Rule: Q[4, 5, 10, 54]

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)
-9.1311779648545484331 - 3.0372242764401713074e-1031j 5.1e-494, 5.1e-494j
-10.61185813551839328 - 1.2163946883883589172e-1040j 2.22e-494, 2.22e-494j
9.1311779648545484331 + 2.8478413347380686072e-1057j 5.42e-494, 5.42e-494j
-9.6101561219620485017 + 4.7603420318987447733e-1070j 4.85e-494, 4.85e-494j
-11.693148366965202667 - 4.6196372689645338697e-1072j 5.18e-495, 5.18e-495j
-12.27674639455530732 - 1.9800456316236635736e-1072j 1.65e-495, 1.65e-495j
13.586242017415185707 - 1.0332249455596035759e-1070j 5.92e-497, 5.92e-497j
-13.586242017415185707 + 7.2148616734936750176e-1074j 6.43e-497, 6.43e-497j
14.369155588108372804 + 4.0898584588436722605e-1073j 5.79e-498, 5.79e-498j
10.61185813551839328 + 1.7783798934813803311e-1077j 2.26e-494, 2.26e-494j
12.27674639455530732 + 4.3859216767640181062e-1094j 1.74e-495, 1.74e-495j
-10.102881267245881537 + 6.5140087653780816149e-1102j 3.19e-494, 3.19e-494j
-2.3344142183389772393 + 5.5479080892674656102e-1122j 8.86e-502, 8.86e-502j
9.6101561219620485017 + 1.7009145009082919819e-1113j 4.38e-494, 4.38e-494j
10.102881267245881537 - 1.3198820559046213752e-1122j 3.7e-494, 3.7e-494j
11.693148366965202667 - 9.0606023867119557657e-1127j 4.88e-495, 4.88e-495j
-15.379501494446524674 - 5.6605392569572428245e-1140j 1.84e-499, 1.84e-499j
5.6223563374454828755 + 1.0805688924933037952e-1133j 4.87e-495, 4.87e-495j
-5.3342504636618002739 - 8.1117585537606704065e-1148j 7.72e-495, 7.72e-495j
6.0400366186535845962 - 4.5541532286832836066e-1156j 5.32e-495, 5.32e-495j
-12.901677216458318879 - 9.6275911057626374194e-1168j 3.97e-496, 3.97e-496j
15.379501494446524674 - 7.6965570745860125793e-1172j 1.9e-499, 1.9e-499j
5.3342504636618002739 + 1.1226847259860217206e-1172j 8.06e-495, 8.06e-495j
12.901677216458318879 + 6.5877725379174171289e-1184j 3.73e-496, 3.73e-496j
-8.6640055391956492571 + 1.683677580148680154e-1200j 4.99e-494, 4.99e-494j
8.2071004437914835306 + 2.4928084308179550105e-1219j 4.29e-494, 4.29e-494j
-5.2430259453952304428 - 3.6009186590585041101e-1236j 5.14e-495, 5.14e-495j
4.070641573242480048 - 1.982872163194430917e-1239j 9.25e-498, 9.25e-498j
-3.7313022243357029508 + 8.1636632384685704174e-1242j 1.97e-498, 1.97e-498j
5.2430259453952304428 + 9.0204467965834182721e-1237j 5.07e-495, 5.07e-495j
2.3344142183389772393 - 3.7672843839078103931e-1263j 8.51e-502, 8.51e-502j
-3.4097822755205397509 + 2.1676643724072327518e-1258j 3.8e-499, 3.8e-499j
-4.070641573242480048 - 6.4555229712639592152e-1255j 9.14e-498, 9.14e-498j
1.9598078256225190198 + 1.6970362623400952739e-1264j 1.67e-502, 1.67e-502j
11.140414911385700212 + 6.9866788196534445137e-1258j 1.35e-494, 1.35e-494j
-5.6223563374454828755 + 6.6424044841123306173e-1287j 5.03e-495, 5.03e-495j
7.3193663208640902085 - 3.7534562178569180702e-1333j 2.13e-494, 2.13e-494j
