Rule: Q[2, 10, 91]

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.

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)
-12.610730936216447613 - 3.5256849586673587059e-1278j 3.55e-493, 3.55e-493j
10.578893318640434361 + 1.3743481167977763347e-1271j 8.66e-489, 8.66e-489j
-9.6036512886523209931 - 1.3098197336402202896e-1275j 1.45e-487, 1.45e-487j
11.301815271188173067 + 1.1731814006973019721e-1274j 4.21e-490, 4.21e-490j
-11.697475863073403675 - 1.7406970012951159063e-1279j 6.35e-491, 6.35e-491j
10.930885180536267515 + 2.4926743803597445777e-1275j 2.11e-489, 2.11e-489j
-10.242025135587344392 + 3.2705986683396775125e-1281j 2.62e-488, 2.62e-488j
13.196218130314174525 + 1.7493951826597220074e-1288j 6.98e-495, 6.98e-495j
7.3388050268763485895 + 3.2233451864291805212e-1282j 6.23e-487, 6.23e-487j
5.8129172509411211846 - 1.7848729386687242388e-1292j 2.72e-488, 2.72e-488j
2.0436541275856649452 - 7.5274216140902475961e-1303j 7.88e-496, 7.88e-496j
-9.2986694965595499171 + 1.8285077990175316081e-1294j 2.78e-487, 2.78e-487j
-12.127528234742711154 + 3.9137852726938196731e-1299j 6.47e-492, 6.47e-492j
-10.578893318640434361 - 4.1710280980171810171e-1296j 8.7e-489, 8.7e-489j
11.697475863073403675 + 7.4364673522859974404e-1294j 6.47e-491, 6.47e-491j
2.1811971996541718089 + 6.7302149212414732092e-1309j 5.77e-497, 5.77e-497j
3.4515088301976455692 - 2.4146804591910936563e-1306j 2.38e-493, 2.38e-493j
-5.8129172509411211846 + 2.4577782562672000163e-1300j 2.73e-488, 2.73e-488j
-0.91946681283136602542 + 4.550620508891908787e-1316j 1.61e-504, 1.61e-504j
-7.873963669558319221 - 4.107615193584212591e-1297j 8.45e-487, 8.45e-487j
-13.196218130314174525 - 6.6621363823084243933e-1308j 7.22e-495, 7.22e-495j
10.242025135587344392 - 3.2233126705086073882e-1299j 2.85e-488, 2.85e-488j
-9.9176017247235654929 + 1.3052460057674246704e-1311j 6.68e-488, 6.68e-488j
-7.6043783181490279149 - 1.1955855453224025992e-1310j 8.24e-487, 8.24e-487j
-3.9076519951229398412 - 6.0816878620905567849e-1316j 3.8e-492, 3.8e-492j
12.127528234742711154 + 1.1223818549651647454e-1310j 6.41e-492, 6.41e-492j
4.1391084911850724509 - 9.2170290343376853057e-1321j 1.5e-491, 1.5e-491j
-5.324775031593370129 - 1.2530104952336602263e-1318j 4.82e-489, 4.82e-489j
-9.0014756886900761371 - 2.8554877749927460514e-1314j 4.44e-487, 4.44e-487j
-3.0088455050555235902 + 2.0561247786821812867e-1333j 1.28e-494, 1.28e-494j
9.2986694965595499171 + 2.7251667250442786625e-1323j 2.97e-487, 2.97e-487j
6.3103154711822542915 + 1.2679334747582388579e-1350j 1.19e-487, 1.19e-487j
3.0088455050555235902 + 4.4810277552163906136e-1383j 1.28e-494, 1.28e-494j
2.7962452403682858841 + 8.1000618335117421138e-1384j 3.06e-495, 3.06e-495j
4.6077545408533123094 + 2.3778201812985962683e-1376j 1.83e-490, 1.83e-490j
-4.1391084911850724509 + 9.3812599392327159698e-1394j 1.55e-491, 1.55e-491j
-3.2279221653981938235 - 4.7030093111396270281e-1406j 5.37e-494, 5.37e-494j
9.9176017247235654929 - 7.0284263545042325801e-1435j 7.1e-488, 7.1e-488j
3.2279221653981938235 + 5.6811641058157157252e-1470j 5.63e-494, 5.63e-494j
7.6043783181490279149 - 7.1982052397776735755e-1480j 8.65e-487, 8.65e-487j
-2.1811971996541718089 + 1.7011977032587663749e-1517j 6.22e-497, 6.22e-497j
