Rule: Q[4, 9, 98]

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)
15.480021391636871319 + 2.9262003278375409213e-1325j 1.58e-486, 1.58e-486j
-18.108007293856034617 + 3.3701778799217961289e-1353j 1.83e-490, 1.83e-490j
16.439428437815984529 + 1.6082557885120141854e-1344j 1e-487, 1e-487j
-19.600288619678485807 + 6.894738407853530857e-1370j 1.74e-493, 1.74e-493j
19.600288619678485807 + 1.8492599287957661172e-1359j 1.63e-493, 1.63e-493j
-15.949089853650497222 - 6.5549484368391060104e-1362j 4.51e-487, 4.51e-487j
15.949089853650497222 + 3.0155520611952704874e-1385j 4.67e-487, 4.67e-487j
-7.0119959692797281814 - 4.8606197254903793619e-1413j 2.57e-488, 2.57e-488j
12.568666085053682582 - 2.1036581795488704022e-1438j 1.53e-484, 1.53e-484j
4.5034750559555244768 - 5.5365309672151871354e-1472j 4.9e-493, 4.9e-493j
2.6305045126765758828 - 9.2930021736249520713e-1478j 5.26e-499, 5.26e-499j
13.754355076186770244 + 1.016453360593884087e-1461j 4.98e-485, 4.98e-485j
-16.439428437815984529 - 2.314697832684279749e-1477j 1e-487, 1e-487j
18.108007293856034617 - 1.3034243886262449644e-1476j 2.1e-490, 2.1e-490j
-8.9917103104648314832 - 1.7524607502771489596e-1475j 8.33e-486, 8.33e-486j
3.8082673913508108363 + 1.3757431813324980932e-1484j 9.54e-495, 9.54e-495j
-11.082593347955994174 - 8.5510797241330925709e-1474j 1.37e-484, 1.37e-484j
-17.508063554509010961 + 2.7610995085417514898e-1479j 2.29e-489, 2.29e-489j
-15.028469443314413804 - 8.7412472795358535817e-1477j 4.73e-486, 4.73e-486j
18.782483760339058572 - 2.0382714836680148355e-1480j 9.66e-492, 9.66e-492j
-10.37012425673788565 - 1.1307301460632732871e-1474j 7.58e-485, 7.58e-485j
16.956381526350129916 - 1.4468269171168419603e-1472j 1.75e-488, 1.75e-488j
-16.956381526350129916 + 4.2592353786076248011e-1480j 1.9e-488, 1.9e-488j
-8.3216138605810351601 - 5.0870029405222626095e-1479j 1.59e-486, 1.59e-486j
-10.724160964592302348 + 1.2865929331006432573e-1475j 1.09e-484, 1.09e-484j
-15.480021391636871319 + 5.156320003861382397e-1478j 1.69e-486, 1.69e-486j
1.5122552015009576337 - 8.977120925854524376e-1495j 5.18e-503, 5.18e-503j
-14.167517766184281714 + 7.3351599260756513926e-1476j 2.49e-485, 2.49e-485j
17.508063554509010961 + 2.6741376175066012529e-1475j 2.4e-489, 2.4e-489j
-0.74196378430272585765 - 2.4518849389284632247e-1498j 1.88e-506, 1.88e-506j
-9.3311964113704385584 + 4.6635363510041348205e-1477j 1.55e-485, 1.55e-485j
5.1115800084649388456 - 9.9371113810599285659e-1484j 7.85e-492, 7.85e-492j
5.4228479113280690393 - 4.0594987734283164187e-1484j 3.24e-491, 3.24e-491j
-13.754355076186770244 + 1.7739059278106520033e-1475j 5.03e-485, 5.03e-485j
-1.7669052547645369387 + 4.2648920361373543706e-1498j 4.77e-502, 4.77e-502j
9.3311964113704385584 + 3.7285757313910712626e-1479j 1.57e-485, 1.57e-485j
11.445800058797037436 - 1.5527536083189116684e-1506j 1.69e-484, 1.69e-484j
