Rule: Q[4, 9, 98]

Type

This rule is of Hermite (physicists') 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)
12.804294751261065648 - 7.8878442652572396086e-1125j 1.41e-490, 1.41e-490j
-12.380070464838370689 + 2.0339782866241468184e-1125j 1.72e-489, 1.72e-489j
11.98997236166847804 - 8.6360060659852724636e-1122j 1.21e-488, 1.21e-488j
-10.946028098939248068 - 8.8158197467336088546e-1122j 1.15e-486, 1.15e-486j
10.946028098939248068 + 4.2796836434655541496e-1118j 1.17e-486, 1.17e-486j
12.380070464838370689 + 1.200258645014379229e-1126j 1.65e-489, 1.65e-489j
-11.98997236166847804 - 1.6853628312850750179e-1125j 1.45e-488, 1.45e-488j
-1.4455572662606065829 - 5.6664348484995602205e-1138j 3.62e-501, 3.62e-501j
-5.650224717912798449 + 6.0192008412553968082e-1126j 4.39e-487, 4.39e-487j
7.5831269405992835696 + 1.0447722702688979612e-1121j 8.17e-485, 8.17e-485j
-8.0934028376807695398 - 4.5744062667300685565e-1123j 1.18e-484, 1.18e-484j
11.277709589269827418 - 5.9830110032482708686e-1122j 3.11e-487, 3.11e-487j
-2.4932521905656966304 - 1.1178661976077395867e-1134j 5.39e-496, 5.39e-496j
-3.1844377509706179149 + 1.0815733407636185817e-1131j 3.64e-493, 3.64e-493j
-13.859496996188172673 + 3.6658959827933078083e-1132j 1.2e-493, 1.2e-493j
-12.804294751261065648 + 1.2414963533173972044e-1128j 1.35e-490, 1.35e-490j
6.5981522590636141978 - 4.3634415248899263823e-1123j 1.09e-485, 1.09e-485j
10.626732654222440886 - 2.2761383531387119576e-1121j 3.33e-486, 3.33e-486j
-0.8997798342295002898 + 2.0832855405845942209e-1145j 3.54e-504, 3.54e-504j
-7.5831269405992835696 + 4.7068045782645524201e-1128j 8.25e-485, 8.25e-485j
1.2493906873581484288 + 1.4663710394136256964e-1143j 3.17e-502, 3.17e-502j
7.085313653540304004 - 8.9132726884601602158e-1125j 3.54e-485, 3.54e-485j
11.624431327210654169 - 1.9766141516528753127e-1127j 7.46e-488, 7.46e-488j
13.281221634461953023 + 1.5505961094222561591e-1134j 6.52e-492, 6.52e-492j
13.859496996188172673 - 7.4792040719392926358e-1136j 1.16e-493, 1.16e-493j
-4.7306470042464748259 - 3.6457894356468846062e-1131j 5.28e-489, 5.28e-489j
0.8997798342295002898 + 4.3740311664720595517e-1145j 3.84e-504, 3.84e-504j
-8.8873890192108352457 - 1.4360615247945938672e-1126j 1.08e-484, 1.08e-484j
-11.624431327210654169 + 6.6469001328741260883e-1130j 7e-488, 7e-488j
-1.2493906873581484288 - 9.3898298248423966163e-1144j 3.13e-502, 3.13e-502j
-10.626732654222440886 - 1.7705668408652565383e-1128j 3.32e-486, 3.32e-486j
2.0714067719269643521 - 1.4513702832332245055e-1139j 3.77e-498, 3.77e-498j
-13.281221634461953023 + 3.5803201207761345745e-1134j 7.1e-492, 7.1e-492j
8.0934028376807695398 + 1.6142572165328279637e-1124j 1.24e-484, 1.24e-484j
-7.8365769094726063227 - 9.0423253360958956525e-1133j 9.93e-485, 9.93e-485j
-7.3327851836864648906 + 1.1972748655746029154e-1135j 5.55e-485, 5.55e-485j
-2.8481077541057567845 + 1.1609570623222029793e-1150j 3.84e-494, 3.84e-494j
