Rule: Q[2, 5, 14, 56]

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)
-15.285825013458475283 - 1.7206231819730847179e-1330j 1.14e-498, 1.14e-498j
-13.671852922631171784 - 3.143817368137989342e-1350j 3.21e-496, 3.21e-496j
11.855600544255356445 - 1.4432072666460491588e-1358j 2.87e-494, 2.87e-494j
10.805494599381424504 + 2.2945816997346147235e-1358j 1.38e-493, 1.38e-493j
14.402505782272790483 + 3.1848841028779356161e-1366j 2.99e-497, 2.99e-497j
13.671852922631171784 + 3.5350793888309789993e-1365j 3.16e-496, 3.16e-496j
11.319438714518061314 + 1.5151655747474707611e-1364j 7.18e-494, 7.18e-494j
-11.319438714518061314 + 2.1414581906981136354e-1384j 6.87e-494, 6.87e-494j
3.9729768769722486258 - 4.1884098623728892224e-1410j 2.5e-496, 2.5e-496j
9.3622918406760416312 + 1.1217430870461830159e-1405j 4.29e-493, 4.29e-493j
-12.41965960859968445 - 8.7727966515901750389e-1414j 8.68e-495, 8.68e-495j
-5.7760012127031578491 - 4.1222005808444014097e-1428j 8.4e-494, 8.4e-494j
12.41965960859968445 + 2.2107456156208849643e-1436j 8.71e-495, 8.71e-495j
-13.020262388141635509 + 5.2277505067557410194e-1444j 2.03e-495, 2.03e-495j
13.020262388141635509 - 2.4523664231343670183e-1464j 1.99e-495, 1.99e-495j
-14.402505782272790483 - 7.9877109302973829003e-1477j 2.9e-497, 2.9e-497j
4.268523920434384988 + 1.8339689872184761707e-1491j 7.93e-496, 7.93e-496j
-8.0255610486374642645 - 2.2419636390077455489e-1497j 3.9e-493, 3.9e-493j
-1.5891303384631702415 + 1.3165591567340475125e-1521j 1.2e-503, 1.2e-503j
3.805293342715869284 - 1.1930433019571060117e-1514j 9.86e-497, 9.86e-497j
8.4613636947751187142 + 3.7123994329127910376e-1510j 4.51e-493, 4.51e-493j
15.285825013458475283 - 1.3647404018757529369e-1522j 1.07e-498, 1.07e-498j
6.0594605151683552015 - 6.821573445083397568e-1516j 1.49e-493, 1.49e-493j
-4.596014865123965931 + 5.2816375398643512486e-1523j 3.67e-495, 3.67e-495j
-3.805293342715869284 + 4.2096984670329687302e-1528j 9.54e-497, 9.54e-497j
8.9066679898305994245 + 1.0211706046573337105e-1540j 4.69e-493, 4.69e-493j
-10.309798376836369771 - 4.3249158342181731004e-1586j 2.29e-493, 2.29e-493j
-2.1290252659381178426 - 6.7119224573642610149e-1630j 9.23e-502, 9.23e-502j
8.0255610486374642645 - 7.7804095033302095219e-1636j 3.83e-493, 3.83e-493j
-11.855600544255356445 + 5.1636628198206721847e-1679j 2.67e-494, 2.67e-494j
-5.4576024383177957111 + 1.7682553432496505504e-1703j 3.59e-494, 3.59e-494j
-10.805494599381424504 + 9.9852236161089001648e-1719j 1.29e-493, 1.29e-493j
-8.4613636947751187142 - 9.0518005449198088139e-1729j 4.45e-493, 4.45e-493j
-7.1820082613038349647 - 1.4402299818986354712e-1737j 2.62e-493, 2.62e-493j
-5.1175449996045946097 + 4.5926131678929731311e-1750j 1.69e-494, 1.69e-494j
4.596014865123965931 - 4.3274771496676983224e-1752j 3.31e-495, 3.31e-495j
10.309798376836369771 - 9.9512703570366735637e-1750j 2.47e-493, 2.47e-493j
1.8789851228602006681 + 2.8747963626086645994e-1758j 1.47e-502, 1.47e-502j
1.2909220585907595212 + 9.8335013280823529667e-1761j 8.25e-505, 8.25e-505j