1.0169160606480331315 - 2.8404781802647662836e-1549j 3.67e-505, 3.67e-505j
-9.6739273996863421377 - 1.8671822530399846734e-1527j 2.93e-485, 2.93e-485j
14.167517766184281714 + 8.8277213405443775641e-1542j 2.55e-485, 2.55e-485j
-3.2290040429144049805 - 1.3459242776144188665e-1572j 6.3e-497, 6.3e-497j
3.2290040429144049805 + 7.2692284315835252685e-1573j 6.76e-497, 6.76e-497j
-13.350853783025173908 - 2.9368575356610772772e-1559j 8.26e-485, 8.26e-485j
12.955925828926612254 - 4.7852576363035714614e-1572j 1.24e-484, 1.24e-484j
10.37012425673788565 - 3.104071218831368457e-1585j 7.87e-485, 7.87e-485j
-4.5034750559555244768 + 4.356545373668755406e-1610j 4.86e-493, 4.86e-493j
-4.8038775513566638735 - 1.2300270279695469978e-1606j 1.89e-492, 1.89e-492j
-2.3344142183389772393 + 6.2082008505413673045e-1614j 5.29e-500, 5.29e-500j
0.74196378430272585765 - 3.3774561295263112058e-1621j 1.82e-506, 1.82e-506j
13.350853783025173908 - 2.3294925072889046815e-1597j 7.9e-485, 7.9e-485j
-12.568666085053682582 - 2.2183129734405810303e-1607j 1.49e-484, 1.49e-484j
-2.6305045126765758828 + 2.070113257463767768e-1622j 5.12e-499, 5.12e-499j
-8.6552491438963443387 - 1.0280790582576755403e-1610j 3.99e-486, 3.99e-486j
1.7669052547645369387 + 7.9742102187808165439e-1625j 4.64e-502, 4.64e-502j
-11.445800058797037436 + 1.7547705940900322111e-1608j 1.69e-484, 1.69e-484j
-7.6621185976832556787 - 1.573660061194014206e-1610j 2.46e-487, 2.46e-487j
-6.0524651252377753435 - 2.5269175627587778861e-1615j 5.47e-490, 5.47e-490j
-1.5122552015009576337 + 8.3598087570065300186e-1626j 5.18e-503, 5.18e-503j
0.460546930293621371 - 3.7564715306111009182e-1631j 9.03e-508, 9.03e-508j
6.6901451522050172645 + 2.2155647467118336086e-1611j 7.71e-489, 7.71e-489j
8.6552491438963443387 + 1.6629530295916717194e-1606j 3.7e-486, 3.7e-486j
3.5259910623144366744 - 6.9992596133095135457e-1626j 8.04e-496, 8.04e-496j
-2.0443266911327251147 + 3.6004015856186608809e-1630j 4.79e-501, 4.79e-501j
15.028469443314413804 - 1.3349500943728558435e-1612j 4.85e-486, 4.85e-486j
10.724160964592302348 + 1.7566297389135119361e-1632j 1.1e-484, 1.1e-484j
7.3359514555495864925 + 1.1494430510969267841e-1648j 7.66e-488, 7.66e-488j
-5.7366011508999351027 + 4.7062535155439292289e-1661j 1.38e-490, 1.38e-490j
4.8038775513566638735 + 8.7060600301929071288e-1663j 1.81e-492, 1.81e-492j
14.591670961721211905 - 4.7181012313317825616e-1654j 1.17e-485, 1.17e-485j
-18.782483760339058572 + 4.0741040278486381899e-1671j 9.56e-492, 9.56e-492j
-7.3359514555495864925 - 6.0797144776852863966e-1667j 8.03e-488, 8.03e-488j
7.9906244265279747668 + 3.080126745718351812e-1662j 6.5e-487, 6.5e-487j
-3.5259910623144366744 + 6.933969230540019613e-1677j 7.73e-496, 7.73e-496j
-11.81420976647520247 + 4.1452931242855016648e-1664j 1.81e-484, 1.81e-484j
-10.020146662503962679 + 4.2293103017585739919e-1671j 4.9e-485, 4.9e-485j
