Rule: Q[14, 99]

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)
-16.425210013909387242 - 5.3509374233681124364e-1215j 1.21e-487, 1.21e-487j
14.583046799605488981 + 1.3936640750914568131e-1210j 1.61e-485, 1.61e-485j
15.936368647016170591 + 3.015134877270800774e-1215j 5.42e-487, 5.42e-487j
-18.088513273243772303 - 4.066648042767158149e-1233j 2.36e-490, 2.36e-490j
-17.490507688463858473 - 1.0223156737085384573e-1232j 2.79e-489, 2.79e-489j
-14.583046799605488981 - 1.9720131983618556836e-1228j 1.56e-485, 1.56e-485j
15.018529551546272947 + 1.2190464323629321174e-1226j 6.06e-486, 6.06e-486j
16.425210013909387242 - 4.5440171392429337933e-1244j 1.23e-487, 1.23e-487j
-10.375308116455165144 + 3.4245070373740592544e-1264j 1.32e-484, 1.32e-484j
-10.026698688837409078 - 2.1309372529986047276e-1264j 8.84e-485, 8.84e-485j
-5.473193091966789637 + 2.5668219882016567847e-1269j 2.53e-490, 2.53e-490j
19.575671695722844825 - 1.4663146888730194593e-1264j 2.21e-493, 2.21e-493j
17.490507688463858473 - 1.9035460862204776269e-1263j 2.82e-489, 2.82e-489j
-3.8869245750597693838 - 6.2264098182364276768e-1299j 2.92e-493, 2.92e-493j
12.187135736346892492 - 1.3954890174365617528e-1288j 2.49e-484, 2.49e-484j
18.088513273243772303 + 4.5602333192667216065e-1310j 2.3e-490, 2.3e-490j
-8.6679232313941548761 - 7.5890612441021866501e-1318j 8.14e-486, 8.14e-486j
-11.447101467107524703 - 3.2979230153388949953e-1316j 2.74e-484, 2.74e-484j
-4.1393993729973987765 - 4.1963433254862170574e-1326j 6.58e-493, 6.58e-493j
3.7955951222571963522 + 2.4816951925008086081e-1325j 1.49e-493, 1.49e-493j
3.548142414772248657 + 7.7955433388543515253e-1327j 6.86e-495, 6.86e-495j
4.8969363973455646837 + 3.192716280826515275e-1323j 2.58e-491, 2.58e-491j
-18.760735544679713688 - 1.0076406372329323649e-1323j 1.31e-491, 1.31e-491j
-12.566266460718843646 - 2.3975975426283679968e-1316j 2.1e-484, 2.1e-484j
-16.940563917725231696 + 1.1234831563079324578e-1320j 2.08e-488, 2.08e-488j
-11.085159819572902904 + 5.8893717835914378292e-1317j 2.31e-484, 2.31e-484j
2.3775241835745905962 - 5.0975531367544327987e-1332j 1.15e-499, 1.15e-499j
18.760735544679713688 + 1.1269164560788566234e-1316j 1.24e-491, 1.24e-491j
-14.160174813994793364 + 5.2742616697121351623e-1328j 3.62e-485, 3.62e-485j
-2.3775241835745905962 + 2.9025458443986925353e-1347j 1.1e-499, 1.1e-499j
-6.7166977701695830707 - 4.138265521039444953e-1336j 2.67e-488, 2.67e-488j
-19.575671695722844825 - 3.34218109259692337e-1340j 1.98e-493, 1.98e-493j
-7.6805859764933177365 - 6.4872443103947857611e-1334j 6.22e-487, 6.22e-487j
-15.46872037351520916 + 1.3934020247537987717e-1330j 2e-486, 2e-486j
-4.8969363973455646837 + 1.068196271898973171e-1340j 2.74e-491, 2.74e-491j
-9.6818997491865225223 - 7.4512496452776214171e-1333j 5.54e-485, 5.54e-485j
-9.340652723533891655 - 2.1659853617687802872e-1334j 3.16e-485, 3.16e-485j