-4.8408589073908322677 - 5.5128491580352875982e-1750j 9.45e-495, 9.45e-495j
6.394054192399003627 + 1.8651481339347568827e-1749j 1.66e-493, 1.66e-493j
2.7598704991643871468 + 6.4989588808901332216e-1756j 4.53e-500, 4.53e-500j
5.4576024383177957111 - 3.6439266161747324382e-1750j 3.62e-494, 3.62e-494j
-9.8294542925689044533 + 5.5438860822520427437e-1748j 3.51e-493, 3.51e-493j
-3.4833773961004847262 - 1.122610940653407602e-1767j 6.42e-498, 6.42e-498j
-3.1204826171650857167 - 1.3438400993606737411e-1768j 4.45e-499, 4.45e-499j
-2.7598704991643871468 - 1.7161437628225500083e-1770j 4.5e-500, 4.5e-500j
-1.2909220585907595212 + 7.5031104524357372522e-1776j 8.73e-505, 8.73e-505j
0.68738169828439628877 + 3.4608276915126759967e-1777j 2.53e-507, 2.53e-507j
2.418104600352902435 - 2.9986768705645111575e-1771j 5.18e-501, 5.18e-501j
-3.9729768769722486258 - 7.8735045192591635887e-1768j 2.56e-496, 2.56e-496j
-1 + 1.8996234907631745902e-1775j 5.75e-506, 5.75e-506j
-7.5989348425545680567 - 3.2609913253515275635e-1762j 3.16e-493, 3.16e-493j
1.5891303384631702415 - 2.7669607466295618621e-1783j 1.14e-503, 1.14e-503j
-6.0594605151683552015 - 9.6238751139863690517e-1772j 1.33e-493, 1.33e-493j
5.7760012127031578491 + 2.8047840739940106033e-1779j 8.38e-494, 8.38e-494j
-8.9066679898305994245 + 8.7757500757370537158e-1780j 4.65e-493, 4.65e-493j
7.5989348425545680567 - 9.2781595675335931801e-1788j 3.32e-493, 3.32e-493j
-1.8789851228602006681 - 2.6109577846039053068e-1797j 1.39e-502, 1.39e-502j
7.1820082613038349647 - 5.4891444244314810803e-1789j 2.54e-493, 2.54e-493j
1 + 7.7538574328536197987e-1801j 5.24e-506, 5.24e-506j
5.1175449996045946097 + 3.9299647233017037641e-1789j 1.69e-494, 1.69e-494j
-2.418104600352902435 + 2.0804152775040103387e-1796j 5.32e-501, 5.32e-501j
-6.394054192399003627 + 4.4531284835158834855e-1787j 1.65e-493, 1.65e-493j
9.8294542925689044533 + 4.3524593807824122006e-1796j 3.58e-493, 3.58e-493j
2.1290252659381178426 - 6.136047010216106047e-1805j 9.94e-502, 9.94e-502j
4.8408589073908322677 + 3.4171576705595434671e-1798j 1.01e-494, 1.01e-494j
-6.7773530756553898237 + 3.113861082842764522e-1795j 2.02e-493, 2.02e-493j
-4.268523920434384988 - 5.8876161274799352691e-1812j 7.53e-496, 7.53e-496j
6.7773530756553898237 + 2.0819211752688134679e-1808j 2.11e-493, 2.11e-493j
2.6514530594139619724e-1844 + 2.0846461092752515087e-1844j 2.6e-1842, 2.6e-1842j
3.4833773961004847262 - 2.6085421004880463408e-1817j 6.36e-498, 6.36e-498j
-0.34932069913931517549 + 7.6549627419466040299e-1828j 1.15e-508, 1.15e-508j
-0.68738169828439628877 + 3.0842488790940216244e-1827j 2.89e-507, 2.89e-507j
-9.3622918406760416312 - 2.053277261277745208e-1811j 4.22e-493, 4.22e-493j
0.34932069913931517549 + 5.5710108374845699567e-1842j 1.15e-508, 1.15e-508j
3.1204826171650857167 + 8.329621097753901824e-1834j 4.68e-499, 4.68e-499j

Weights

Weight (ball center) Error (ball radius)
7.4486414667151202949e-52 - 1.0696805525182670588e-1380j 1.98e-173, 4.42e-421j
