Rule: Q[4, 5, 10, 52]

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)
12.400929102038988778 + 9.2671358037516579936e-1139j 2.19e-496, 2.19e-496j
14.693366853783081732 + 1.7077904651929791379e-1150j 1.65e-499, 1.65e-499j
9.6537663707695862268 + 3.9188699053073833716e-1157j 1.45e-494, 1.45e-494j
-13.799897518223437719 + 2.997790499865670184e-1170j 3.81e-498, 3.81e-498j
-14.693366853783081732 + 1.1005336427201642356e-1170j 1.86e-499, 1.86e-499j
13.799897518223437719 - 6.7084674631479014054e-1165j 3.93e-498, 3.93e-498j
5.2972440506903246902 - 6.7090448889993933168e-1164j 1.22e-494, 1.22e-494j
4.8336228378257066539 + 3.1572749623765479726e-1169j 1.95e-496, 1.95e-496j
-13.060539572706624146 + 4.3482595626041422481e-1171j 4.09e-497, 4.09e-497j
6.8916469294369058587 - 1.3360259189092043526e-1166j 8.13e-495, 8.13e-495j
13.060539572706624146 + 4.263044457754422931e-1171j 3.88e-497, 3.88e-497j
-9.6537663707695862268 + 2.0078237325302950448e-1171j 1.47e-494, 1.47e-494j
-10.156683014599307167 + 9.2678313695011880073e-1181j 9.9e-495, 9.9e-495j
-1.9968883871674586753 + 7.2107290181594989107e-1192j 5.86e-502, 5.86e-502j
-2.7069726121917125129 + 8.9463794400043241662e-1192j 8.19e-501, 8.19e-501j
7.7742955519210410256 + 3.6099317091863003674e-1184j 1.47e-494, 1.47e-494j
10.156683014599307167 - 7.5920478562017781269e-1191j 1.08e-494, 1.08e-494j
10.67782979015328029 + 1.9666285544073941914e-1198j 5.65e-495, 5.65e-495j
-11.22124887597511354 + 1.6347171811745414573e-1199j 2.48e-495, 2.48e-495j
-6.0337394757204462712 - 5.1803781849216988859e-1203j 3.28e-495, 3.28e-495j
-11.792699039978095315 + 1.4680481995638312894e-1206j 8.51e-496, 8.51e-496j
0.74196378430272585765 + 5.0905766205923231272e-1228j 4.69e-507, 4.69e-507j
-3.0705100502673370573 - 1.1223609800641358177e-1219j 6.06e-500, 6.06e-500j
3.0705100502673370573 + 1.735294401271659759e-1220j 5.82e-500, 5.82e-500j
2.3344142183389772393 + 1.864949208295840407e-1221j 1.32e-501, 1.32e-501j
-10.67782979015328029 - 2.1720594682837092552e-1214j 6.01e-495, 6.01e-495j
3.7313022243357029508 - 1.952337582593689732e-1224j 1.73e-498, 1.73e-498j
11.22124887597511354 - 1.8041859485084618139e-1219j 2.59e-495, 2.59e-495j
-5.5959934348863280396 - 2.5158822471671391697e-1225j 3.85e-495, 3.85e-495j
-7.7742955519210410256 + 3.5071737485564978698e-1238j 1.45e-494, 1.45e-494j
11.792699039978095315 - 3.3435295715490475063e-1247j 8.91e-496, 8.91e-496j
-9.166106471023367127 - 5.5851590133201418619e-1248j 1.81e-494, 1.81e-494j
1.0379709584894152952 - 3.9331969420980024756e-1272j 1.17e-505, 1.17e-505j
-8.227976899426284728 - 2.400515809993913607e-1259j 1.74e-494, 1.74e-494j
-4.0693223734716234656 - 1.368356229432259995e-1275j 7.29e-498, 7.29e-498j
-6.8916469294369058587 - 9.4849025440033072394e-1273j 7.61e-495, 7.61e-495j