1.6506801238857845559 + 1.0120096759991810062e-1155j 3.06e-500, 3.06e-500j
3.1844377509706179149 + 1.2285549112114278858e-1148j 3.5e-493, 3.5e-493j
8.3539078402349537194 + 4.7630224647599990463e-1139j 1.29e-484, 1.29e-484j
-6.5981522590636141978 + 9.7301296920522424221e-1153j 1.22e-485, 1.22e-485j
10.317869485875900464 + 8.8307008839483911341e-1163j 8.83e-486, 8.83e-486j
-6.1201853625081651439 - 1.2328121244006474805e-1181j 2.93e-486, 2.93e-486j
7.8365769094726063227 + 2.5782922333276261845e-1184j 1.02e-484, 1.02e-484j
-8.3539078402349537194 + 2.6263483641253667452e-1200j 1.28e-484, 1.28e-484j
-2.9899278943630500681 - 5.3678301132821600146e-1220j 1.22e-493, 1.22e-493j
5.4179360186773902366 - 5.434580137905115897e-1210j 1.71e-487, 1.71e-487j
2.4932521905656966304 + 2.0004202333876154001e-1221j 5.93e-496, 5.93e-496j
5.650224717912798449 + 1.9963742927062075419e-1209j 4.76e-487, 4.76e-487j
-2.0714067719269643521 - 2.1794127338575587634e-1234j 3.78e-498, 3.78e-498j
2.9899278943630500681 + 1.0459148833450224463e-1230j 1.24e-493, 1.24e-493j
4.0563895747638971068 - 3.7441333379892975521e-1227j 1.03e-490, 1.03e-490j
-5.1873010206744362738 - 1.179607197318870226e-1220j 5.71e-488, 5.71e-488j
-4.0563895747638971068 - 2.0492851438583984052e-1231j 9.97e-491, 9.97e-491j
1.0693259078659559849 - 7.5415956657610398491e-1255j 3.72e-503, 3.72e-503j
6.3580993349946789024 - 1.0148305215731499922e-1234j 5.97e-486, 5.97e-486j
-0.71906824238173465526 - 2.4315163106480644032e-1301j 2.43e-505, 2.43e-505j
10.017947885049793462 - 6.340551976900414622e-1279j 1.76e-485, 1.76e-485j
4.9582298995304339721 + 3.2529589996598175395e-1301j 1.7e-488, 1.7e-488j
2.8481077541057567845 + 2.3112912223093875707e-1320j 3.73e-494, 3.73e-494j
-3.3968543925541242392 + 1.7107295402382915298e-1318j 1.38e-492, 1.38e-492j
-6.3580993349946789024 - 3.061837167328403844e-1310j 5.79e-486, 5.79e-486j
3.3968543925541242392 - 1.7826708596233458753e-1329j 1.42e-492, 1.42e-492j
4.5044943682467484706 + 1.0025344668576254101e-1321j 1.62e-489, 1.62e-489j
9.7257977452192777515 + 2.8819254574478703397e-1332j 3.72e-485, 3.72e-485j
9.4404792446071718861 - 7.8274546580894393641e-1351j 5.79e-485, 5.79e-485j
6.1201853625081651439 - 1.6085004135914906687e-1359j 2.61e-486, 2.61e-486j
-2.6928516969957619463 + 2.7412475693358305069e-1367j 6.59e-495, 6.59e-495j
-6.8404996650245570063 - 2.1017147144373125953e-1356j 2.09e-485, 2.09e-485j
0.71906824238173465526 + 9.5321507793328903906e-1385j 2.34e-505, 2.34e-505j
2.6928516969957619463 + 1.6571613737826895472e-1374j 6.42e-495, 6.42e-495j
-11.277709589269827418 + 1.573212768509149921e-1363j 3.14e-487, 3.14e-487j
-5.8842695912328150265 - 1.2614770739039589598e-1372j 1.18e-486, 1.18e-486j
-5.4179360186773902366 - 2.1187069684065409576e-1376j 1.69e-487, 1.69e-487j
-9.4404792446071718861 + 5.2193577221454519298e-1381j 5.52e-485, 5.52e-485j