7.7592236546667828917 + 1.338976638814994274e-1367j 3.25e-494, 3.25e-494j
-2.7080131506945144622 - 6.7252800597443374343e-1386j 6.61e-501, 6.61e-501j
-4.4397138267678565547 - 1.1767853211726239917e-1382j 4.35e-497, 4.35e-497j
-11.140414911385700212 - 4.5616111559971602899e-1378j 1.26e-494, 1.26e-494j
-1.9598078256225190198 - 2.2997725681812053572e-1405j 1.83e-502, 1.83e-502j
-6.8866990406552843832 + 1.1814041938257951626e-1398j 1.52e-494, 1.52e-494j
-7.3193663208640902085 - 1.3390368109788562458e-1429j 2.07e-494, 2.07e-494j
-6.4605144082402146964 + 8.6989565037108767339e-1457j 8.18e-495, 8.18e-495j
-14.369155588108372804 - 2.3307346721033749789e-1465j 5.77e-498, 5.77e-498j
8.6640055391956492571 - 9.6890643883173079368e-1468j 4.85e-494, 4.85e-494j
2.3150820158318346518e-1519 - 1.0224878654341057763e-1519j 1.85e-1517, 1.85e-1517j
1.2513621980658841184 + 9.1007799596419763152e-1486j 1.17e-504, 1.17e-504j
4.8287916008719804731 + 1.8995316834036398329e-1475j 2.48e-496, 2.48e-496j
-1.6959742253608550613 - 6.0750122625627943014e-1486j 7.06e-503, 7.06e-503j
-4.8287916008719804731 + 3.1529952162772181895e-1476j 2.59e-496, 2.59e-496j
-3.0705100502673370573 + 1.049017865549828283e-1481j 5.27e-500, 5.27e-500j
2.7080131506945144622 + 2.8611182876106889217e-1481j 6.4e-501, 6.4e-501j
1.0379709584894152952 - 5.924295179191631088e-1486j 1.58e-505, 1.58e-505j
6.4605144082402146964 + 2.2201490559248321983e-1474j 8.55e-495, 8.55e-495j
-0.74196378430272585765 + 7.4340173520381496754e-1491j 5.67e-507, 5.67e-507j
-8.2071004437914835306 - 5.4011735189692299356e-1477j 4.41e-494, 4.41e-494j
3.4097822755205397509 - 1.0009870638353844798e-1487j 3.88e-499, 3.88e-499j
0.74196378430272585765 - 2.7148962301397105481e-1497j 5.95e-507, 5.95e-507j
-0.37650565818011098979 + 1.5230973958726941386e-1497j 1.5e-508, 1.5e-508j
-7.7592236546667828917 - 4.2440252194074900184e-1484j 3.18e-494, 3.18e-494j
-1.5738770477342024144 - 1.657557497433805292e-1494j 2.89e-503, 2.89e-503j
-1.0379709584894152952 - 2.0925703983514541417e-1496j 1.6e-505, 1.6e-505j
1.6959742253608550613 + 9.6411154340385181354e-1494j 7.94e-503, 7.94e-503j
1.5738770477342024144 + 1.2532527146138119143e-1493j 2.85e-503, 2.85e-503j
3.7313022243357029508 - 2.5221979471521682469e-1488j 2.15e-498, 2.15e-498j
-1.2513621980658841184 + 1.4622691998313689717e-1495j 1.23e-504, 1.23e-504j
4.4397138267678565547 - 2.2781555210300025735e-1485j 4.38e-497, 4.38e-497j
6.8866990406552843832 - 1.3014587445861127647e-1491j 1.48e-494, 1.48e-494j
0.37650565818011098979 - 4.4216332417298428961e-1507j 1.42e-508, 1.42e-508j
-6.0400366186535845962 + 1.6663140854124495883e-1502j 5.18e-495, 5.18e-495j
3.0705100502673370573 + 1.5944806726370545759e-1509j 5.75e-500, 5.75e-500j

Weights

Weight (ball center) Error (ball radius)
1.4797419680054794635e-19 - 2.496144766408234938e-1049j 1.61e-161, 3.34e-408j
