813731579272110688e-1374j 4.62e-498, 4.62e-498j
13.401297819057230217 + 3.7132217836469266867e-1373j 1.68e-491, 1.68e-491j
-15.79641556089935575 - 2.0990179559394455195e-1385j 1.73e-494, 1.73e-494j
-10.597010089396194068 + 1.4588156531248310956e-1395j 4.61e-490, 4.61e-490j
-1.3422817985360332488 + 2.7024387402627353175e-1417j 3.43e-504, 3.43e-504j
-14.502637011469551693 - 6.6639434572294406548e-1403j 1.16e-492, 1.16e-492j
1.9364261552246506445 - 6.327978368656058136e-1418j 5.25e-502, 5.25e-502j
15.115180026291916792 + 7.6101252568609343483e-1406j 1.7e-493, 1.7e-493j
-2.511857163044217673 - 6.7512663042704251606e-1416j 6.03e-500, 6.03e-500j
-8.5465668375552736216 + 7.2651648076604052892e-1404j 1.76e-490, 1.76e-490j
15.79641556089935575 + 3.8262165661955175887e-1411j 1.8e-494, 1.8e-494j
-3.4215630331028556842 + 7.401432910710453746e-1416j 1.08e-496, 1.08e-496j
12.404432022398626869 - 2.9679934331315633571e-1408j 9.83e-491, 9.83e-491j
-7.3864901899688589617 + 3.5529860908594808287e-1415j 3e-491, 3e-491j
16.604757065970951671 + 1.3422966247436507676e-1419j 8.3e-496, 8.3e-496j
5.5194392862815053177 + 1.8405304759742561388e-1415j 5.84e-493, 5.84e-493j
3.1111659281751050145 + 5.004139844177422536e-1421j 6.19e-498, 6.19e-498j
10.17209104233678826 - 9.1746788470480441746e-1412j 4.59e-490, 4.59e-490j
11.031239566577225673 - 1.6003894378643671389e-1411j 3.79e-490, 3.79e-490j
11.476077127420471114 - 9.1729649119554343069e-1419j 2.83e-490, 2.83e-490j
-6.6336991403182893007 + 1.4914369572307764886e-1430j 5.91e-492, 5.91e-492j
10.597010089396194068 - 5.2036177635429041716e-1427j 4.65e-490, 4.65e-490j
11.933129682636761345 - 1.1937070467772923176e-1441j 1.9e-490, 1.9e-490j
7.0083416616804912679 - 3.189503146356589911e-1455j 1.3e-491, 1.3e-491j
13.935455503992532208 - 2.4990988586907501423e-1470j 4.87e-492, 4.87e-492j
-12.404432022398626869 + 4.2123054472148930513e-1486j 1.08e-490, 1.08e-490j
-16.604757065970951671 - 3.965087026587042008e-1503j 8.08e-496, 8.08e-496j
14.502637011469551693 - 2.3429257725516003646e-1500j 1.07e-492, 1.07e-492j
2.511857163044217673 + 1.6424992244763455395e-1507j 6.08e-500, 6.08e-500j
-8.1551537395928137263 + 7.9659175897474623163e-1496j 1.02e-490, 1.02e-490j
-4.5006245202708609904 + 2.54887142373890131e-1505j 1.56e-494, 1.56e-494j
12.892632278272556755 + 2.4709469708715329427e-1502j 4.52e-491, 4.52e-491j
8.5465668375552736216 - 8.7080535048900130123e-1503j 1.79e-490, 1.79e-490j
0.80593919185227963139 + 2.4837372568553862677e-1521j 2.28e-506, 2.28e-506j
5.8918730094612552215 - 3.5092027897598692503e-1507j 1.16e-492, 1.16e-492j
-6.2619412218357956931 + 4.6279909791353633565e-1506j 2.57e-492, 2.57e-492j
-0.80593919185227963139 + 2.773000539602734296e-1520j 2.47e-506, 2.47e-506j