7.0346565877186975766e-42 - 2.5911477433367692766e-1376j 9.1e-170, 2.03e-417j
6.5959016272829471781e-32 + 7.3139914479229988387e-1372j 1.19e-166, 2.66e-414j
8.9070670195813337108e-27 + 8.1480842212493717437e-1369j 6.22e-164, 1.39e-411j
2.8417178370580918234e-46 + 5.0724703995659615638e-1380j 5.67e-174, 1.26e-421j
7.0346565877186975766e-42 - 1.4441904320455328576e-1377j 3.65e-172, 8.13e-420j
3.1438477208483255978e-29 - 2.7663454399145808612e-1370j 8.74e-166, 1.95e-413j
3.1438477208483255978e-29 - 1.8555769520299652904e-1369j 1.14e-169, 2.54e-417j
2.9364542218300703021e-05 + 2.448465278903058002e-1352j 1.3e-138, 2.89e-386j
1.7031711187048415251e-20 - 6.7581713099824444803e-1365j 4.85e-162, 1.08e-409j
7.4170171097333657388e-35 - 1.3744010090580001975e-1372j 2.01e-172, 4.48e-420j
6.5977923387032493529e-09 + 2.4942265531877326621e-1355j 2.8e-152, 6.25e-400j
7.4170171097333657388e-35 - 1.4218342246317349119e-1373j 8.01e-170, 1.78e-417j
3.8282631587908932184e-38 + 2.3331277358950993742e-1374j 7.28e-174, 1.62e-421j
3.8282631587908932184e-38 + 1.8673887787950611382e-1375j 1.11e-171, 2.47e-419j
2.8417178370580918234e-46 + 1.7048556609791805229e-1378j 2.16e-177, 4.8e-425j
1.5032942372610601983e-05 - 6.7651132747110268149e-1353j 4.39e-145, 9.77e-393j
1.775118443405326693e-15 + 5.7103254542889040967e-1361j 2.35e-163, 5.23e-411j
0.034122393927176259768 + 1.0036308377189201774e-1350j 1.08e-122, 2.4e-370j
6.9083694569797200766e-05 - 3.3204318978831747076e-1352j 3.04e-142, 6.77e-390j
4.9914059191105483714e-17 - 1.4113987024560470659e-1362j 1.08e-162, 2.4e-410j
7.4486414667151202949e-52 - 4.1922189906504450824e-1383j 1.58e-179, 3.51e-427j
1.2690385944042791219e-09 - 2.4256338968447416387e-1356j 1.01e-155, 2.25e-403j
3.0344666972027031058e-06 + 4.5606266362147349078e-1353j 4.6e-152, 1.02e-399j
6.9083694569797200766e-05 - 5.5215873423050217628e-1352j 7.31e-148, 1.63e-395j
1.0675544181983251553e-18 + 1.029405670013933209e-1363j 7.38e-164, 1.64e-411j
1.6142748147937992626e-24 - 1.0024940176463974426e-1366j 1.11e-171, 2.47e-419j
0.010501320367070463331 + 6.3564149938325530873e-1351j 4.49e-137, 9.99e-385j
1.775118443405326693e-15 + 1.7784643955849932889e-1361j 6.5e-163, 1.45e-410j
6.5959016272829471781e-32 + 5.7871476399232379982e-1371j 1.79e-174, 3.99e-422j
4.6249062185926886796e-08 - 1.0193217491207213613e-1354j 4.71e-158, 1.05e-405j
8.9070670195813337108e-27 + 4.7450578417384408444e-1368j 1.17e-172, 2.61e-420j
4.9914059191105483714e-17 - 4.911266950553422101e-1362j 2.19e-168, 4.87e-416j
1.0341140677080986219e-12 + 6.6520974719025664274e-1359j 2.7e-165, 6.02e-413j
2.6701354204356581111e-07 + 5.2535246811022386457e-1354j 7.74e-158, 1.72e-405j
3.0344666972027031058e-06 + 2.4520986586905829313e-1353j 1.89e-157, 4.21e-405j
1.6142748147937992626e-24 - 1.9489413712635961841e-1367j 1.07e-172, 2.37e-420j
0.018239573340237117119 - 7.0343800039733242681e-1351j 9.21e-145, 2.05e-392j
0.050493510606264124673 - 9.1401423660907396166e-1351j 7.17e-139, 1.6e-386j