2.088344745701944171 - 3.5685349597981514831e-1355j 8.32e-501, 8.32e-501j
10.026698688837409078 + 3.7731409887210288639e-1338j 9.24e-485, 9.24e-485j
-10.728019106021514351 - 3.3088080248415656206e-1364j 1.99e-484, 1.99e-484j
-11.814265959828761462 - 2.0044504450034498021e-1364j 2.81e-484, 2.81e-484j
-13.748267826566740261 - 1.4603507813057967241e-1363j 6.58e-485, 6.58e-485j
6.400586311440601719 + 8.9310891669114900763e-1371j 8.57e-489, 8.57e-489j
14.160174813994793364 - 3.3743467237641346278e-1405j 3.43e-485, 3.43e-485j
12.952303612417615296 + 2.8909451827554239314e-1447j 1.7e-484, 1.7e-484j
11.814265959828761462 + 4.8441827026472732732e-1462j 2.7e-484, 2.7e-484j
8.336060897433150292 + 5.8236311000896874883e-1469j 3.76e-486, 3.76e-486j
10.728019106021514351 + 7.3584848474766787099e-1467j 1.78e-484, 1.78e-484j
0.96661353308016335253 + 7.9389203635255440379e-1492j 1.46e-505, 1.46e-505j
-8.0069897094761625736 - 3.6751549324689144773e-1473j 1.51e-486, 1.51e-486j
11.085159819572902904 - 1.2567205438617397582e-1469j 2.29e-484, 2.29e-484j
8.6679232313941548761 + 7.00379137869718932e-1478j 7.99e-486, 7.99e-486j
3.2570482627860673382 - 2.5560489154013256219e-1487j 3.51e-496, 3.51e-496j
4.6434638412724226488 + 1.6843144413654275755e-1483j 9.31e-492, 9.31e-492j
9.340652723533891655 + 5.4098223482671175279e-1476j 3.23e-485, 3.23e-485j
-3.7955951222571963522 - 2.534449522041369774e-1492j 1.48e-493, 1.48e-493j
7.3567585510566054624 + 9.848973837208122276e-1487j 2.27e-487, 2.27e-487j
6.0874095469012913223 - 1.0246904994088898388e-1488j 2.65e-489, 2.65e-489j
-13.346004477966891459 - 1.76467898998322623e-1483j 1.06e-484, 1.06e-484j
0.69058833158348190147 - 8.1006319852411954452e-1506j 9.38e-507, 9.38e-507j
15.46872037351520916 + 4.6311608374909117765e-1484j 1.97e-486, 1.97e-486j
-7.0354584921537173309 - 1.3325094490511374087e-1511j 8.41e-488, 8.41e-488j
16.940563917725231696 - 2.2492526787353322721e-1508j 2.16e-488, 2.16e-488j
-2.6694108075894433386 - 9.9017042327490311723e-1550j 1.61e-498, 1.61e-498j
13.748267826566740261 - 1.3955561303505118665e-1532j 6.68e-485, 6.68e-485j
-15.936368647016170591 - 4.9752656649830349139e-1557j 5.26e-487, 5.26e-487j
-9.0027281248741207104 + 2.5994041897956106299e-1556j 1.59e-485, 1.59e-485j
-0.96661353308016335253 - 2.1503612509922196522e-1575j 1.59e-505, 1.59e-505j
-5.1769424839668232208 - 1.5503857097558506464e-1561j 7.79e-491, 7.79e-491j
5.1769424839668232208 + 4.4142037185830352232e-1560j 7.7e-491, 7.7e-491j
-1.8026600132883557532 - 3.1998853812613208005e-1572j 5.79e-502, 5.79e-502j
-5.7778040114280886792 - 4.3089098982674670682e-1560j 8.38e-490, 8.38e-490j
-8.336060897433150292 + 7.0895883202079894428e-1556j 3.47e-486, 3.47e-486j
-7.3567585510566054624 - 4.1361781768732090821e-1557j 2.17e-487, 2.17e-487j
-2.9630365798386675025 - 8.6919637407346636303e-1567j 2.27e-497, 2.27e-497j
4.4009694330501990264 + 2.9514892788229373132e-1563j 2.44e-492, 2.44e-492j