-4.8336228378257066539 + 3.7285027992138179939e-1284j 1.86e-496, 1.86e-496j
-12.400929102038988778 - 7.671256615932671175e-1283j 2.24e-496, 2.24e-496j
-1.2461599630973153528 + 7.7729690507067386336e-1301j 7.9e-505, 7.9e-505j
5.5959934348863280396 + 4.8356059535440114557e-1288j 4.27e-495, 4.27e-495j
-7.3292024436104300608 + 5.5933805498813809946e-1315j 1.06e-494, 1.06e-494j
1.9076489786401048975 + 1.0721393369739572511e-1339j 3.05e-502, 3.05e-502j
8.227976899426284728 - 2.60499592572731304e-1340j 1.79e-494, 1.79e-494j
4.0693223734716234656 + 1.1931155837178271778e-1356j 7.22e-498, 7.22e-498j
-3.7313022243357029508 - 3.9377468229486070827e-1358j 1.85e-498, 1.85e-498j
-5.2972440506903246902 + 1.9108003346644273928e-1351j 1.2e-494, 1.2e-494j
-8.6914363209572878757 - 6.2879221359723421415e-1353j 1.88e-494, 1.88e-494j
5.3342504636618002739 - 1.1501738444057779414e-1372j 1.43e-494, 1.43e-494j
1.9968883871674586753 + 5.2667926222422922377e-1408j 5.4e-502, 5.4e-502j
6.4605144082402146964 + 4.9691948372354975702e-1416j 4.85e-495, 4.85e-495j
-4.4397138267678565547 + 9.1294214483889354932e-1444j 3.27e-497, 3.27e-497j
-1.9076489786401048975 - 2.2402390841469738328e-1469j 2.92e-502, 2.92e-502j
-0.74196378430272585765 + 1.0029778346275186871e-1476j 5.01e-507, 5.01e-507j
3.4109381072137965233 + 4.6379193968416349862e-1464j 3.9e-499, 3.9e-499j
1.3765667399527046859e-1508 + 5.8237729927499356709e-1508j 4.25e-1506, 4.25e-1506j
-2.3344142183389772393 - 2.3578531500681313897e-1484j 1.33e-501, 1.33e-501j
7.3292024436104300608 - 5.4598162818112726251e-1495j 1.14e-494, 1.14e-494j
9.166106471023367127 - 2.7736723861957650665e-1536j 1.86e-494, 1.86e-494j
6.0337394757204462712 - 4.0782670196829673047e-1556j 3.25e-495, 3.25e-495j
0.37620094485896308559 + 4.3078256890461917024e-1609j 1.04e-508, 1.04e-508j
4.4397138267678565547 - 1.6352473763594339539e-1566j 3.32e-497, 3.32e-497j
-1.5738770477342024144 - 2.0945450678969969688e-1573j 9.27e-504, 9.27e-504j
-1.0379709584894152952 + 7.3940408138587780457e-1575j 1.29e-505, 1.29e-505j
-5.3342504636618002739 - 6.33536708072949701e-1562j 1.47e-494, 1.47e-494j
1.5738770477342024144 - 8.3518866642304390155e-1594j 8.94e-504, 8.94e-504j
1.2461599630973153528 - 3.5910487549611320417e-1596j 6.59e-505, 6.59e-505j
-6.4605144082402146964 + 1.4255933906806361449e-1584j 4.75e-495, 4.75e-495j
-0.37620094485896308559 + 1.6666626097349395744e-1624j 1.39e-508, 1.39e-508j
-3.4109381072137965233 + 9.9987808723416119703e-1602j 3.71e-499, 3.71e-499j
8.6914363209572878757 + 1.2192746455647530889e-1610j 2.08e-494, 2.08e-494j
2.7069726121917125129 + 4.8936543755136303141e-1642j 7.94e-501, 7.94e-501j

Weights

Weight (ball center) Error (ball radius)
1.0167322480442250457e-34 - 6.5615051124984313577e-1172j 5.27e-177, 7.29e-424j