7.2788268362380873317e-26 - 5.8176242093681213121e-1054j 1.24e-166, 2.58e-413j
1.4797419680054794635e-19 - 2.4609684782115156217e-1051j 2.04e-164, 4.23e-411j
1.7077844233643209668e-21 - 6.3993633223044016238e-1051j 2.02e-163, 4.2e-410j
4.611795634198061334e-31 - 3.899940878827793494e-1057j 2.33e-170, 4.84e-417j
4.4920934505419364558e-34 + 6.8692273732671100268e-1059j 3.06e-172, 6.36e-419j
2.3904208450765812987e-41 - 1.0969269069164631088e-1063j 1.54e-179, 3.19e-426j
2.3904208450765812987e-41 + 5.5934884303035281494e-1063j 7.38e-177, 1.53e-423j
5.0027609121895571552e-46 + 3.5512487569318373787e-1066j 2.07e-181, 4.31e-428j
7.2788268362380873317e-26 + 4.363078081458099924e-1055j 5.51e-173, 1.14e-419j
4.4920934505419364558e-34 - 1.0093283402465333689e-1059j 2.7e-177, 5.61e-424j
1.3689141971364660427e-23 + 1.8348278939229282024e-1052j 1.82e-169, 3.77e-416j
0.0098288182881732690538 - 1.7335979322553693509e-1038j 2.72e-135, 5.65e-382j
1.7077844233643209668e-21 + 1.6355053682813421666e-1052j 9.23e-171, 1.92e-417j
1.3689141971364660427e-23 - 9.2695374508563560079e-1054j 4.77e-172, 9.92e-419j
4.611795634198061334e-31 + 4.798010241649841993e-1058j 2.02e-176, 4.21e-423j
2.2118279216584694151e-52 + 7.3651092835250320486e-1069j 5.65e-187, 1.17e-433j
2.2989442395658152947e-08 - 5.3688370703728532468e-1043j 1.7e-161, 3.54e-408j
-2.9682657315072907994e-08 + 2.4175079844439060178e-1041j 3.72e-161, 7.74e-408j
1.9960439052605769871e-09 + 3.4770929450849842357e-1044j 3.51e-163, 7.29e-410j
1.8595583622965575321e-37 - 8.182862898606594421e-1061j 2.44e-180, 5.07e-427j
2.2118279216584694151e-52 - 1.8775320247933837593e-1069j 2.92e-187, 6.06e-434j
-2.9682657315072907994e-08 + 6.3455448940531682688e-1042j 2.9e-161, 6.02e-408j
1.8595583622965575321e-37 + 1.4003395466132441373e-1061j 2.56e-180, 5.32e-427j
9.2303370135416443821e-18 + 1.2302747777885112077e-1048j 1.67e-172, 3.47e-419j
4.2654836469490810802e-16 - 3.7727725636128203383e-1049j 1.23e-170, 2.56e-417j
2.1138274828315945948e-07 - 3.0399572601450705179e-1041j 3.32e-163, 6.9e-410j
3.5768677381272086918e-05 + 7.9951114514680450363e-1041j 7.56e-159, 1.57e-405j
0.00012280409040575291876 - 5.8680362316792718762e-1040j 3.51e-158, 7.29e-405j
2.1138274828315945948e-07 - 8.2229360553821889205e-1042j 1.24e-161, 2.58e-408j
0.0098288182881732690538 - 1.0276709121277133068e-1038j 1.7e-150, 3.52e-397j
0.00038848839309970373389 + 1.3398086155350810658e-1039j 5.47e-157, 1.14e-403j
3.5768677381272086918e-05 + 2.0857476441473443874e-1040j 4.51e-160, 9.38e-407j
0.02164842804584878565 + 5.222093803194357135e-1038j 8.46e-149, 1.76e-395j
2.4165880873313011362e-28 - 1.6498915460356289885e-1056j 1.62e-177, 3.36e-424j
2.2989442395658152947e-08 - 2.2574336997492591206e-1042j 1.03e-166, 2.13e-413j
4.0483380693068624078e-13 - 3.9355118241292284765e-1047j 1.8e-170, 3.73e-417j