5.1873010206744362738 - 7.3231042281929803975e-1399j 5.61e-488, 5.61e-488j
0.52464762327529031788 + 2.6080019840241459754e-1417j 1.33e-506, 1.33e-506j
1.4455572662606065829 + 7.3348548871671208477e-1412j 3.26e-501, 3.26e-501j
-0.3256558574652678822 + 3.8981459059104974731e-1488j 5.79e-508, 5.79e-508j
7.3327851836864648906 - 1.0688113132956950886e-1394j 5.74e-485, 5.74e-485j
1.8600475788554213714 + 8.3870723048079237335e-1430j 3.45e-499, 3.45e-499j
-10.317869485875900464 + 1.1174929600503857909e-1415j 8.63e-486, 8.63e-486j
-4.9582298995304339721 - 5.2340386123044361066e-1438j 1.89e-488, 1.89e-488j
-1.0693259078659559849 - 1.080594340226854618e-1464j 3.85e-503, 3.85e-503j
-8.6184375068955028738 - 7.9859807663705026797e-1445j 1.2e-484, 1.2e-484j
-9.1612230101839493657 - 2.7626356716852548614e-1467j 8.65e-485, 8.65e-485j
8.6184375068955028738 + 1.8963573941954824421e-1494j 1.26e-484, 1.26e-484j
-10.017947885049793462 - 3.1809155442227343264e-1533j 1.75e-485, 1.75e-485j
-1.8600475788554213714 - 6.483897449619750168e-1585j 3.86e-499, 3.86e-499j
-1.6506801238857845559 + 4.9513574516499996263e-1586j 3.33e-500, 3.33e-500j
-9.7257977452192777515 + 2.9692701183830017422e-1569j 3.38e-485, 3.38e-485j
9.1612230101839493657 - 3.5650109863864991583e-1590j 8.84e-485, 8.84e-485j
2.2832506552235534748 - 6.8385574123520452303e-1616j 4.66e-497, 4.66e-497j
4.2797391329507175684 - 1.7137568896504048571e-1607j 4.1e-490, 4.1e-490j
-0.52464762327529031788 + 2.8234016551353626018e-1624j 1.33e-506, 1.33e-506j
0.13597180311251526908 - 1.8206656306037637175e-1626j 3.25e-509, 3.25e-509j
4.7306470042464748259 - 1.2012283448160328211e-1606j 5.26e-489, 5.26e-489j
0.3256558574652678822 - 2.0611163411788458813e-1625j 6.04e-508, 6.04e-508j
5.8842695912328150265 + 2.5007523332305219776e-1603j 1.18e-486, 1.18e-486j
-4.5044943682467484706 + 5.4230631231171115015e-1608j 1.47e-489, 1.47e-489j
-2.2832506552235534748 - 5.0795438389190607387e-1616j 4.51e-497, 4.51e-497j
-3.6144328865631482548 - 1.4628433597135367548e-1610j 5.48e-492, 5.48e-492j
6.8404996650245570063 + 3.9943853921486633355e-1601j 2.08e-485, 2.08e-485j
-1.1476280317813832461e-1686 + 5.2541075575800021528e-1687j 1.4e-1684, 1.4e-1684j
-0.13597180311251526908 - 1.656804853206776084e-1628j 3.25e-509, 3.25e-509j
-4.2797391329507175684 - 2.3289641650696714878e-1610j 4.09e-490, 4.09e-490j
8.8873890192108352457 + 2.1976698133209598426e-1602j 1.16e-484, 1.16e-484j
3.6144328865631482548 + 1.2748765415615775377e-1613j 5.54e-492, 5.54e-492j
3.8345325314433831864 + 2.0514771015949925171e-1613j 2.34e-491, 2.34e-491j
-7.085313653540304004 + 6.67087885935030011e-1607j 3.44e-485, 3.44e-485j
-3.8345325314433831864 + 6.5250784098623653971e-1614j 2.34e-491, 2.34e-491j

Weights

Weight (ball center) Error (ball radius)
1.5791123902554009925e-72 + 3.7045241203557069647e-1171j 7.62e-123, 6.89e-366j
