Rule: Q[6, 9, 76]

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)
-13.982662903615627777 - 7.5294601083083395461e-1263j 1.94e-491, 1.94e-491j
15.09755886346545897 + 1.0020232384358759331e-1268j 8.7e-493, 8.7e-493j
12.506509857399374937 - 3.2735794230280666326e-1298j 3.74e-490, 3.74e-490j
-15.722348653545334421 - 7.5317388153446341425e-1325j 9.97e-494, 9.97e-494j
-6.1477704214465170744 + 4.9025491149435134214e-1325j 4.07e-492, 4.07e-492j
17.273056305143165157 + 1.0578953330044900516e-1319j 1.87e-496, 1.87e-496j
-16.423820601129936045 + 6.9049038532887838173e-1330j 6.89e-495, 6.89e-495j
11.169272200962178971 + 1.7123686957778345234e-1327j 1.22e-489, 1.22e-489j
15.722348653545334421 + 1.3534689976669694812e-1336j 9.61e-494, 9.61e-494j
-12.04853738941679248 - 7.3609849130370480126e-1341j 5.92e-490, 5.92e-490j
-11.169272200962178971 - 1.0192618349202805985e-1340j 1.21e-489, 1.21e-489j
16.423820601129936045 + 8.1987785993381766266e-1341j 6.83e-495, 6.83e-495j
-6.8616879061542398137 - 9.9006603762063955874e-1345j 2.09e-491, 2.09e-491j
-1.8891758777537106755 + 1.3301719167151600842e-1353j 4.82e-502, 4.82e-502j
-8.7356586964426829111 + 7.1154046705055641005e-1341j 5.8e-490, 5.8e-490j
-5.3328810219315944432 - 1.6034643894157837385e-1343j 4.28e-493, 4.28e-493j
6.1477704214465170744 + 9.4577887767547082384e-1340j 4.23e-492, 4.23e-492j
13.982662903615627777 - 1.4744527933281146322e-1351j 1.93e-491, 1.93e-491j
1.8891758777537106755 + 4.1681496755546993475e-1380j 4.89e-502, 4.89e-502j
-6.5009688739839230656 - 1.0644604240530765111e-1369j 9.62e-492, 9.62e-492j
-9.5198665219617116897 - 3.2687845444393361061e-1367j 1.08e-489, 1.08e-489j
12.979451187839597921 + 1.1681799447713173431e-1378j 1.57e-490, 1.57e-490j
-9.1249196389327468661 - 8.7402236271266921887e-1396j 8.14e-490, 8.14e-490j
-2.9984458682133088812 - 3.0698185365409741645e-1408j 8.52e-499, 8.52e-499j
7.5977557429122309674 + 5.8323665098908714259e-1399j 9.84e-491, 9.84e-491j
10.329142490403533762 + 1.4119195115239702763e-1421j 1.49e-489, 1.49e-489j
14.522320490385058284 - 2.5299418017803224669e-1451j 4.92e-492, 4.92e-492j
-12.979451187839597921 - 5.9870271152262717197e-1471j 1.63e-490, 1.63e-490j
13.47021136423031242 + 1.6729063475395098878e-1487j 6.25e-491, 6.25e-491j
12.04853738941679248 - 1.9526928336433805098e-1510j 5.8e-490, 5.8e-490j
-17.273056305143165157 + 1.7307617942530954806e-1530j 1.75e-496, 1.75e-496j
-14.522320490385058284 - 5.764932357309160498e-1525j 5.15e-492, 5.15e-492j
2.6973105238948190436 - 1.1554588696924764366e-1532j 1.69e-499, 1.69e-499j
3.9995288851549173329 + 1.2201187167841259823e-1528j 1.97e-496, 1.97e-496j
-5.0229397655408401629 + 2.6935035836592503455e-1527j 6.23e-494, 6.23e-494j
4.3418637687749014379 + 3.1863181241731475053e-1528j 1.29e-495, 1.29e-495j
7.9724115019926781901 + 2.9058305039687164933e-1521j 1.92e-490, 1.92e-490j