4.1393993729973987765 - 5.1994852577809231902e-1562j 7.12e-493, 7.12e-493j
10.375308116455165144 - 1.050663449675499271e-1553j 1.31e-484, 1.31e-484j
-0.69058833158348190147 + 1.713562861614535632e-1588j 8.56e-507, 8.56e-507j
-4.6434638412724226488 + 5.852631853086356074e-1574j 9.12e-492, 9.12e-492j
7.6805859764933177365 + 1.7960994255425366662e-1567j 6.49e-487, 6.49e-487j
2.9630365798386675025 + 2.3005698239870596064e-1584j 2.24e-497, 2.24e-497j
-15.018529551546272947 + 1.9357603778386587666e-1572j 6.01e-486, 6.01e-486j
7.0354584921537173309 + 4.6519102260034113494e-1574j 7.93e-488, 7.93e-488j
-1.242688955485464179 - 9.3682935873257490489e-1599j 2.57e-504, 2.57e-504j
3.8869245750597693838 + 1.6292544204865683423e-1588j 3.05e-493, 3.05e-493j
1.8026600132883557532 - 2.171920572350142606e-1596j 5.35e-502, 5.35e-502j
5.473193091966789637 + 1.9900363827378011914e-1584j 2.55e-490, 2.55e-490j
-3.548142414772248657 - 2.7437749004466389758e-1589j 7.06e-495, 7.06e-495j
-6.400586311440601719 + 2.0845874405328268164e-1583j 8.7e-489, 8.7e-489j
-2.088344745701944171 + 1.0580372911580941439e-1595j 8.01e-501, 8.01e-501j
1.242688955485464179 - 4.0508615535847207296e-1599j 2.43e-504, 2.43e-504j
1.5208950960150867895 - 1.0950086387911880355e-1597j 3.76e-503, 3.76e-503j
9.6818997491865225223 - 6.8274459805717086668e-1578j 5.36e-485, 5.36e-485j
-4.4009694330501990264 - 4.4197640790160074619e-1617j 2.48e-492, 2.48e-492j
13.346004477966891459 - 2.134708714511786178e-1608j 1.09e-484, 1.09e-484j
-12.952303612417615296 + 1.5354122558767861115e-1630j 1.57e-484, 1.57e-484j
9.0027281248741207104 - 3.1287974468584393843e-1631j 1.64e-485, 1.64e-485j
6.7166977701695830707 - 3.4519240275181571787e-1646j 2.65e-488, 2.65e-488j
-6.0874095469012913223 + 6.1465103751603102641e-1658j 2.62e-489, 2.62e-489j
-1.5208950960150867895 + 5.2035998250161501044e-1672j 4.25e-503, 4.25e-503j
-7.1176873081238750223e-1730 - 1.2819927454135055399e-1729j 1.66e-1727, 1.66e-1727j
0.41259045795460183817 - 2.0969889087003684271e-1676j 4.7e-508, 4.7e-508j
0.12576397275166955575 - 4.232482355733271439e-1678j 2.22e-509, 2.22e-509j
11.447101467107524703 - 8.5075802241602913026e-1654j 2.64e-484, 2.64e-484j
-3.2570482627860673382 - 3.3648781492355361431e-1684j 3.55e-496, 3.55e-496j
-12.187135736346892492 + 1.0358930911982865072e-1671j 2.6e-484, 2.6e-484j
5.7778040114280886792 + 1.2415945843224339652e-1677j 8.11e-490, 8.11e-490j
2.6694108075894433386 - 3.4216930750821615777e-1687j 1.63e-498, 1.63e-498j
8.0069897094761625736 - 8.2489118201306196841e-1673j 1.42e-486, 1.42e-486j
-0.41259045795460183817 + 1.7739745554637140545e-1709j 4.43e-508, 4.43e-508j
-0.12576397275166955575 + 1.4475144860218880222e-1710j 2.22e-509, 2.22e-509j
12.566266460718843646 + 9.5733489659792467295e-1685j 2.26e-484, 2.26e-484j

Weights

Weight (ball center) Error (ball radius)