-5.0188869747707898609 - 2.8581275629347874638e-1505j 1.73e-491, 1.73e-491j
4.1445471861258943321 + 1.4921845181273442636e-1509j 2.66e-495, 2.66e-495j
-1.0668273675044222989 + 1.5619343627011858599e-1519j 3.16e-505, 3.16e-505j
7.7686142759149524181 - 3.9850233640178607685e-1505j 5.68e-491, 5.68e-491j
-4.9639840200927492835 - 4.2886038764324211924e-1506j 3.45e-492, 3.45e-492j
3.4215630331028556842 - 1.2542483201164242959e-1511j 1.07e-496, 1.07e-496j
-3.1111659281751050145 + 1.9089769691203777354e-1513j 6.25e-498, 6.25e-498j
-15.115180026291916792 - 9.8289540740897086563e-1504j 1.71e-493, 1.71e-493j
9.7554147908729819877 - 6.5987175761521116765e-1514j 4.3e-490, 4.3e-490j
-5.0362221132301111783 - 1.6787358681649145828e-1522j 1.41e-491, 1.41e-491j
-11.933129682636761345 - 6.1177558200162498482e-1535j 1.76e-490, 1.76e-490j
-5.5194392862815053177 - 1.7604404629574935682e-1549j 5.94e-493, 5.94e-493j
9.3460888013759856932 - 1.3849388633422289326e-1544j 3.7e-490, 3.7e-490j
8.1551537395928137263 - 6.3166640061137625054e-1553j 9.77e-491, 9.77e-491j
5.0362221132301111783 + 1.2580097823719686821e-1559j 1.41e-491, 1.41e-491j
-10.17209104233678826 - 7.2445027882486812228e-1571j 4.54e-490, 4.54e-490j
-11.031239566577225673 - 3.120923429287102186e-1586j 3.91e-490, 3.91e-490j
3.806468849188998684 + 9.7252634442333705298e-1606j 7.52e-496, 7.52e-496j
7.3864901899688589617 + 2.0115258696988660329e-1600j 3.09e-491, 3.09e-491j
6.6336991403182893007 + 1.2376870285923248437e-1601j 6.12e-492, 6.12e-492j
-13.401297819057230217 + 3.9783972711615782893e-1599j 1.66e-491, 1.66e-491j
4.9639840200927492835 + 1.3258111233904161508e-1611j 3.68e-492, 3.68e-492j
-2.8024858612875416991 - 2.1196656088972107934e-1618j 6.24e-499, 6.24e-499j
0.53907981135137510807 - 1.1383636104332839103e-1626j 1.64e-507, 1.64e-507j
8.9433562674830625874 - 5.442180200384565433e-1609j 2.52e-490, 2.52e-490j
-9.3460888013759856932 - 1.9544229337625387725e-1608j 3.68e-490, 3.68e-490j
-1.6365190424351079992 - 1.8561554573645865899e-1634j 5.09e-503, 5.09e-503j
-4.1445471861258943321 + 1.5388361593727105677e-1626j 2.63e-495, 2.63e-495j
-3.806468849188998684 + 6.3760138966477156324e-1627j 7.31e-496, 7.31e-496j
2.8024858612875416991 + 2.483795956012366307e-1630j 5.27e-499, 5.27e-499j
-7.7686142759149524181 + 7.6548576347938718889e-1621j 6.09e-491, 6.09e-491j
-0.53907981135137510807 + 2.3218946447186609588e-1647j 1.64e-507, 1.64e-507j
1.0668273675044222989 - 1.293165102489786271e-1645j 2.73e-505, 2.73e-505j
2.2288115845706893975 - 7.4382879528271192203e-1641j 6.29e-501, 6.29e-501j
3.5826575051299170185 - 2.4343785552096137736e-1636j 3.32e-496, 3.32e-496j
4.5006245202708609904 - 1.4872383628016558072e-1635j 1.59e-494, 1.59e-494j
-7.0083416616804912679 - 4.4015026698170071031e-1630j 1.39e-491, 1.39e-491j