2.9294115500505854709 + 3.3517146233885086385e-1684j 5.68e-498, 5.68e-498j
8.3216138605810351601 + 5.7159849734798647293e-1670j 1.66e-486, 1.66e-486j
-3.8082673913508108363 - 3.1551073527715813504e-1690j 9.76e-495, 9.76e-495j
-1.2724808447171745315 - 4.8419621426972708759e-1699j 5.1e-504, 5.1e-504j
7.6621185976832556787 + 5.9555157001278543573e-1679j 2.27e-487, 2.27e-487j
5.7366011508999351027 + 1.426270447081472769e-1689j 1.42e-490, 1.42e-490j
4.2283965787258560516 + 1.3249450669599904688e-1701j 1.62e-493, 1.62e-493j
11.81420976647520247 + 5.333746331957830498e-1691j 1.78e-484, 1.78e-484j
-4.0278326129563373285 + 7.645682505713459256e-1713j 5.46e-494, 5.46e-494j
8.9917103104648314832 + 7.4984540357478860156e-1702j 7.88e-486, 7.88e-486j
2.0443266911327251147 - 2.0674325459562131337e-1729j 4.76e-501, 4.76e-501j
10.020146662503962679 - 8.0412303443863474075e-1711j 5.04e-485, 5.04e-485j
9.6739273996863421377 + 1.1578466356300760884e-1727j 2.84e-485, 2.84e-485j
-5.4228479113280690393 - 3.5136623806876677374e-1744j 3.35e-491, 3.35e-491j
-2.9294115500505854709 - 4.8847943477967272716e-1752j 5.56e-498, 5.56e-498j
7.0119959692797281814 + 4.3917623311017545092e-1741j 2.64e-488, 2.64e-488j
-7.9906244265279747668 - 5.6680512881788325746e-1740j 6.82e-487, 6.82e-487j
1.2724808447171745315 - 1.1615147700579746258e-1757j 5.38e-504, 5.38e-504j
-4.2283965787258560516 - 2.5333780929994732991e-1747j 1.64e-493, 1.64e-493j
-6.6901451522050172645 - 7.2949376928557941922e-1742j 7.29e-489, 7.29e-489j
-14.591670961721211905 - 1.7832570950581835947e-1737j 1.18e-485, 1.18e-485j
-12.188311208716585043 - 9.2901645351523520963e-1738j 1.7e-484, 1.7e-484j
2.3344142183389772393 + 1.6397222245664912133e-1771j 4.7e-500, 4.7e-500j
-5.1115800084649388456 - 3.5709492099562919993e-1763j 7.4e-492, 7.4e-492j
-12.955925828926612254 - 7.7066273189735163932e-1754j 1.22e-484, 1.22e-484j
-1.0169160606480331315 + 7.289289625412382966e-1788j 3.4e-505, 3.4e-505j
-0.19229316806204331199 + 7.5212158289445877343e-1792j 5.76e-509, 5.76e-509j
4.0278326129563373285 - 1.4126239751798125288e-1775j 5.75e-494, 5.75e-494j
6.0524651252377753435 - 7.3602297289766127935e-1766j 5.48e-490, 5.48e-490j
-6.3703170272077783956 - 6.1504430577852737323e-1778j 2.26e-489, 2.26e-489j
4.1139454663596323902e-1823 - 2.2473097267629293188e-1824j 4.57e-1821, 4.57e-1821j
12.188311208716585043 + 1.0773325258144390728e-1779j 1.71e-484, 1.71e-484j
6.3703170272077783956 + 3.4282003044320867604e-1801j 2.09e-489, 2.09e-489j
0.19229316806204331199 - 6.6285078012316224024e-1828j 5.76e-509, 5.76e-509j
11.082593347955994174 + 4.020086600556384771e-1802j 1.46e-484, 1.46e-484j
-0.460546930293621371 - 6.4374424917751056744e-1837j 9.18e-508, 9.18e-508j

Weights

Weight (ball center) Error (ball radius)
1.6913655481322894479e-53 - 3.9837581369017747126e-1377j 2.59e-109, 5.24e-350j
1.5791123902554009925e-72 + 2.1673804063949232564e-1389j 4.06e-118, 8.22e-359j