6.2565081016882640574e-68 + 1.3327793378682666046e-1169j 1.23e-122, 1.11e-365j
7.8237482129752076079e-64 + 1.2889324254081797764e-1166j 4.48e-120, 4.05e-363j
1.6913655481322894479e-53 + 3.273597030097897386e-1162j 1.53e-117, 1.38e-360j
1.6913655481322894479e-53 - 3.6329214793496422326e-1161j 1.07e-116, 9.69e-360j
6.2565081016882640574e-68 - 9.2504212922941635762e-1169j 1.37e-121, 1.24e-364j
7.8237482129752076079e-64 - 1.6739238892761662195e-1167j 4.39e-122, 3.97e-365j
0.014083351892580360737 + 8.9592977354531905409e-1132j 4.94e-29, 4.47e-272j
1.7955173593953762504e-15 + 7.6326786062333013856e-1140j 4.73e-90, 4.28e-333j
1.5100263384097552539e-26 - 4.643756598630720965e-1146j 4.58e-103, 4.15e-346j
5.2048489348624490441e-30 - 5.9907688591759866411e-1150j 4.26e-106, 3.86e-349j
1.1084685399673310046e-56 + 7.4826116918104422992e-1163j 3.04e-118, 2.75e-361j
0.00023366290888155744429 - 4.8842870765830183268e-1133j 9.29e-56, 8.4e-299j
4.6178090052350879326e-06 - 3.2955639171030758884e-1134j 2.66e-66, 2.4e-309j
1.4302336507111851919e-84 - 4.1062770643611546326e-1178j 8.56e-131, 7.74e-374j
1.5791123902554009925e-72 - 5.894392293942156277e-1172j 5.05e-126, 4.57e-369j
1.6845233275319518595e-20 + 5.4284446225795827708e-1142j 4.37e-100, 3.95e-343j
1.6006944540860991747e-50 + 1.3926710488482557185e-1159j 5.31e-118, 4.8e-361j
0.04328731481910650077 - 4.8678665552866589785e-1131j 8.18e-36, 7.4e-279j
1.5100263384097552539e-26 - 1.0493181217688307781e-1147j 4.37e-106, 3.96e-349j
0.022404466899071121564 - 2.2972131933324433894e-1131j 8.18e-36, 7.4e-279j
2.1889955901138522861e-23 - 3.8469669750204180898e-1144j 4.13e-103, 3.74e-346j
4.1402632119052457413e-60 - 1.1648078160806643779e-1164j 3.52e-121, 3.19e-364j
7.1973379203654329838e-78 - 6.2176300333877528189e-1174j 2.1e-129, 1.9e-372j
1.4302336507111851919e-84 + 2.1096328168399865001e-1177j 1.88e-132, 1.7e-375j
2.4439783204469277432e-11 + 5.4924352731874032348e-1138j 3.56e-92, 3.22e-335j
0.04328731481910650077 - 5.7266655819447482744e-1131j 9.93e-44, 8.98e-287j
7.6180586624455397384e-36 - 9.3054897768454121608e-1154j 1.15e-116, 1.04e-359j
4.1402632119052457413e-60 + 1.3538200512166632284e-1165j 7.62e-127, 6.89e-370j
0.022404466899071121564 - 1.8338852028383994392e-1131j 7.12e-47, 6.44e-290j
1.6006944540860991747e-50 - 1.0791937127564343427e-1160j 9.17e-124, 8.3e-367j
0.0016369150237258936198 - 1.8291453729498652753e-1132j 8.34e-68, 7.55e-311j
7.1973379203654329838e-78 + 1.0911917584808051028e-1174j 9.68e-134, 8.76e-377j
5.2048489348624490441e-30 - 2.4846599324899717108e-1148j 2.25e-115, 2.04e-358j
3.0708163655490134814e-28 + 8.5433681885053106443e-1149j 2.14e-112, 1.94e-355j
6.2444688678562470317e-25 + 1.1480169011509370892e-1146j 1.13e-110, 1.02e-353j
2.1426087562733713821e-05 - 2.8853003451154944711e-1133j 6.34e-80, 5.73e-323j
0.0076848405825079875073 - 5.9704748797288785287e-1132j 3.77e-64, 3.41e-307j