-4.8448542617818612035 - 4.2715123823265002127e-1508j 6.06e-490, 6.06e-490j
8.7111217327779875449 - 2.1763977807732729713e-1523j 6.07e-487, 6.07e-487j
12.610730936216447613 - 2.5138533939079374716e-1543j 3.52e-493, 3.52e-493j
-10.930885180536267515 + 7.4183150151769145598e-1539j 2.29e-489, 2.29e-489j
1.789260572929120167 - 8.2168963908844407497e-1550j 2.45e-499, 2.45e-499j
-7.076897254073180582 + 1.1127996367337588268e-1535j 4.62e-487, 4.62e-487j
-7.3388050268763485895 - 8.3001899419847824525e-1548j 7.13e-487, 7.13e-487j
2.0415226242456913014 + 4.3937190095531030924e-1587j 7.56e-496, 7.56e-496j
7.076897254073180582 - 7.7059072114672559694e-1577j 4.88e-487, 4.88e-487j
-3.6783246397895513046 - 2.2391914826494631962e-1612j 9.69e-493, 9.69e-493j
-2.0436541275856649452 + 4.0655486836020600679e-1627j 7.97e-496, 7.97e-496j
1.3532153932168790075 + 3.5598582330861568984e-1633j 5.66e-502, 5.66e-502j
8.4268316627831962922 + 2.5148382049078943969e-1618j 7.63e-487, 7.63e-487j
5.324775031593370129 + 8.5091259485121214936e-1636j 5.01e-489, 5.01e-489j
-6.8183520508391540748 + 1.6109111804298774244e-1635j 3.15e-487, 3.15e-487j
-2.0415226242456913014 + 1.7340854196209017649e-1648j 7.77e-496, 7.77e-496j
-4.6077545408533123094 + 1.1663698421912756732e-1642j 1.83e-490, 1.83e-490j
3.6783246397895513046 - 4.7471457746009947204e-1645j 1.04e-492, 1.04e-492j
-8.4268316627831962922 - 4.6668260824239637697e-1638j 7.73e-487, 7.73e-487j
-4.3725025584508029797 - 2.0026543862314186094e-1649j 5.52e-491, 5.52e-491j
-11.301815271188173067 - 8.2758388576953310779e-1644j 4.43e-490, 4.43e-490j
8.1479602437888235143 - 2.2565583902940285769e-1651j 8.57e-487, 8.57e-487j
9.6036512886523209931 + 4.3321540030239868969e-1677j 1.42e-487, 1.42e-487j
4.8448542617818612035 + 3.191374463784629862e-1692j 5.99e-490, 5.99e-490j
1.5711805073045216422 - 8.2401183542078639564e-1713j 1.03e-500, 1.03e-500j
-2.5916501902306078633 - 1.4571766312396062636e-1707j 7.39e-496, 7.39e-496j
-2.391901598382282013 + 4.0177556424694558817e-1708j 1.96e-496, 1.96e-496j
0.91946681283136602542 + 4.6254680292011303348e-1717j 1.73e-504, 1.73e-504j
2.5916501902306078633 - 1.0233692547787460803e-1707j 7.1e-496, 7.1e-496j
2.391901598382282013 - 6.0378595264432347159e-1708j 1.74e-496, 1.74e-496j
6.8183520508391540748 - 2.745573096139260848e-1697j 3.37e-487, 3.37e-487j
-5.567761857907887281 + 1.6662700913496750158e-1710j 1.19e-488, 1.19e-488j
-1.1355926934307227024 + 4.7661390481210016318e-1726j 2.9e-503, 2.9e-503j
-6.3103154711822542915 - 1.8968673687214547559e-1709j 1.12e-487, 1.12e-487j
1.1355926934307227024 - 1.0139778861719247533e-1736j 3.12e-503, 3.12e-503j
9.0014756886900761371 + 7.6052260284448311979e-1720j 4.57e-487, 4.57e-487j
-8.7111217327779875449 - 5.5018498737660245394e-1731j 6.61e-487, 6.61e-487j
-0.7071067811865475244 - 2.7707106131923052744e-1750j 1.14e-505, 1.14e-505j
-6.5629031196759010149 + 1.3811236843614508685e-1731j 2.07e-487, 2.07e-487j
-1.5711805073045216422 + 7.9408746927427744579e-1747j 1.1e-500, 1.1e-500j
4.3725025584508029797 + 5.9858678006377153327e-1737j 5.47e-491, 5.47e-491j
-8.1479602437888235143 + 1.9252119678728329446e-1731j 8.34e-487, 8.34e-487j
-0.16761481870756104368 + 1.1628042218238365722e-1798j 5.06e-509, 5.06e-509j