5.4173543249517075135e-48 - 1.9345436926148553932e-1180j 2.08e-182, 2.87e-429j
1.1436978036780765139e-21 + 1.3009067625832529215e-1165j 4.09e-170, 5.65e-417j
1.4094756249637425228e-42 - 1.5494310549262325048e-1178j 1e-182, 1.38e-429j
5.4173543249517075135e-48 + 1.6368098291165916713e-1181j 1.25e-184, 1.73e-431j
1.4094756249637425228e-42 + 2.9018792676463121145e-1177j 5.44e-181, 7.51e-428j
4.5773643475386223874e-07 - 9.7792142529181318811e-1155j 8.07e-156, 1.12e-402j
1.3642583291183958012e-06 + 3.5516923475289237606e-1155j 1.89e-153, 2.61e-400j
2.5180548764013246824e-38 + 3.5714168422539071248e-1176j 2.16e-182, 2.98e-429j
8.4172278919241048675e-12 + 2.1920031343410015044e-1159j 1.23e-163, 1.7e-410j
2.5180548764013246824e-38 - 1.3785942173033958278e-1174j 7.8e-180, 1.08e-426j
1.1436978036780765139e-21 + 1.6204270784141731062e-1166j 9.65e-176, 1.33e-422j
8.1134060042710289964e-24 - 8.0693179978450457659e-1168j 5.69e-177, 7.86e-424j
0.010493706916164923089 + 3.0111589328837785947e-1151j 3.24e-137, 4.48e-384j
0.0037867950081281475711 + 9.2979686400749837032e-1153j 6.87e-145, 9.5e-392j
1.3460037248051425046e-14 + 2.5420813889219920218e-1161j 4.76e-169, 6.58e-416j
8.1134060042710289964e-24 - 8.1107213001309071018e-1167j 1.06e-175, 1.47e-422j
3.69946127254555951e-26 + 4.3739006160662325405e-1168j 3.42e-177, 4.72e-424j
1.0087928791434223339e-28 - 1.0310281875090865961e-1170j 3.81e-182, 5.26e-429j
2.1142014088328598074e-09 + 7.0795264029819724092e-1158j 1.38e-169, 1.9e-416j
1.48639137912620868e-31 + 2.4012513327063971524e-1172j 1.18e-183, 1.63e-430j
0.10627915972680244096 - 2.4117989129660791269e-1151j 3e-144, 4.14e-391j
0.0012674911563694356867 - 3.4595898943248032347e-1153j 2.6e-154, 3.6e-401j
0.0012674911563694356867 - 5.7365949208696536984e-1153j 5.39e-155, 7.44e-402j
0.0097357793959429743524 - 5.2066934879760688534e-1152j 8.51e-150, 1.18e-396j
3.69946127254555951e-26 + 3.2656284408548731134e-1169j 4.45e-181, 6.15e-428j
0.00012202984872599692017 - 1.068106481242950969e-1153j 3.56e-159, 4.92e-406j
1.0087928791434223339e-28 - 2.0645536652723344317e-1169j 1.1e-181, 1.52e-428j
3.0594310103981836078e-08 - 1.6396407687301325914e-1156j 1.25e-169, 1.72e-416j
1.3460037248051425046e-14 + 5.8295653420693463561e-1162j 1.09e-176, 1.5e-423j
1.48639137912620868e-31 + 9.5514814940560411565e-1171j 5.76e-184, 7.96e-431j
1.0932885181018092349e-19 - 2.7297569404574913454e-1165j 1.43e-179, 1.97e-426j
0.050090394918588565055 + 4.157892896733387329e-1151j 2.67e-144, 3.69e-391j
3.6419150874536501388e-16 - 5.0618701818172536399e-1163j 5.67e-178, 7.83e-425j
3.5951675083150616292e-05 + 1.7924512956713286749e-1154j 2.92e-167, 4.04e-414j
8.4172278919241048675e-12 + 6.2595911352695447368e-1160j 1.16e-175, 1.61e-422j