7.362168599331161639e-07 - 2.0265641269017962554e-1353j 5.59e-158, 1.24e-405j
1.9321687347706186037e-10 + 2.9453686130434402124e-1357j 2.11e-164, 4.71e-412j
0.0031396936867155699389 + 8.8189666163303283293e-1352j 7.89e-152, 1.76e-399j
4.6249062185926886796e-08 - 4.8295398864676530403e-1355j 1.12e-161, 2.49e-409j
1.9760860319924799012e-22 + 1.799919190432826771e-1365j 7.22e-174, 1.61e-421j
0.00033075475982592836173 + 4.7507962888313010929e-1352j 3.38e-156, 7.54e-404j
0.0011162187610962626969 - 6.5863721520632651931e-1352j 2.5e-155, 5.57e-403j
0.0031396936867155699389 + 1.2705170381440728991e-1351j 3.16e-154, 7.03e-402j
0.050493510606264124673 - 1.0826357902861212967e-1350j 2.27e-146, 5.05e-394j
0.10318469636766742778 - 7.9212489178581947234e-1351j 2.64e-146, 5.88e-394j
0.0069201886629782920394 - 2.1763268205866341458e-1351j 2.78e-154, 6.18e-402j
2.9364542218300703021e-05 + 4.1682260004807602159e-1352j 3.93e-158, 8.75e-406j
0.07200255580246255981 + 1.0372569063507608991e-1350j 3.48e-148, 7.76e-396j
4.8672274660537751286e-14 - 6.2679045648018201679e-1360j 2.65e-170, 5.9e-418j
0.034122393927176259768 + 8.1460512718218413183e-1351j 1.94e-151, 4.32e-399j
1.2690385944042791219e-09 - 5.611728013310351699e-1356j 7.21e-166, 1.61e-413j
6.5977923387032493529e-09 + 1.1261917549446676596e-1355j 4.19e-167, 9.34e-415j
1.0675544181983251553e-18 + 3.9039467718252142119e-1363j 3.24e-174, 7.22e-422j
4.8672274660537751286e-14 - 2.1053615722639626195e-1360j 9.23e-173, 2.06e-420j
0.018239573340237117119 - 9.0061340465169518887e-1351j 1.85e-156, 4.13e-404j
1.0341140677080986219e-12 + 2.3993136441119435897e-1359j 4.76e-172, 1.06e-419j
0.07200255580246255981 + 9.0987534533145973331e-1351j 2.16e-155, 4.8e-403j
2.6701354204356581111e-07 + 2.6181611166654699274e-1354j 6.75e-167, 1.51e-414j
0.0069201886629782920394 - 2.9942783656593860576e-1351j 8.37e-160, 1.87e-407j
1.9321687347706186037e-10 + 7.1813856916183199109e-1357j 7.15e-170, 1.59e-417j
1.9760860319924799012e-22 + 3.9103791166232411832e-1366j 9.26e-179, 2.06e-426j
0.010501320367070463331 + 4.8022278598015281759e-1351j 1.04e-161, 2.31e-409j
7.362168599331161639e-07 - 1.0517079564872802186e-1353j 1.26e-166, 2.81e-414j
1.6789665295806608433e-11 - 6.9900321664976133362e-1358j 1.81e-171, 4.04e-419j
1.5032942372610601983e-05 - 1.2007240651230947942e-1352j 2.42e-165, 5.37e-413j
1.6789665295806608433e-11 - 2.6956448564556977241e-1358j 7.56e-172, 1.68e-419j
0.14002076230069325334 - 6.6718598799370381124e-1351j 2.49e-163, 5.63e-411j
0.00033075475982592836173 + 2.9873951549008699405e-1352j 2.44e-166, 5.43e-414j
0.12982113936491520966 + 7.2405599930619547564e-1351j 3.63e-164, 8.9e-412j
0.10318469636766742778 - 8.6672081158544880533e-1351j 3.11e-164, 7.69e-412j
1.7031711187048415251e-20 - 2.8121087754533774194e-1364j 3.36e-179, 7.8e-427j
0.12982113936491520966 + 6.9170225568999586565e-1351j 1.19e-164, 3.15e-412j
0.0011162187610962626969 - 4.3531529509999237046e-1352j 2.86e-166, 6.12e-414j

Download

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