5.2138868744280780896e-60 - 1.445296200350533078e-1265j 1.2e-101, 3.33e-345j
1.1312620464964211865e-47 - 1.2291644464944048056e-1256j 2.31e-96, 6.42e-340j
1.3535722780922790341e-56 - 2.1029556599269767538e-1262j 1.08e-100, 3e-344j
2.2397998941499924278e-72 + 4.466524690992418696e-1272j 3.81e-107, 1.06e-350j
8.4794568412296386686e-68 - 1.1290602742150977083e-1269j 2.13e-105, 5.92e-349j
1.1312620464964211865e-47 - 5.4055894312581021652e-1259j 7.69e-98, 2.14e-341j
1.852902853488893757e-50 - 1.1802391628020925784e-1258j 1.9e-99, 5.28e-343j
5.2138868744280780896e-60 + 2.4327982707776163106e-1264j 4.97e-104, 1.38e-347j
5.8949453932489999057e-25 + 1.8796259405091816077e-1246j 1.33e-84, 3.7e-328j
2.0416538871579113065e-23 - 1.4654206533848222835e-1245j 3.79e-83, 1.05e-326j
3.7585238106132193642e-08 - 2.1430335790699904844e-1235j 5.36e-58, 1.49e-301j
2.3080737195164811589e-84 - 1.6785931389235227527e-1277j 1.56e-115, 4.34e-359j
8.4794568412296386686e-68 + 1.2455189469437320959e-1268j 2.04e-109, 5.68e-353j
3.6922411038802001862e-05 - 7.5871408140767181712e-1232j 6.11e-47, 1.7e-290j
8.3928979070668208851e-34 - 2.1558302614029404849e-1250j 8.89e-96, 2.47e-339j
2.2397998941499924278e-72 - 4.1628790602801038796e-1271j 2.43e-111, 6.76e-355j
6.4395127961903042318e-18 - 2.8033904558197969133e-1242j 1.92e-81, 5.35e-325j
5.1103065010152186148e-30 - 2.4892846615412066442e-1249j 5.41e-93, 1.51e-336j
2.0512916202167642763e-05 + 1.4304089814320066607e-1232j 3.51e-51, 9.78e-295j
4.0617677249898780538e-05 + 1.5786880693757117941e-1231j 7.39e-51, 2.05e-294j
0.00021095733276972897172 - 8.0875762584870640151e-1232j 3.24e-48, 9.02e-292j
6.6290591313883295235e-07 - 8.7126594945519070286e-1234j 6.73e-62, 1.87e-305j
1.0789181906906783111e-77 - 7.3810224777884725199e-1275j 5.86e-117, 1.63e-360j
7.8262841867376479416e-36 + 1.4591276683301925443e-1252j 4.45e-99, 1.24e-342j
1.0197315989009166488e-63 + 1.5882386864204236017e-1267j 2.12e-111, 5.91e-355j
2.9741264154062869747e-28 + 2.4620496535786172666e-1248j 1.78e-93, 4.96e-337j
0.0068686945535902158675 - 1.7142685429220617674e-1231j 7.41e-40, 2.06e-283j
1.0789181906906783111e-77 + 5.8910852873344874998e-1274j 4.77e-119, 1.33e-362j
4.796062656710809024e-45 + 1.4030473118465973552e-1257j 2.27e-104, 6.32e-348j
0.0068686945535902158675 - 1.2336579641855876784e-1231j 1.07e-41, 2.97e-285j
2.0240423566831817682e-11 - 5.1136862647120695613e-1238j 4.69e-78, 1.31e-321j
2.3080737195164811589e-84 + 2.4534251471788244947e-1278j 4.89e-121, 1.36e-364j
2.009609714406361814e-14 + 4.5462390036009304804e-1240j 5.71e-83, 1.59e-326j
2.0085012299433975188e-53 - 4.5350545354207506627e-1262j 1.43e-108, 3.98e-352j
6.6290591313883295235e-07 - 4.3322307266801432563e-1234j 1.47e-68, 4.09e-312j
6.0391665213931325686e-22 + 1.0653185098687767855e-1244j 3.5e-90, 9.75e-334j
1.5353097905767742644e-20 - 7.2518043208436724478e-1244j 2.06e-89, 5.72e-333j