-1.9364261552246506445 + 3.4813834648636635097e-1649j 6.15e-502, 6.15e-502j
5.0188869747707898609 + 5.6089107202579004498e-1639j 1.75e-491, 1.75e-491j
1.6365190424351079992 + 1.7382992335586489295e-1650j 5.05e-503, 5.05e-503j
1.3422817985360332488 + 1.4338501004251206735e-1651j 3.41e-504, 3.41e-504j
-5.8918730094612552215 + 1.2708873302765756797e-1637j 1.13e-492, 1.13e-492j
-3.5826575051299170185 - 9.7936165210149213363e-1650j 3.46e-496, 3.46e-496j
-2.2288115845706893975 + 3.6015415401643057409e-1663j 7.09e-501, 7.09e-501j
-8.9433562674830625874 + 1.0457309580271462368e-1655j 2.67e-490, 2.67e-490j
6.2619412218357956931 + 6.6722356822283161354e-1689j 2.84e-492, 2.84e-492j
0.26705763477974246222 - 1.8560961187276053686e-1735j 8.1e-509, 8.1e-509j
2.2957573003000779569e-1735 + 7.1468382634691015363e-1735j 6.83e-1733, 6.83e-1733j
-0.26705763477974246222 + 1.1119707393277889448e-1735j 7.51e-509, 7.51e-509j
-9.7554147908729819877 - 2.8581175003128835294e-1736j 4.66e-490, 4.66e-490j

Weights

Weight (ball center) Error (ball radius)
4.5329314091675165081e-30 + 6.7522518309652105644e-1326j 7.92e-130, 3.8e-373j
1.5984742601600465652e-37 + 4.8662059633554724121e-1331j 1.42e-134, 6.84e-378j
1.4833896736779722397e-43 + 1.4051494372493450039e-1334j 5.69e-138, 2.73e-381j
1.9109197984374941695e-71 - 2.0229700000802938104e-1349j 1.62e-149, 7.75e-393j
1.9109197984374941695e-71 + 4.5394657091029710783e-1350j 2.56e-152, 1.23e-395j
2.0832730222085227479e-40 + 7.1945621190402112885e-1334j 7.28e-141, 3.49e-384j
1.9043426085367808344e-55 - 3.5471972980859615864e-1341j 4.52e-144, 2.17e-387j
7.060726100897277886e-26 + 3.0763508654398654658e-1324j 4.4e-130, 2.11e-373j
0.046417598202821368712 + 7.32438741449072234e-1308j 4.38e-60, 2.1e-303j
4.9875706077648583449e-47 - 1.5229800513759561986e-1336j 2.86e-140, 1.37e-383j
0.018228811375282901276 + 2.1357827319783579112e-1308j 2.51e-74, 1.2e-317j
6.2626654380448570454e-51 - 1.4200883521328784634e-1339j 5.05e-147, 2.42e-390j
0.0048212057835012925548 + 1.3441396223601536432e-1308j 2.03e-84, 9.74e-328j
2.1635139305739027353e-17 - 1.3518574591207185804e-1319j 4.03e-125, 1.94e-368j
1.9043426085367808344e-55 + 5.6192490335203630386e-1342j 7.7e-149, 3.69e-392j
0.00032551308215558341623 - 5.1644042340296881856e-1309j 1.15e-96, 5.53e-340j
7.3966870972420065353e-35 + 8.6938901817248041725e-1331j 2.42e-141, 1.16e-384j
2.1535769156553234679e-13 + 4.6810897126968450243e-1317j 2.06e-122, 9.91e-366j
4.9275525527615783198e-61 - 6.5727722767576425191e-1345j 4.14e-151, 1.99e-394j
3.6561750836061040384e-08 - 2.7165301423015307197e-1313j 5.98e-117, 2.87e-360j
0.00099561178066821983717 + 2.9266631827746304701e-1309j 1.12e-98, 5.36e-342j