4.1402632119052457413e-60 + 1.91903030495208259e-1381j 1.39e-112, 2.81e-353j
1.4302336507111851919e-84 + 1.3911668567728768154e-1395j 2.89e-122, 5.85e-363j
1.4302336507111851919e-84 - 1.1844514423948126668e-1394j 3.92e-122, 7.92e-363j
1.1084685399673310046e-56 + 3.4968663942770449943e-1381j 3.39e-113, 6.86e-354j
1.1084685399673310046e-56 - 2.3430141187460093946e-1379j 4.72e-111, 9.55e-352j
2.711729232810771511e-12 + 5.8274220220891101771e-1357j 6.95e-78, 1.41e-318j
7.6180586624455397384e-36 + 3.1766051240529789363e-1369j 1.47e-102, 2.97e-343j
4.6178090052350879326e-06 + 4.8227405756167471555e-1352j 2.61e-59, 5.29e-300j
0.0037358336186639858905 - 3.0554830159135944434e-1350j 3.75e-36, 7.58e-277j
1.3530090745884142794e-42 - 1.4410710639770865178e-1372j 4.41e-106, 8.92e-347j
4.1402632119052457413e-60 - 5.7680542936658754428e-1383j 4.86e-116, 9.82e-357j
1.5791123902554009925e-72 - 2.7701075261056288356e-1388j 5.17e-119, 1.05e-359j
3.7428995278989534473e-19 + 4.8265587245586738592e-1361j 6.22e-92, 1.26e-332j
7.4385904076427342135e-05 - 5.5200252790429336459e-1351j 4.19e-55, 8.48e-296j
3.0708163655490134814e-28 + 4.2014292814818284011e-1366j 4.74e-101, 9.58e-342j
6.2565081016882640574e-68 - 5.12105488044141929e-1387j 2.26e-119, 4.57e-360j
1.6006944540860991747e-50 + 5.7536683770194925932e-1378j 1.23e-113, 2.48e-354j
7.1973379203654329838e-78 + 3.9952009154181780782e-1391j 2.29e-123, 4.63e-364j
6.2444688678562470317e-25 + 2.7526874817588495145e-1364j 1.43e-99, 2.89e-340j
7.8237482129752076079e-64 - 1.4834286065507392838e-1383j 3.98e-118, 8.06e-359j
7.8237482129752076079e-64 + 6.7519042199043773687e-1385j 3.39e-118, 6.86e-359j
1.216561785738451114e-16 + 1.3714080076849352222e-1359j 2.24e-92, 4.53e-333j
1.5100263384097552539e-26 - 3.5424939207575327081e-1365j 5.76e-101, 1.17e-341j
1.6913655481322894479e-53 - 1.5986006402134844769e-1379j 5.79e-115, 1.17e-355j
0.030837466420167592893 - 4.0237101684109373627e-1349j 1.13e-34, 2.28e-275j
4.3354427628523604325e-45 + 4.1051395879611917328e-1375j 6.63e-113, 1.34e-353j
6.2565081016882640574e-68 + 8.3298955269564146107e-1386j 3.34e-123, 6.75e-364j
0.084943657874149918394 + 7.4719647811551019276e-1349j 1.43e-33, 2.9e-274j
1.6845233275319518595e-20 - 8.2608635042025472061e-1362j 1.91e-97, 3.86e-338j
2.6198313732081905829e-07 + 3.4449559871764678282e-1353j 1.7e-80, 3.43e-321j
5.1309673641249371675e-08 - 9.8365595521852804078e-1354j 6.2e-83, 1.25e-323j
1.3530090745884142794e-42 - 8.5064506028105706517e-1374j 1.45e-112, 2.93e-353j
0.022404466899071121564 + 1.7915781718309388856e-1349j 1.71e-47, 3.45e-288j
1.6845233275319518595e-20 - 3.3333536781657175129e-1361j 2e-104, 4.04e-345j
5.2048489348624490441e-30 - 3.0498697160332165257e-1366j 3.66e-111, 7.39e-352j
0.063559480396266884856 - 6.7895296258404953348e-1349j 1.43e-33, 2.9e-274j