0.012959731877032056973 + 2.5791040607368109747e-1231j 1.55e-47, 4.32e-291j
2.0416538871579113065e-23 - 7.9150294133535877531e-1245j 8.45e-104, 2.35e-347j
1.4434945531667003338e-26 - 2.2380775463849052066e-1247j 6.93e-94, 1.93e-337j
7.2493069107682582595e-32 + 2.299928700494647133e-1250j 1.57e-98, 4.36e-342j
1.4666517364608438459e-42 - 3.0967758090628868495e-1256j 1.95e-105, 5.43e-349j
1.5953037369130979187e-10 + 5.993324669721025444e-1237j 1.55e-90, 4.3e-334j
4.796062656710809024e-45 + 9.5367158858186052576e-1256j 1.68e-116, 4.67e-360j
5.7887419814309013978e-38 - 1.6657590982748965548e-1252j 2.59e-114, 7.21e-358j
7.2493069107682582595e-32 + 2.1927317742968444485e-1249j 1.39e-111, 3.86e-355j
1.0726673806520303573e-16 + 5.887039293140036884e-1241j 2e-102, 5.55e-346j
1.4434945531667003338e-26 - 1.4694609943931549002e-1246j 1.29e-109, 3.6e-353j
0.068936426716172478926 + 1.373654816769877769e-1230j 1.68e-62, 4.68e-306j
1.5656452450421410884e-15 - 8.7380491954520052583e-1241j 4.55e-95, 1.27e-338j
2.9741264154062869747e-28 + 1.8067021484060705975e-1247j 1.53e-110, 4.25e-354j
6.4395127961903042318e-18 - 1.1019473511053526038e-1241j 2.01e-104, 5.6e-348j
0.00058199158147819340128 + 7.2325069683301133046e-1232j 7.35e-77, 2.04e-320j
2.0044062011428099557e-06 + 3.0357103318903119324e-1233j 5.91e-87, 1.64e-330j
1.5353097905767742644e-20 - 3.3093656268192357737e-1243j 7.78e-107, 2.16e-350j
4.0617677249898780538e-05 + 9.2662022223025288106e-1232j 2.12e-81, 5.88e-325j
2.2756206617118080247e-13 - 6.8927010688268673879e-1239j 4.63e-101, 1.29e-344j
1.1160841473917305735e-09 - 2.5626441088692484597e-1236j 8.92e-96, 2.48e-339j
3.3360535569346458444e-40 + 5.906510382596664985e-1255j 6.08e-116, 1.69e-359j
0.08696150154200311109 - 2.1315514174646605753e-1230j 6.17e-69, 1.72e-312j
2.0085012299433975188e-53 + 1.5387881869908619638e-1260j 2.12e-124, 5.89e-368j
2.2794442399062216858e-12 + 1.09371246426687681e-1238j 4.89e-99, 1.36e-342j
1.0197315989009166488e-63 - 2.1237181177954681285e-1266j 3.28e-129, 9.12e-373j
0.0033139241969109383145 + 8.1498017038675429972e-1232j 1.99e-80, 5.54e-324j
1.4666517364608438459e-42 - 1.0510055071024603029e-1254j 3e-120, 8.33e-364j
1.3535722780922790341e-56 + 9.3251320763801368768e-1264j 3.22e-125, 8.94e-369j
3.3735586855319304803e-19 + 4.6409946242053379559e-1243j 2.28e-104, 6.33e-348j
0.068936426716172478926 + 1.2028738084042702769e-1230j 8.55e-76, 2.38e-319j
1.7521659600776676067e-07 + 9.8159246127978481039e-1235j 2.24e-94, 6.24e-338j
1.7521659600776676067e-07 + 2.0620924311455700645e-1234j 1.62e-97, 4.51e-341j
0.022294728375722759631 - 3.0733810099581783075e-1231j 7.45e-78, 2.07e-321j
6.912786736274363016e-09 + 4.7313877757694954493e-1236j 4.82e-97, 1.34e-340j
1.0726673806520303573e-16 + 1.6046109628426377825e-1241j 1.66e-103, 4.62e-347j
2.2756206617118080247e-13 - 2.2702409587404832383e-1239j 2.96e-101, 8.22e-345j
0.0014552985971929251904 - 5.7450664336470057021e-1232j 1.09e-87, 3.04e-331j