4.6178090052350879326e-06 - 5.7718833205633007303e-1134j 3.49e-87, 3.15e-330j
7.2783862080814953804e-32 + 2.1973563409450722835e-1149j 8.47e-118, 7.66e-361j
1.6845233275319518595e-20 - 9.4963474203952381027e-1144j 6.04e-109, 5.46e-352j
1.0005495461417115369e-47 - 4.3553984558803021832e-1158j 3.94e-125, 3.56e-368j
7.2235702994233368175e-18 - 7.6062483175313918907e-1142j 7.8e-107, 7.05e-350j
3.0708163655490134814e-28 + 2.432487908849882004e-1147j 2.15e-115, 1.95e-358j
7.2783862080814953804e-32 + 2.8825367952337221462e-1151j 2.1e-116, 1.9e-359j
1.2796265141137677372e-05 + 1.3248943722371810621e-1133j 2.38e-85, 2.15e-328j
2.3312068155057232113e-14 - 2.1822887242252744593e-1139j 2.61e-107, 2.36e-350j
0.00023366290888155744429 - 7.609454556922795023e-1133j 1.37e-84, 1.24e-327j
1.7955173593953762504e-15 + 5.9219159638852403632e-1140j 1.92e-108, 1.74e-351j
0.0016369150237258936198 - 1.2624767660887020511e-1132j 9.84e-80, 8.91e-323j
1.2796265141137677372e-05 + 2.2480286379918925704e-1133j 2.65e-90, 2.4e-333j
8.9741601451906598155e-09 - 3.9420071207979274733e-1136j 4.34e-100, 3.92e-343j
2.6718577532089237223e-13 + 5.5808389476273862777e-1139j 1.3e-105, 1.18e-348j
8.9741601451906598155e-09 - 2.0705741284125897135e-1136j 3.5e-99, 3.17e-342j
0.030837466420167592893 + 4.0746243436427612046e-1131j 2.38e-66, 2.15e-309j
3.7428995278989534473e-19 - 1.7554981880172563075e-1141j 3.37e-112, 3.05e-355j
0.063559480396266884856 + 5.9780596819310853412e-1131j 8.66e-68, 7.84e-311j
4.3354427628523604325e-45 + 1.1397677798355956219e-1156j 3.62e-127, 3.28e-370j
2.711729232810771511e-12 - 2.8683216123350320276e-1138j 1.3e-106, 1.18e-349j
2.1426087562733713821e-05 - 4.7732441514183115736e-1133j 1.04e-91, 9.43e-335j
1.1864068400077947671e-06 + 8.661715406015864103e-1135j 1.91e-96, 1.73e-339j
3.7428995278989534473e-19 + 8.3131951387084942123e-1143j 6.19e-113, 5.6e-356j
1.1864068400077947671e-06 + 1.5352975708787840373e-1134j 4.66e-97, 4.21e-340j
1.9608236916501448261e-10 - 3.4838019931721506969e-1137j 8.39e-105, 7.59e-348j
1.3530090745884142794e-42 - 2.5470747614782496039e-1155j 2.76e-127, 2.5e-370j
3.1366287712066129291e-40 + 4.9427141402661631445e-1154j 1.03e-126, 9.3e-370j
7.2235702994233368175e-18 + 4.7638366704420997695e-1141j 2.97e-113, 2.68e-356j
7.4385904076427342135e-05 + 3.8639380552638543128e-1133j 1.06e-95, 9.63e-339j
6.5511498424156159264e-22 + 1.0682279102672792766e-1144j 7.06e-119, 6.39e-362j
0.063559480396266884856 + 6.8074235975578332217e-1131j 2.96e-82, 2.68e-325j
7.4385904076427342135e-05 + 6.2265324470614817224e-1133j 5.33e-96, 4.82e-339j
1.1084685399673310046e-56 - 7.7073416072974462024e-1164j 1.95e-138, 1.77e-381j
1.216561785738451114e-16 + 8.6676678628861339064e-1141j 4.11e-115, 3.72e-358j
2.3312068155057232113e-14 - 2.3374174916896867052e-1139j 1.29e-113, 1.17e-356j
3.1366287712066129291e-40 - 1.4569002031322802044e-1155j 6.67e-133, 6.03e-376j