-12.506509857399374937 - 1.8071478170533183109e-1537j 3.35e-490, 3.35e-490j
8.3516166108344414689 - 2.2092395545240759886e-1538j 3.36e-490, 3.36e-490j
-11.603359957883255265 - 7.7364692398108382856e-1550j 8.51e-490, 8.51e-490j
-0.93418988765918212034 + 1.7035778218396482398e-1574j 9.01e-506, 9.01e-506j
-7.22749066408729038 - 4.915780488438205839e-1559j 4.6e-491, 4.6e-491j
11.603359957883255265 - 2.3789844756365819377e-1561j 9.13e-490, 9.13e-490j
1.2661003420239348876 - 8.7484288067675149866e-1590j 9.69e-504, 9.69e-504j
-15.09755886346545897 - 9.8373895261004422384e-1580j 8.53e-493, 8.53e-493j
-2.6973105238948190436 + 6.5107245469426646989e-1587j 1.79e-499, 1.79e-499j
-13.47021136423031242 + 3.110344914557367488e-1577j 6.41e-491, 6.41e-491j
-1.3498952853218839149 + 1.9976404137315562263e-1590j 2.5e-503, 2.5e-503j
0.93418988765918212034 + 9.7068084465055993649e-1592j 8.81e-506, 8.81e-506j
6.8616879061542398137 + 1.6323635651547420198e-1575j 2.2e-491, 2.2e-491j
-10.329142490403533762 - 3.789165630796084147e-1580j 1.47e-489, 1.47e-489j
9.9210552269264724847 + 1.5269195512882337082e-1586j 1.38e-489, 1.38e-489j
8.7356586964426829111 - 1.8661936380645937686e-1609j 5.5e-490, 5.5e-490j
1.5672332906423312197 - 4.215898742471374682e-1640j 6.24e-503, 6.24e-503j
3.3242574335521189524 + 5.0770054071907111969e-1635j 4.9e-498, 4.9e-498j
-7.5977557429122309674 - 5.2553064856089743535e-1627j 9.52e-491, 9.52e-491j
-1.5672332906423312197 + 8.0504676242145284585e-1640j 6.16e-503, 6.16e-503j
-2.189044438249322899 - 1.252749181840337943e-1638j 5.27e-501, 5.27e-501j
-7.9724115019926781901 + 1.096397369747141544e-1626j 1.76e-490, 1.76e-490j
-5.5533529315903281928 - 2.38106902490306742e-1629j 1.27e-492, 1.27e-492j
-9.9210552269264724847 - 4.3996120141087515832e-1625j 1.33e-489, 1.33e-489j
-3.3242574335521189524 - 3.9726095939076700516e-1642j 4.92e-498, 4.92e-498j
-3.6596057638765869373 + 8.8417344656758723189e-1642j 3.24e-497, 3.24e-497j
9.5198665219617116897 - 1.5932646475022509835e-1632j 1.17e-489, 1.17e-489j
2.4440098084964929991 - 2.2012962264297822019e-1657j 3.58e-500, 3.58e-500j
5.8135707224171662465 + 5.9392784595100426637e-1647j 2.22e-492, 2.22e-492j
-4.6846259706492073551 + 5.8892810968237926396e-1655j 9.61e-495, 9.61e-495j
-2.4440098084964929991 + 7.515529098033902752e-1661j 3.52e-500, 3.52e-500j
5.0229397655408401629 - 1.3552152434477514321e-1652j 6.26e-494, 6.26e-494j
2.189044438249322899 - 4.3784780474959912776e-1661j 5.63e-501, 5.63e-501j
0.61670659019259415219 - 2.6948682001474304611e-1667j 2.28e-507, 2.28e-507j
5.3328810219315944432 - 5.1821294893606806374e-1651j 4.44e-493, 4.44e-493j
-3.9995288851549173329 - 5.8923574881694937994e-1656j 1.99e-496, 1.99e-496j
-1.2661003420239348876 + 8.5346238348970116184e-1664j 9.04e-504, 9.04e-504j