-1.3532153932168790075 + 1.1959364818610929955e-1746j 5.92e-502, 5.92e-502j
5.567761857907887281 - 2.3943688921312714816e-1732j 1.23e-488, 1.23e-488j
0.7071067811865475244 + 5.9580922120963747008e-1751j 1.19e-505, 1.19e-505j
3.9076519951229398412 + 8.8138442540233053416e-1737j 3.98e-492, 3.98e-492j
6.0603813533313000304 + 1.9838856074954413218e-1732j 6e-488, 6e-488j
-1.789260572929120167 - 1.4301133703544368247e-1754j 2.36e-499, 2.36e-499j
7.873963669558319221 + 4.3748706144232644103e-1740j 8.63e-487, 8.63e-487j
-6.0603813533313000304 + 1.2700304317055443516e-1756j 5.96e-488, 5.96e-488j
0.16761481870756104368 - 9.7988345154251263375e-1778j 5.06e-509, 5.06e-509j
-0.50420427611133531053 + 5.3994220366280050977e-1776j 8.27e-507, 8.27e-507j
-3.4515088301976455692 - 5.9832737285743181629e-1763j 2.49e-493, 2.49e-493j
-2.7962452403682858841 + 1.2765815770940473934e-1764j 3.13e-495, 3.13e-495j
0.50420427611133531053 - 1.2483879963806540448e-1777j 8.05e-507, 8.05e-507j
0.32429280050097623645 - 1.9905508933851953232e-1777j 6.5e-508, 6.5e-508j
5.0838378716295755464 + 1.3221764996468834212e-1758j 1.69e-489, 1.69e-489j
6.5629031196759010149 + 3.9437491145699770019e-1756j 2.04e-487, 2.04e-487j
-0.32429280050097623645 - 1.0659974984574848677e-1783j 7.1e-508, 7.1e-508j
-5.2145865739041542787e-1818 + 1.5798454415754148434e-1818j 5.61e-1816, 5.61e-1816j
-5.0838378716295755464 + 1.294984620213717016e-1764j 1.74e-489, 1.74e-489j

Weights

Weight (ball center) Error (ball radius)
2.5246746897879077174e-70 - 1.0615429182204032878e-1332j 1.65e-152, 6.15e-396j
4.8381090688899503142e-50 - 9.1045751666726129365e-1320j 3.95e-145, 1.47e-388j
1.5370851021555116479e-41 - 2.1597715932908870729e-1315j 1.98e-141, 7.38e-385j
7.2563816674441316244e-57 - 1.1599903613777674205e-1324j 1.79e-148, 6.67e-392j
8.7114850262930671003e-61 + 7.8461060477351712987e-1328j 2.8e-150, 1.04e-393j
2.6134795601249698609e-53 - 7.1153808701071506265e-1323j 7.94e-147, 2.96e-390j
5.1665546156867879446e-47 + 2.7436468507004734698e-1319j 7.88e-145, 2.94e-388j
9.0001619372940517856e-77 - 7.3748424933475954896e-1335j 1.27e-156, 4.73e-400j
6.0569684666723257835e-25 - 1.5973030103219918152e-1305j 9.52e-133, 3.55e-376j
2.9379799662824115502e-16 - 1.2563151267800831225e-1301j 1.07e-123, 3.99e-367j
-0.050319020616795130283 + 3.2496642448237610499e-1290j 8.25e-83, 3.07e-326j
4.7696101602947914014e-39 + 1.6321099759352865277e-1314j 4.96e-142, 1.85e-385j
3.404733385762562102e-65 + 1.1639327099214617875e-1330j 4.28e-153, 1.59e-396j
4.8381090688899503142e-50 - 3.5721680096458163332e-1321j 3.85e-147, 1.43e-390j
8.7114850262930671003e-61 + 1.4821024834554536738e-1326j 1.72e-152, 6.42e-396j
0.0011673556184981900802 - 3.884576570389310042e-1292j 2.42e-89, 9.01e-333j
8.5229017630943886391e-07 - 1.2308537560806988917e-1295j 2.5e-107, 9.31e-351j
2.9379799662824115502e-16 - 1.9351703694563733985e-1302j 2.58e-128, 9.62e-372j
0.052030842786173085528 + 5.7341356399962082541e-1292j 8.08e-89, 3.01e-332j
1.8179851891237490611e-28 - 2.6734932958597030707e-1309j 1.1e-138, 4.11e-382j
9.0001619372940517856e-77 + 7.7196674473262232864e-1336j 6.26e-159, 2.33e-402j
5.1665546156867879446e-47 + 1.5387457958150629745e-1318j 1.96e-149, 7.3e-393j