6.5511498424156159264e-22 + 1.3240181458561660843e-1362j 4.46e-101, 9.02e-342j
4.3354427628523604325e-45 + 9.2729105140896655749e-1374j 1.44e-117, 2.92e-358j
0.00064961728624473012231 - 6.730434459192121483e-1351j 5.03e-72, 1.02e-312j
0.00064961728624473012231 - 1.0278319416120708045e-1350j 2.92e-70, 5.9e-311j
3.1366287712066129291e-40 + 1.5218877152753248869e-1372j 1.9e-113, 3.85e-354j
5.5407374402718664245e-38 - 2.6833953184127606384e-1370j 7.35e-115, 1.49e-355j
6.2444688678562470317e-25 + 1.3925402106813811069e-1363j 3.21e-109, 6.49e-350j
4.6178090052350879326e-06 + 2.6490376962839047974e-1352j 3.2e-84, 6.47e-325j
1.1864068400077947671e-06 - 6.5458350823124048312e-1353j 4.03e-86, 8.14e-327j
0.0076848405825079875073 + 4.2390278337935361745e-1350j 2.72e-66, 5.5e-307j
0.084943657874149918394 + 8.2242928576098562489e-1349j 6.3e-45, 1.27e-285j
3.1366287712066129291e-40 + 2.0607750452095359776e-1371j 3.58e-116, 7.23e-357j
7.6180586624455397384e-36 + 3.2972046169777427597e-1370j 2.11e-113, 4.26e-354j
0.0037358336186639858905 - 2.1678818601842587488e-1350j 7.96e-71, 1.61e-311j
7.2235702994233368175e-18 - 2.6497707579433586697e-1360j 2.97e-101, 6e-342j
0.022404466899071121564 + 2.2532600907374496183e-1349j 3.31e-63, 6.7e-304j
5.2048489348624490441e-30 - 4.5695354154571549054e-1367j 5.47e-110, 1.11e-350j
2.3312068155057232113e-14 + 3.1181192053173007613e-1358j 1.2e-99, 2.43e-340j
1.4033830284248786728e-09 - 3.4991841610548058577e-1355j 4.41e-95, 8.92e-336j
0.030837466420167592893 - 3.3075169499025881706e-1349j 2.7e-62, 5.47e-303j
0.10043345425721201788 - 1.1653182291145185843e-1348j 2.6e-54, 5.26e-295j
2.4439783204469277432e-11 - 5.9594043127717746304e-1356j 1.05e-102, 2.11e-343j
7.2235702994233368175e-18 - 9.3707059779585638614e-1360j 6.03e-110, 1.22e-350j
0.00023366290888155744429 + 6.8809175314965793633e-1351j 2.16e-84, 4.37e-325j
0.014083351892580360737 - 8.6654996054064623759e-1350j 1.95e-71, 3.95e-312j
1.6006944540860991747e-50 + 3.8873874777813270441e-1376j 6.84e-125, 1.38e-365j
1.5100263384097552539e-26 - 1.9518688178376543263e-1364j 1.17e-115, 2.37e-356j
2.6718577532089237223e-13 - 3.8632260211205759884e-1357j 9.92e-107, 2.01e-347j
8.9741601451906598155e-09 + 1.2952197102795606909e-1354j 1.4e-98, 2.84e-339j
1.1864068400077947671e-06 - 1.243661187911100283e-1352j 8.34e-95, 1.69e-335j
1.0005495461417115369e-47 - 5.6990460241829497955e-1375j 7.8e-124, 1.58e-364j
7.1973379203654329838e-78 - 3.8508569703380725805e-1392j 4.53e-138, 9.17e-379j
2.6718577532089237223e-13 - 1.3789630232137112485e-1357j 6.44e-104, 1.3e-344j
1.7955173593953762504e-15 - 2.1037761863801927663e-1358j 9.38e-110, 1.9e-350j
0.00023366290888155744429 + 4.3278250534859561738e-1351j 5.02e-91, 1.02e-331j
7.2783862080814953804e-32 + 4.5325438179644408274e-1368j 1.07e-116, 2.16e-357j
2.1889955901138522861e-23 - 1.9801115728261865168e-1363j 1.07e-110, 2.16e-351j