2.9984458682133088812 + 2.2804884168905304657e-1658j 8.48e-499, 8.48e-499j
5.5533529315903281928 + 1.6474970395372929184e-1649j 1.23e-492, 1.23e-492j
-5.8135707224171662465 - 3.2486377409766579657e-1655j 2.23e-492, 2.23e-492j
-8.3516166108344414689 - 6.605603349314197986e-1653j 3.5e-490, 3.5e-490j
-0.30597294479635185239 + 7.2061318928403511535e-1671j 9.92e-509, 9.92e-509j
6.5009688739839230656 - 8.0875680151030035685e-1652j 9.47e-492, 9.47e-492j
3.6596057638765869373 + 4.6166903940427558138e-1676j 3.1e-497, 3.1e-497j
0.30597294479635185239 + 6.2143481391056221423e-1692j 9.92e-509, 9.92e-509j
9.1249196389327468661 + 4.680609345774849082e-1672j 8.5e-490, 8.5e-490j
6.3460629384341786418e-1752 - 6.5971647326837533701e-1752j 8.33e-1750, 8.33e-1750j
7.22749066408729038 - 6.0554399187659335151e-1694j 4.67e-491, 4.67e-491j
-10.74490576269506756 - 1.3913019493156687976e-1707j 1.38e-489, 1.38e-489j
1.3498952853218839149 + 1.2997218517354675094e-1731j 2.51e-503, 2.51e-503j
4.6846259706492073551 + 5.9217675535951418079e-1718j 9.33e-495, 9.33e-495j
10.74490576269506756 + 1.5099436033956207317e-1732j 1.39e-489, 1.39e-489j
-0.61670659019259415219 + 9.4812500489798814794e-1774j 2.28e-507, 2.28e-507j
-4.3418637687749014379 + 1.4990235538238602818e-1761j 1.3e-495, 1.3e-495j

Weights

Weight (ball center) Error (ball radius)
7.3369832107140594762e-44 - 4.1563247333647633208e-1305j 9.68e-147, 2.76e-391j
7.6056836012836606948e-51 - 3.4652834167948759691e-1311j 4.08e-150, 1.16e-394j
2.0128029335321979615e-35 + 7.9811969515663547306e-1303j 3.89e-143, 1.11e-387j
5.5107612463002270157e-55 - 3.6590511319679212975e-1312j 3.08e-152, 8.79e-397j
8.6010801868929104488e-10 + 1.1744412872362775109e-1286j 9.31e-118, 2.65e-362j
6.3892055268482988795e-66 + 3.4877816929991314872e-1319j 3.23e-156, 9.21e-401j
8.0496857634547521438e-60 + 7.2393136861565377027e-1315j 2.96e-154, 8.44e-399j
1.3921882455570943928e-28 - 5.2591721970842193392e-1299j 1.87e-140, 5.33e-385j
5.5107612463002270157e-55 + 2.1429376897186617451e-1313j 3.47e-152, 9.9e-397j
5.4033803607296835869e-33 - 2.3783232875182983327e-1300j 4.91e-144, 1.4e-388j
1.3921882455570943928e-28 - 4.7017414627230040359e-1298j 1.28e-141, 3.64e-386j
8.0496857634547521438e-60 - 5.812019012834472329e-1316j 1.01e-154, 2.87e-399j
8.6587287071912553257e-12 + 3.2875175355195693103e-1288j 9.74e-126, 2.78e-370j
0.021023446176933828063 + 7.5469961190149422933e-1281j 1.69e-84, 4.83e-329j
4.1425524721452930844e-18 - 3.1706500335837499126e-1292j 2.78e-134, 7.92e-379j
7.2301298005616728327e-08 - 5.8571555696214703939e-1285j 2.29e-118, 6.54e-363j
8.6010801868929104488e-10 + 4.5710000756649406342e-1287j 4.79e-126, 1.37e-370j
7.3369832107140594762e-44 - 1.9754292808589119574e-1307j 8.04e-151, 2.29e-395j
0.021023446176933828063 + 5.7504049115262916389e-1281j 3.2e-89, 9.13e-334j