3.4545339663727975662e-44 - 2.1242873215988384722e-1317j 4.51e-145, 1.68e-388j
1.1614946339370949585e-26 + 2.5030851540111843946e-1308j 4.42e-138, 1.65e-381j
3.0367589415464666146e-08 - 3.4191190224854631458e-1297j 3.06e-118, 1.14e-361j
3.404733385762562102e-65 - 8.0084726760104475205e-1329j 1.48e-157, 5.51e-401j
4.7568446259679283999e-09 + 2.6231744563244887317e-1297j 1.42e-120, 5.31e-364j
6.6296248220077617613e-14 - 5.2228097965995960289e-1301j 3.29e-128, 1.23e-371j
1.0711204997529927575e-36 - 1.7151567045790703948e-1313j 7.02e-143, 2.61e-386j
1.4274654192584687226e-05 - 7.199496294002536836e-1295j 2.22e-111, 8.28e-355j
4.7696101602947914014e-39 - 2.3218248479695872483e-1314j 8.83e-149, 3.29e-392j
7.2086199816454473799e-19 - 5.3912990311892080888e-1303j 5.83e-136, 2.17e-379j
1.4274654192584687226e-05 - 1.5392670530352822486e-1294j 3.83e-112, 1.43e-355j
4.7328355753910239464e-05 + 5.3686655084709789925e-1294j 5.1e-110, 1.9e-353j
8.0163165702973567943e-11 + 1.8132499741102442177e-1298j 2.46e-126, 9.17e-370j
4.7568446259679283999e-09 + 8.6344197258045107283e-1298j 7.4e-124, 2.76e-367j
3.7314819514012112827e-06 + 1.9140304695400514244e-1295j 8.55e-117, 3.18e-360j
3.4545339663727975662e-44 - 3.9402991507450284158e-1317j 2.67e-151, 9.96e-395j
3.7314819514012112827e-06 + 4.3590597906740906887e-1295j 8.43e-116, 3.14e-359j
1.1614946339370949585e-26 - 8.1841161764669680876e-1307j 9.55e-144, 3.56e-387j
0.0011673556184981900802 - 2.274075009148139225e-1292j 7.62e-110, 2.84e-353j
8.5908308921293664164e-12 - 1.1476369066963548875e-1299j 8.48e-131, 3.16e-374j
1.7937822433821071174e-34 - 8.9161999310708329579e-1312j 1.84e-148, 6.87e-392j
2.5246746897879077174e-70 + 1.7074913558402411212e-1331j 8.33e-163, 3.1e-406j
2.6134795601249698609e-53 + 3.6859567908744426727e-1323j 4.23e-156, 1.58e-399j
0.0050268435911451899184 + 3.2722817030984379512e-1292j 9.11e-107, 3.4e-350j
2.6070856788270454406e-23 + 1.7274273896628775491e-1306j 3.24e-143, 1.21e-386j
6.0569684666723257835e-25 - 2.1624538510937488169e-1307j 8.13e-144, 3.03e-387j
0.052078956023558409219 - 3.2337520706575436092e-1290j 5.04e-109, 1.88e-352j
2.6070856788270454406e-23 + 6.1318372421614917117e-1305j 3.58e-144, 1.34e-387j
1.7124709065404457815e-07 + 1.3246688950741778021e-1296j 5.02e-127, 1.87e-370j
-0.050319020616795130283 + 1.9713288378109472989e-1290j 3.14e-115, 1.17e-358j
0.019700415527933845833 + 3.5885488458007035487e-1292j 6.4e-107, 2.39e-350j
2.2960289357498939303e-32 + 1.5301608005422918092e-1310j 1.08e-149, 4.02e-393j
6.6296248220077617613e-14 - 2.5766613635832920673e-1300j 1.27e-137, 4.71e-381j
9.3533058899268386322e-22 - 1.2796184909324836856e-1305j 1.03e-143, 3.84e-387j
0.052078956023558409219 - 1.9627525012748748621e-1290j 2.05e-115, 7.62e-359j
8.0163165702973567943e-11 + 5.0293062159073952664e-1299j 4.55e-134, 1.7e-377j
1.7124709065404457815e-07 + 3.4582376713498248127e-1296j 2.31e-129, 8.6e-373j
2.2960289357498939303e-32 - 2.4018773433625385321e-1311j 3.87e-150, 1.44e-393j
6.5776684500033306152e-10 - 2.1196144791455542771e-1298j 5.11e-133, 1.9e-376j
7.2563816674441316244e-57 - 2.5152540550321909271e-1325j 6.31e-161, 2.35e-404j
2.2929677753863579916e-30 - 2.4968802507341540726e-1309j 5.91e-151, 2.2e-394j