1.3642583291183958012e-06 + 1.5594686675809400056e-1155j 1.57e-170, 2.16e-417j
1.0167322480442250457e-34 - 3.7989878585504538504e-1174j 1.6e-188, 2.21e-435j
0.04917306807642742224 - 3.2922799845872066037e-1151j 5.2e-153, 7.19e-400j
3.0594310103981836078e-08 - 4.3363360576142062978e-1156j 4.68e-175, 6.46e-422j
3.8102797475380461485e-13 - 6.1946021300035837057e-1161j 1.19e-176, 1.64e-423j
0.013013396814348234999 - 5.024150097565011876e-1151j 1.05e-160, 1.45e-407j
3.6419150874536501388e-16 - 2.5023254305890801741e-1162j 2.36e-182, 3.26e-429j
3.5951675083150616292e-05 + 3.5433889955565515588e-1154j 1.22e-170, 1.68e-417j
0.00012202984872599692017 - 5.7401139809431671319e-1154j 6.21e-169, 8.58e-416j
4.5773643475386223874e-07 - 3.9251767684101701196e-1155j 7.03e-173, 9.72e-420j
7.3852412092372981504e-18 + 3.9598527857541556057e-1164j 2.96e-180, 4.08e-427j
-2.9712571350607762122e-07 + 9.1361207623082453838e-1155j 2.84e-174, 3.93e-421j
0.010493706916164923089 + 4.1670460482419363316e-1151j 7.13e-165, 9.85e-412j
1.4771707281540927708e-10 - 2.0036812147848603098e-1158j 3.09e-179, 4.27e-426j
8.0226508091657829681e-06 - 4.9707275574331177117e-1155j 1.24e-172, 1.71e-419j
0.013013396814348234999 - 3.6844901050608213031e-1151j 4.9e-166, 6.77e-413j
0.10627915972680244096 - 2.1394893896493251129e-1151j 5.75e-164, 7.95e-411j
0.00038724643756077727581 + 2.5794280497926808636e-1153j 1.43e-171, 1.98e-418j
0.15050354083976451373 - 1.2981865227203391342e-1151j 2.09e-164, 2.88e-411j
0.0097357793959429743524 - 3.5569756572344031739e-1152j 5.51e-168, 7.61e-415j
3.8102797475380461485e-13 - 2.4098363955557561506e-1160j 9.49e-182, 1.31e-428j
1.0932885181018092349e-19 - 1.819968874835529014e-1164j 1.32e-186, 1.83e-433j
2.1142014088328598074e-09 + 2.0497068657576582661e-1157j 1.42e-178, 1.96e-425j
0.13895510943616918829 + 1.5174018145040486109e-1151j 1.28e-168, 1.77e-415j
8.0226508091657829681e-06 - 1.0514757483210621196e-1154j 2.24e-175, 3.09e-422j
0.04139851978490628089 + 2.0881405584246122115e-1151j 3.36e-170, 4.64e-417j
0.050090394918588565055 + 3.515612344622665005e-1151j 1.71e-169, 2.35e-416j
-2.9712571350607762122e-07 + 3.6403369466583689653e-1155j 9.81e-177, 1.35e-423j
0.04139851978490628089 + 2.695226675839280865e-1151j 6.45e-172, 8.9e-419j
0.04917306807642742224 - 4.0278770109346766912e-1151j 1.94e-171, 2.68e-418j
1.4771707281540927708e-10 - 6.3105972369033136403e-1159j 8.56e-181, 1.18e-427j
0.13895510943616918829 + 1.4280471637723385042e-1151j 2.04e-172, 2.83e-419j
0.00038724643756077727581 + 1.4665589226468221914e-1153j 3.73e-175, 5.15e-422j
7.3852412092372981504e-18 + 2.2515925197194375986e-1163j 1.29e-186, 1.8e-433j
0.0037867950081281475711 + 1.449075993928482846e-1152j 6.13e-175, 8.24e-422j

Download

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