1.4946693488243280851e-14 + 4.000846172253201263e-1048j 3.14e-171, 6.54e-418j
0.0037723348006034717041 + 6.180835600394572673e-1039j 3.33e-157, 6.91e-404j
7.9653829419243015705e-06 - 6.7975959017476465445e-1041j 6.06e-164, 1.26e-410j
2.4165880873313011362e-28 + 1.6646085355352919875e-1055j 8.49e-182, 1.77e-428j
0.02164842804584878565 + 8.0763043941798970116e-1038j 3.79e-155, 7.87e-402j
8.6124042825757077826e-12 + 2.63318872121051769e-1045j 1.25e-173, 2.59e-420j
4.0483380693068624078e-13 - 3.5732915043663667888e-1046j 5.24e-175, 1.09e-421j
1.4590907981155284023e-10 - 2.0072989877640469024e-1044j 1.29e-172, 2.69e-419j
5.0027609121895571552e-46 - 1.593277717470693894e-1065j 8.75e-193, 1.82e-439j
9.2303370135416443821e-18 + 3.2298090774686566866e-1050j 2.66e-178, 5.52e-425j
0.15065549331740399027 - 7.7672016072109031998e-1038j 1.73e-158, 3.59e-405j
0.049143239136566832548 - 2.4550840321119350256e-1037j 1.68e-158, 3.49e-405j
1.3686391406030427267e-06 + 7.9394241237153181175e-1042j 6.66e-171, 1.38e-417j
0.0039348387011313678607 - 3.6678145431530681774e-1037j 3.42e-160, 7.1e-407j
1.3686391406030427267e-06 + 2.5761079958863538379e-1041j 1.25e-168, 2.6e-415j
0.0012621621985444093701 - 2.7648687455392846721e-1039j 1.26e-164, 2.62e-411j
0.0037723348006034717041 + 3.3533140366674314572e-1039j 1.45e-167, 3.02e-414j
0.051019854860166925526 + 2.313490690489486536e-1037j 6.95e-161, 1.44e-407j
1.4590907981155284023e-10 - 3.4382542482043184395e-1045j 4.34e-175, 9.02e-422j
0.10599403082389698296 - 1.5611200777320950402e-1037j 7.79e-161, 1.62e-407j
4.2654836469490810802e-16 - 7.0787763569017913731e-1048j 2.73e-178, 5.66e-425j
0.00038848839309970373389 + 6.1124308589825503301e-1040j 5.95e-171, 1.24e-417j
0.10599403082389698296 - 1.3264846212475227561e-1037j 5.76e-163, 1.2e-409j
0.13899137547400169878 + 9.3086441871114709655e-1038j 1.15e-162, 2.38e-409j
1.4946693488243280851e-14 + 4.9255210735161590752e-1047j 2.59e-177, 5.37e-424j
0.038520568988876035801 + 4.3444077253350358874e-1037j 2.33e-164, 4.84e-411j
0.051019854860166925526 + 2.9069108631294413936e-1037j 6.39e-164, 1.33e-410j
0.0039348387011313678607 - 2.5187554333691520287e-1037j 1.41e-166, 2.94e-413j
0.038520568988876035801 + 3.0669619584774235109e-1037j 2.55e-166, 5.3e-413j
0.00012280409040575291876 - 2.4634958441807084718e-1040j 2.44e-172, 5.07e-419j
0.049143239136566832548 - 3.2348482910198623107e-1037j 5.71e-167, 1.2e-413j
7.9653829419243015705e-06 - 2.3499323322242016599e-1041j 1.39e-173, 2.9e-420j
8.6124042825757077826e-12 + 3.6897128041133965138e-1046j 1.62e-178, 3.44e-425j
0.13899137547400169878 + 8.5713968521365958712e-1038j 6.1e-169, 1.35e-415j
1.9960439052605769871e-09 + 1.7065451653167385566e-1043j 1.62e-176, 3.84e-423j
0.0012621621985444093701 - 1.3733305812577792536e-1039j 8.16e-172, 1.61e-418j

Download

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