9.4880219116676970845e-11 - 1.9296664767643281767e-1287j 2.22e-124, 6.33e-369j
3.3202285173649623982e-21 - 5.1549478458648905248e-1294j 7.29e-138, 2.08e-382j
5.0277115770371718552e-38 - 2.9609746932351674699e-1304j 5.58e-149, 1.59e-393j
1.2990768550954689013e-19 + 4.2014980401461618826e-1293j 2.48e-136, 7.08e-381j
0.0014137480586794681255 + 3.5780309913313805089e-1282j 7.02e-106, 2e-350j
4.3346836662117232975e-14 + 2.7445967464542856815e-1290j 1.98e-135, 5.64e-380j
1.1165638046236163131e-24 - 8.9990569949109097077e-1297j 7.7e-144, 2.2e-388j
3.5472424892404193546e-47 + 3.2169584277719920174e-1309j 5.69e-153, 1.62e-397j
5.0277115770371718552e-38 - 7.9578553040288741445e-1303j 4.6e-152, 1.31e-396j
7.9431202327205801377e-41 + 8.7487205889686646173e-1306j 1.61e-150, 4.59e-395j
5.4033803607296835869e-33 - 1.7671009131632793385e-1301j 7.48e-148, 2.13e-392j
6.3892055268482988795e-66 - 3.3130727281219938663e-1318j 6.76e-165, 1.93e-409j
3.5472424892404193546e-47 - 1.6992134526263373859e-1307j 5.9e-157, 1.68e-401j
0.002927442002278737574 - 7.696880278681973563e-1282j 7.1e-114, 2.02e-358j
4.5777542453768194457e-05 - 7.5580287437389930349e-1284j 2.86e-124, 8.14e-369j
4.3980736060521185694e-07 + 1.0003820789026307314e-1284j 3.42e-128, 9.76e-373j
1.1029189351314742533e-05 + 2.7230900826965070658e-1284j 1.76e-126, 5.02e-371j
2.3735036306873136635e-15 - 4.0434824135922581901e-1291j 1.97e-141, 5.62e-386j
2.0128029335321979615e-35 + 1.4322044980742178769e-1301j 9.86e-153, 2.81e-397j
1.0878515547341322243e-16 + 5.6269359151875830816e-1292j 3.44e-143, 9.8e-388j
1.0173918129042983675e-30 + 3.5398448881738676614e-1299j 1.13e-150, 3.24e-395j
0.082820652211898959085 + 1.8255588014514452601e-1280j 4.27e-106, 1.22e-350j
6.6651145203404667242e-13 - 5.5924459865268171208e-1289j 3.44e-139, 9.81e-384j
1.0173918129042983675e-30 + 3.2917829635081750456e-1300j 4.96e-151, 1.41e-395j
0.068080405186430768737 - 6.0971084069247155752e-1280j 4.26e-106, 1.22e-350j
7.6056836012836606948e-51 + 9.0386184953982569338e-1310j 1.56e-160, 4.45e-405j
0.002927442002278737574 - 1.1376140871313490373e-1281j 2.11e-122, 6.03e-367j
7.9431202327205801377e-41 + 4.6868338723424557452e-1304j 1.03e-155, 2.92e-400j
-0.012329250865960376594 + 8.0489433031034314437e-1280j 1.24e-110, 3.55e-355j
0.082820652211898959085 + 1.5969021815395923684e-1280j 9.5e-110, 2.71e-354j
8.6587287071912553257e-12 + 1.1231019102905315912e-1288j 2.51e-142, 7.16e-387j
1.1165638046236163131e-24 - 5.9882879203016566115e-1296j 3.15e-149, 8.98e-394j
6.8332082082551728718e-23 + 9.8802364220918149389e-1296j 4.76e-150, 1.36e-394j
4.1425524721452930844e-18 - 7.3229063311629310406e-1293j 3.46e-147, 9.86e-392j
0.038758160319013020455 - 1.8535462255442724502e-1280j 1.3e-117, 3.72e-362j
0.00052753150867431308205 - 6.927387213514057947e-1283j 8.79e-131, 2.51e-375j
4.3346836662117232975e-14 + 9.276493016629233763e-1290j 9.03e-144, 2.58e-388j