1.5370851021555116479e-41 + 1.006861659750595175e-1315j 8.11e-156, 3.02e-399j
8.5908308921293664164e-12 - 4.5516341090299426826e-1299j 9.05e-139, 3.37e-382j
0.010413661667575315059 - 3.0462090202689726521e-1292j 6.01e-119, 2.24e-362j
0.00013725758634835675697 - 9.5245830729517487919e-1294j 9.8e-128, 3.65e-371j
0.00037072569446640540043 + 3.4369269378940020623e-1293j 2.72e-126, 1.01e-369j
0.052030842786173085528 + 7.1478986993682875175e-1292j 1.08e-118, 4.04e-362j
0.00013725758634835675697 - 1.8140928743576014357e-1293j 9.36e-127, 3.49e-370j
0.00037072569446640540043 + 6.2050887673241979894e-1293j 1.84e-125, 6.85e-369j
9.3533058899268386322e-22 - 2.3366356955129173457e-1304j 1.16e-147, 4.31e-391j
4.7400853236740955945e-15 + 1.0334063073556739361e-1301j 2.52e-143, 9.38e-387j
0.033734927012504188804 - 3.6611382842587550666e-1292j 7e-124, 2.61e-367j
7.2086199816454473799e-19 - 5.6724657083527924708e-1304j 6.97e-147, 2.6e-390j
0.033734927012504188804 - 4.8098872716227081002e-1292j 1.16e-123, 4.33e-367j
1.0711204997529927575e-36 + 4.7869209826235508997e-1313j 2.82e-156, 1.05e-399j
1.7937822433821071174e-34 + 2.0539584347114539054e-1312j 3.79e-155, 1.41e-398j
0.071551037643828285933 - 9.9616243039733838776e-1292j 9.49e-127, 3.53e-370j
2.8211532485711600391e-20 + 8.8183085419377715936e-1305j 6.96e-148, 2.59e-391j
0.010413661667575315059 - 2.0826435347382557641e-1292j 1.44e-130, 5.37e-374j
6.5776684500033306152e-10 - 6.9949735106960366248e-1298j 7.62e-142, 2.84e-385j
2.2929677753863579916e-30 + 2.6338819437073672293e-1310j 3.14e-153, 1.17e-396j
0.086871131586818289342 + 4.7330187743691798867e-1291j 3.09e-129, 1.15e-372j
0.019700415527933845833 + 2.5895842981594392112e-1292j 1.42e-130, 5.29e-374j
4.7400853236740955945e-15 + 5.7952705236019875043e-1301j 4.16e-147, 1.55e-390j
0.071551037643828285933 - 1.1797393631115959518e-1291j 7.28e-132, 2.71e-375j
3.0367589415464666146e-08 - 9.6089551311171845398e-1297j 1.51e-140, 5.61e-384j
1.5710318667500031503e-17 + 2.6346024485509099718e-1302j 5.19e-149, 1.93e-392j
0.0050268435911451899184 + 2.1180683348332939405e-1292j 9.74e-136, 3.61e-379j
1.8179851891237490611e-28 + 4.1166305998398402569e-1308j 5.46e-155, 2.03e-398j
1.5710318667500031503e-17 + 3.4175910476148229165e-1303j 4.85e-149, 1.8e-392j
0.086871131586818289342 + 4.9260926743150174584e-1291j 2.51e-135, 9.1e-379j
0.085039126872327196084 + 1.9080209806783238356e-1291j 4.72e-135, 1.73e-378j
8.5229017630943886391e-07 - 5.0565978599845374604e-1296j 8.88e-142, 3.26e-385j
4.7328355753910239464e-05 + 2.6652682206496945951e-1294j 9.26e-140, 3.38e-383j
0.085039126872327196084 + 2.1522160928006864392e-1291j 1.21e-136, 3.94e-380j
0.083230757803192074108 - 3.7607976700216702475e-1291j 8.07e-137, 2.42e-380j
8.0727489325793715519e-13 + 1.1031821724437654734e-1299j 5.52e-147, 2.06e-390j
2.8211532485711600391e-20 + 1.0979010941564595628e-1303j 1.14e-151, 4.27e-395j
0.083230757803192074108 - 3.4807211471606699213e-1291j 2.6e-137, 7.84e-381j
0.097799174602855868164 - 5.0910323833092932482e-1291j 3.46e-137, 9.48e-381j
8.0727489325793715519e-13 + 2.5072409174577446833e-1300j 2.78e-147, 1.17e-390j

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