5.7053125697283895457e-24 - 1.6579140446831274525e-1324j 2.37e-136, 1.14e-379j
6.5977978457554265051e-28 - 7.9734023533572892224e-1327j 7.48e-139, 3.59e-382j
4.5329314091675165081e-30 + 4.5022199682505918998e-1328j 3.41e-140, 1.64e-383j
4.1393256039871535579e-11 + 1.974514030934008808e-1315j 5.01e-126, 2.4e-369j
7.060726100897277886e-26 + 1.2251655677531704314e-1325j 3.51e-138, 1.69e-381j
2.2159462797307416628e-32 - 2.1666766160988528138e-1329j 1.28e-141, 6.15e-385j
3.242408597732937122e-12 - 7.3953432805851687035e-1317j 4.52e-130, 2.17e-373j
1.4833896736779722397e-43 - 1.359931410650724134e-1335j 6.11e-148, 2.93e-391j
7.3966870972420065353e-35 - 2.2363702195708979214e-1329j 1.48e-147, 7.12e-391j
4.9275525527615783198e-61 + 3.598760903506798653e-1344j 5.29e-159, 2.54e-402j
4.9875706077648583449e-47 + 1.7742950259425039721e-1337j 8.74e-150, 4.19e-393j
0.0048212057835012925548 + 8.613969001758704833e-1309j 2.29e-106, 1.1e-349j
5.6109255503791229754e-16 + 9.9329494974479141574e-1319j 1.66e-136, 7.95e-380j
5.837337488545223783e-06 - 6.7656974797181890194e-1311j 1.56e-122, 7.48e-366j
1.5984742601600465652e-37 - 2.828729666285866691e-1332j 2.41e-145, 1.16e-388j
2.1635139305739027353e-17 - 1.97790079264887089e-1320j 1.16e-137, 5.55e-381j
0.075377424472367553075 + 1.298613066485370901e-1307j 9.34e-96, 4.48e-339j
4.276197938092881697e-09 + 2.8993181304307240669e-1314j 4.9e-129, 2.35e-372j
4.5194069688478956561e-10 - 1.2916833052507700562e-1314j 1.8e-131, 8.65e-375j
0.075377424472367553075 + 1.4947873187119046966e-1307j 1.94e-96, 9.3e-340j
-1.8720944351508255072e-05 - 1.1776991259178534052e-1309j 6.65e-127, 3.19e-370j
2.5865777506831583001e-05 + 1.0462683601198550667e-1310j 3.95e-124, 1.9e-367j
0.059827815747741306282 - 1.1302029106745134697e-1307j 1.61e-96, 7.74e-340j
1.2033722313510501959e-14 - 1.3402400426793016632e-1318j 2.83e-137, 1.36e-380j
6.3700778889144457841e-06 + 3.6328487207681374899e-1310j 3.92e-127, 1.88e-370j
0.00032551308215558341623 - 2.792171528076730925e-1309j 1.61e-120, 7.74e-364j
0.00099561178066821983717 + 5.1036940108638445799e-1309j 2.35e-119, 1.13e-362j
6.2626654380448570454e-51 + 1.0376715251516445951e-1338j 2.63e-159, 1.26e-402j
3.5581456138708428974e-22 + 2.0013241120868082804e-1323j 1.53e-142, 7.32e-386j
1.3516382664683918831e-05 + 8.3513080456439881597e-1310j 3.52e-127, 1.69e-370j
2.2159462797307416628e-32 + 1.1097231689859122903e-1327j 2.14e-151, 1.03e-394j
3.6561750836061040384e-08 - 7.7508208242812880606e-1313j 1.68e-131, 8.04e-375j
1.7444835910623532727e-20 - 2.1796567367661955672e-1322j 1.28e-142, 6.15e-386j
5.6109255503791229754e-16 + 1.6803105480061201562e-1319j 3.21e-140, 1.54e-383j
1.3516382664683918831e-05 + 3.2570396290050373484e-1310j 9.22e-133, 4.42e-376j
5.7053125697283895457e-24 - 2.7523914910487342045e-1323j 4.62e-149, 2.22e-392j