0.038758160319013020455 - 2.321502540640459443e-1280j 1.46e-119, 4.16e-364j
0.010180486966820036042 - 4.3683648535553048457e-1281j 9.28e-125, 2.65e-369j
2.3735036306873136635e-15 - 1.4770589635373538002e-1290j 3.87e-145, 1.1e-389j
1.636600697359080156e-08 + 3.0134838675349824928e-1285j 3.17e-139, 9.04e-384j
6.8332082082551728718e-23 + 5.8148005543836267457e-1295j 6.86e-150, 1.96e-394j
0.00052753150867431308205 - 1.124856235812354696e-1282j 1.74e-133, 4.97e-378j
0.00016663754356262415823 + 3.7947775084413010749e-1283j 3.14e-135, 8.95e-380j
3.3202285173649623982e-21 - 9.7885135032577774188e-1295j 1.46e-153, 4.16e-398j
0.0047887405644800797763 + 1.8376670533181975693e-1281j 3.97e-133, 1.13e-377j
5.7129499401271374237e-09 - 3.1226373584790407627e-1286j 2.37e-146, 6.75e-391j
2.3407985775094274995e-06 - 2.1243252084542724486e-1284j 2.06e-140, 5.88e-385j
0.0047887405644800797763 + 2.6161420206695190433e-1281j 6.96e-133, 1.99e-377j
4.3980736060521185694e-07 + 4.7160548523801483501e-1285j 5.33e-145, 1.52e-389j
0.010180486966820036042 - 3.1857383598085755204e-1281j 1.28e-134, 3.65e-379j
0.10357013340969829466 - 1.2647242311815620056e-1280j 8.94e-130, 2.55e-374j
7.2301298005616728327e-08 - 2.6229195708477008336e-1285j 6.66e-146, 1.9e-390j
4.5777542453768194457e-05 - 1.3613953499053511499e-1283j 1.15e-140, 3.27e-385j
0.068080405186430768737 - 7.3112023872023564365e-1280j 1.73e-131, 4.93e-376j
0.0014137480586794681255 + 2.3144465723613114537e-1282j 1.85e-139, 5.27e-384j
1.636600697359080156e-08 + 1.300244116349167072e-1285j 1.97e-146, 5.61e-391j
5.7129499401271374237e-09 - 7.5671148305414271035e-1286j 7.56e-145, 2.16e-389j
1.0878515547341322243e-16 + 2.2317976573725228654e-1291j 2.07e-151, 5.91e-396j
0.11716713091098831958 + 1.2679828805595699616e-1280j 4.56e-136, 1.3e-380j
9.4880219116676970845e-11 - 7.0481515862876818817e-1288j 8.06e-150, 2.3e-394j
0.00016663754356262415823 + 2.2204460106544755157e-1283j 1.14e-143, 3.24e-388j
0.11716713091098831958 + 1.2136784025786136182e-1280j 5.29e-138, 1.51e-382j
1.2990768550954689013e-19 + 8.8325115035898289555e-1294j 1.93e-156, 5.51e-401j
0.12169010664828899796 - 1.2294114310373693132e-1280j 2.43e-139, 6.93e-384j
6.6651145203404667242e-13 - 1.7811250553662416589e-1289j 5.41e-152, 1.54e-396j
1.4247919879896972185e-26 + 5.5913384068682615499e-1297j 3.02e-160, 8.56e-405j
-0.012329250865960376594 + 6.6316676639773282354e-1280j 1.09e-140, 3.09e-385j
2.3407985775094274995e-06 - 1.0581104947075767553e-1284j 3.94e-147, 1.12e-391j
1.4247919879896972185e-26 + 7.3211386750166072115e-1298j 1.04e-160, 2.97e-405j
0.10357013340969829466 - 1.3814332415592358314e-1280j 6.3e-143, 2.05e-387j
1.1029189351314742533e-05 + 5.1758506850107218256e-1284j 3.7e-147, 9.95e-392j

Download

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