2.6718577532089237223e-13 + 7.9791879466480484755e-1139j 9.64e-114, 8.73e-357j
0.084943657874149918394 - 8.2150232785898436481e-1131j 2.51e-88, 2.27e-331j
0.014083351892580360737 + 1.1623251779978037626e-1131j 1.18e-92, 1.07e-335j
0.10043345425721201788 + 1.0946279190102766229e-1130j 7.81e-90, 7.07e-333j
6.2444688678562470317e-25 + 3.9302972814959409392e-1145j 4.82e-122, 4.36e-365j
0.0037358336186639858905 + 3.2156148952559508355e-1132j 2.3e-96, 2.08e-339j
1.0005495461417115369e-47 + 2.8362165303868161378e-1159j 1.34e-136, 1.21e-379j
2.711729232810771511e-12 - 1.6902153415180554934e-1138j 1.02e-114, 9.24e-358j
0.030837466420167592893 + 3.3595716274183113494e-1131j 2.87e-94, 2.6e-337j
8.3005198773528086112e-34 - 5.7229711085811017218e-1153j 3.14e-129, 2.84e-372j
5.5407374402718664245e-38 + 1.5345434081614235289e-1154j 4.4e-132, 3.98e-375j
8.3005198773528086112e-34 - 1.7650048120296599857e-1150j 2.92e-132, 2.64e-375j
4.3354427628523604325e-45 - 6.0391131786127156517e-1158j 1.81e-136, 1.64e-379j
0.0037358336186639858905 + 2.3030865844476401278e-1132j 1.98e-106, 1.79e-349j
0.0076848405825079875073 - 4.4372616281831115136e-1132j 3.01e-105, 2.73e-348j
1.3530090745884142794e-42 + 1.0467477626573191546e-1156j 3.24e-135, 2.93e-378j
5.5407374402718664245e-38 - 8.4469552687153680529e-1153j 1.64e-135, 1.48e-378j
0.00064961728624473012231 + 1.1157740041845836026e-1132j 9.1e-110, 8.24e-353j
1.4033830284248786728e-09 + 1.1796731446908388138e-1136j 3.96e-119, 3.58e-362j
0.084943657874149918394 - 7.4717728052432879242e-1131j 6.82e-106, 6.17e-349j
0.096021689139400556892 - 2.0774197265476522591e-1130j 1.58e-106, 1.43e-349j
2.4439783204469277432e-11 + 1.0100856882738131075e-1137j 1.61e-120, 1.45e-363j
0.10043345425721201788 + 1.161016177962007951e-1130j 3.66e-107, 3.31e-350j
1.216561785738451114e-16 - 1.6275187688819950895e-1140j 2.84e-124, 2.57e-367j
1.9608236916501448261e-10 - 1.831868101957232564e-1137j 4.73e-122, 4.28e-365j
0.00064961728624473012231 + 7.4237534067649960303e-1133j 2.62e-114, 2.37e-357j
2.6198313732081905829e-07 - 2.4119821220616428105e-1135j 1.22e-119, 1.11e-362j
6.5511498424156159264e-22 + 4.980982932786489145e-1143j 7.28e-129, 6.59e-372j
0.06074702503102981979 + 2.7306202072911443694e-1130j 6.69e-111, 6.06e-354j
0.096021689139400556892 - 2.026962060203709646e-1130j 4.4e-111, 3.99e-354j
1.4033830284248786728e-09 + 6.1529554307536414755e-1137j 5.1e-122, 4.62e-365j
7.6180586624455397384e-36 + 1.2866969872027356399e-1151j 6.68e-137, 6.05e-380j
2.6198313732081905829e-07 - 4.407948245689091584e-1135j 7.02e-121, 6.35e-364j
5.1309673641249371675e-08 + 1.3114285179458125389e-1135j 1.68e-121, 1.52e-364j
2.1889955901138522861e-23 - 1.1466175123969385315e-1145j 6.15e-132, 5.6e-375j
5.1309673641249371675e-08 + 7.0061578197302573491e-1136j 2.12e-122, 1.9e-365j

Download

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