6.5977978457554265051e-28 - 4.0342791997036015548e-1325j 1.74e-150, 8.36e-394j
9.1434764994142642798e-05 - 6.0329136673120055829e-1310j 1.69e-129, 8.09e-373j
2.1535769156553234679e-13 + 1.014905501460324051e-1317j 7.78e-140, 3.74e-383j
4.1393256039871535579e-11 + 5.2796584216515547202e-1316j 1.33e-138, 6.39e-382j
2.0832730222085227479e-40 - 9.2966910333237711602e-1333j 4.49e-158, 2.16e-401j
6.3700778889144457841e-06 + 1.4390122337262125084e-1310j 3.91e-134, 1.88e-377j
0.0023570011688318239757 - 8.0482892061966334586e-1309j 1.28e-129, 6.13e-373j
0.09371241347151927988 - 1.5691857972927806355e-1307j 2.65e-120, 1.27e-363j
6.829333452437914386e-19 + 2.1640527184725923255e-1321j 1.46e-143, 7.03e-387j
1.7444835910623532727e-20 - 2.1307710322078479892e-1321j 1.86e-149, 8.92e-393j
0.031321577216982561831 - 4.5580753191150405565e-1308j 6.1e-126, 2.93e-369j
2.5865777506831583001e-05 + 2.229188875370893782e-1310j 6.77e-135, 3.25e-378j
9.1434764994142642798e-05 - 1.2021250258021167782e-1309j 4.46e-134, 2.14e-377j
0.0023570011688318239757 - 4.8889773446659385089e-1309j 7.67e-132, 3.68e-375j
1.2033722313510501959e-14 - 6.9569155675511330881e-1318j 6.77e-146, 3.25e-389j
0.09371241347151927988 - 1.7238747597444753856e-1307j 1.28e-125, 6.16e-369j
0.059827815747741306282 - 9.3794578292095532742e-1308j 1.19e-126, 5.73e-370j
0.0095262990853900519797 - 1.389650378009798451e-1308j 8.74e-131, 4.19e-374j
6.2959616107954618768e-05 + 2.1239071550116242653e-1309j 1.07e-133, 5.11e-377j
5.837337488545223783e-06 - 2.9539139657718647076e-1311j 7.64e-137, 3.67e-380j
3.242408597732937122e-12 - 3.0596847851836499009e-1316j 6.08e-145, 2.93e-388j
0.018228811375282901276 + 3.0028554490272677436e-1308j 3.39e-133, 1.63e-376j
-1.8720944351508255072e-05 - 4.610272051244215251e-1310j 2.57e-136, 1.23e-379j
0.031321577216982561831 - 3.4203331115522795718e-1308j 1.02e-132, 4.9e-376j
0.046417598202821368712 + 5.7904325660289211402e-1308j 1.08e-132, 5.19e-376j
4.276197938092881697e-09 + 9.0174376968656741165e-1314j 3.05e-142, 1.47e-385j
6.2959616107954618768e-05 + 4.051900920252104085e-1309j 8.72e-137, 4.18e-380j
0.0095262990853900519797 - 2.0595281589947216251e-1308j 1.68e-135, 7.97e-379j
6.829333452437914386e-19 + 1.7447137995698060876e-1320j 1.22e-150, 5.61e-394j
4.5194069688478956561e-10 - 3.7969361446932550972e-1315j 4.64e-143, 1.77e-386j
0.10401364073964730837 + 1.7904320274301582178e-1307j 1.65e-135, 6.23e-379j
0.10577556705207614823 - 1.9191670101665336525e-1307j 6.39e-136, 2.44e-379j
0.10401364073964730837 + 1.8757469905798476288e-1307j 5.14e-136, 1.87e-379j
3.5581456138708428974e-22 + 2.4694616607297468512e-1322j 3.71e-153, 2.23e-396j

Download

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