0.0016369150237258936198 + 1.7130623807967692136e-1350j 7.01e-90, 1.42e-330j
1.216561785738451114e-16 + 4.5599182554605344199e-1359j 1.54e-111, 3.11e-352j
7.4385904076427342135e-05 - 3.340284763321022243e-1351j 2.21e-95, 4.47e-336j
0.04328731481910650077 + 4.8216323217843284129e-1349j 8.16e-80, 1.65e-320j
2.3312068155057232113e-14 + 9.23009060801437401e-1358j 8.71e-110, 1.76e-350j
8.9741601451906598155e-09 + 2.8203841180699063776e-1354j 2.19e-104, 4.43e-345j
1.2796265141137677372e-05 - 1.9266154379369158448e-1351j 2.67e-98, 5.4e-339j
7.2783862080814953804e-32 + 3.3747587533589472614e-1367j 7.43e-122, 1.5e-362j
2.1426087562733713821e-05 + 2.4423365690960566639e-1351j 1.57e-99, 3.17e-340j
3.7428995278989534473e-19 + 1.8204159553105468459e-1360j 2.45e-114, 4.95e-355j
0.014083351892580360737 - 1.1302521736412134307e-1349j 5.59e-93, 1.13e-333j
2.1889955901138522861e-23 - 9.248046956754222923e-1363j 7.19e-118, 1.45e-358j
6.5511498424156159264e-22 + 5.7360911975970781261e-1362j 7.19e-117, 1.45e-357j
5.1309673641249371675e-08 - 4.7327467072515120429e-1354j 1.16e-108, 2.35e-349j
0.0016369150237258936198 + 1.1678783178048514702e-1350j 7.51e-100, 1.52e-340j
2.711729232810771511e-12 + 1.5478281033990029964e-1356j 1.49e-111, 3.02e-352j
1.7955173593953762504e-15 - 6.7130726216958167037e-1359j 1.28e-114, 2.59e-355j
0.04328731481910650077 + 5.6853194250486527629e-1349j 3.31e-96, 6.69e-337j
1.2796265141137677372e-05 - 1.0999134531765491968e-1351j 7.59e-105, 1.54e-345j
2.4439783204469277432e-11 - 2.3627439273590111718e-1356j 2e-112, 4.05e-353j
1.0005495461417115369e-47 - 1.6835600491658725993e-1376j 6.24e-134, 1.26e-374j
8.3005198773528086112e-34 - 4.0749077630941199632e-1369j 4.07e-127, 8.23e-368j
0.0076848405825079875073 + 5.744572114356385656e-1350j 4.61e-105, 9.33e-346j
2.6198313732081905829e-07 + 1.7346307131056743901e-1353j 1.36e-110, 2.76e-351j
5.5407374402718664245e-38 - 2.3818957616101933209e-1371j 2.07e-129, 4.19e-370j
0.063559480396266884856 - 5.9524795078130985491e-1349j 2.54e-103, 5.13e-344j
0.096021689139400556892 + 2.0364992123950937149e-1348j 1.17e-103, 2.36e-344j
2.1426087562733713821e-05 + 4.1603178344999605215e-1351j 1.37e-109, 2.75e-350j
1.4033830284248786728e-09 - 7.9921173248804991387e-1355j 1.55e-115, 3.14e-356j
1.9608236916501448261e-10 + 9.2344844421304838907e-1356j 2.12e-114, 4.38e-355j
0.06074702503102981979 - 2.7446551045602987547e-1348j 1.22e-106, 2.48e-347j
8.3005198773528086112e-34 - 3.4251467182638274911e-1368j 2.67e-130, 5.53e-371j
1.9608236916501448261e-10 + 2.2149633194682964545e-1355j 8.91e-117, 1.69e-357j
0.096021689139400556892 + 2.0877304849007658625e-1348j 3.55e-108, 4.2e-349j
3.0708163655490134814e-28 + 2.5378686416487772811e-1365j 2.25e-127, 4.71e-368j
0.10043345425721201788 - 1.097982645790862648e-1348j 1.53e-108, 1.59e-349j

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