6.2104821882771174831e-06 - 8.4691706397616473712e-1233j 1.04e-96, 2.89e-340j
2.0512916202167642763e-05 + 2.5643105388218972397e-1232j 9.02e-96, 2.51e-339j
5.8949453932489999057e-25 + 1.1149069575504432145e-1245j 4.86e-117, 1.35e-360j
0.08696150154200311109 - 1.9387977573912423271e-1230j 5.26e-83, 1.46e-326j
2.0044062011428099557e-06 + 1.5693796573247555287e-1233j 2.54e-96, 7.07e-340j
2.009609714406361814e-14 + 1.4663726210640078719e-1239j 1.52e-110, 4.24e-354j
0.0014552985971929251904 - 8.6749850266094981305e-1232j 1.72e-93, 4.79e-337j
1.852902853488893757e-50 + 1.7363054997054820089e-1260j 2.12e-127, 5.89e-371j
2.2794442399062216858e-12 + 3.1327130910564667054e-1238j 8.93e-109, 2.48e-352j
0.051023826899651377352 - 7.6839494455572090556e-1231j 6.14e-86, 1.71e-329j
3.6922411038802001862e-05 - 1.3101409156541051923e-1231j 2.32e-96, 6.46e-340j
0.022294728375722759631 - 3.9403752793691959804e-1231j 1.4e-90, 3.91e-334j
3.7585238106132193642e-08 - 4.7180994269723002723e-1235j 1.59e-103, 4.41e-347j
0.00021095733276972897172 - 4.922216058853056178e-1232j 7.81e-97, 2.17e-340j
1.5953037369130979187e-10 + 2.3370663241579870181e-1237j 8.94e-105, 2.49e-348j
0.012959731877032056973 + 1.9329602281413712062e-1231j 5.85e-93, 1.63e-336j
0.051023826899651377352 - 9.1155091116700216719e-1231j 1.63e-89, 4.53e-333j
0.03511781225267985482 + 6.0210201096048311318e-1231j 7.33e-91, 2.04e-334j
6.0391665213931325686e-22 + 5.2742544620792646042e-1244j 6.12e-117, 1.7e-360j
6.2104821882771174831e-06 - 4.5424397886811281385e-1233j 7.39e-100, 2.06e-343j
3.3360535569346458444e-40 + 1.3335294070495715111e-1253j 2.11e-127, 5.87e-371j
5.7887419814309013978e-38 - 9.8652287336395102125e-1254j 3.9e-124, 1.08e-367j
3.3735586855319304803e-19 + 1.9615627890544885272e-1242j 1.61e-115, 4.47e-359j
2.0240423566831817682e-11 - 1.3846348648118614087e-1237j 7.57e-110, 2.11e-353j
1.1160841473917305735e-09 - 1.0532566089301072302e-1236j 3.32e-106, 9.24e-350j
0.03511781225267985482 + 4.8837408003376124912e-1231j 1.99e-97, 5.54e-341j
-0.030397061381664338906 + 2.2390502946139898114e-1229j 2.74e-96, 7.62e-340j
0.10251822527315767718 + 3.7794640528898504542e-1230j 1.38e-96, 3.83e-340j
0.12284825968067284762 - 1.3732815401048668163e-1229j 2.21e-96, 6.16e-340j
5.1103065010152186148e-30 - 2.0662493108302622559e-1248j 1.07e-122, 2.97e-366j
0.00058199158147819340128 + 4.5916438816095023436e-1232j 3.37e-102, 9.34e-346j
8.3928979070668208851e-34 - 1.9294517572127449527e-1251j 4.47e-123, 1.24e-366j
6.912786736274363016e-09 + 1.0940650127403842471e-1235j 6.08e-109, 1.68e-352j
0.0033139241969109383145 + 1.1801947658769419487e-1231j 6.68e-104, 1.84e-347j
1.5656452450421410884e-15 - 3.0016900346309922516e-1240j 3e-114, 8.25e-358j
0.10251822527315767718 + 3.57148745574598707e-1230j 6.4e-103, 1.58e-346j
0.12284825968067284762 - 1.3497977459539605497e-1229j 2.1e-102, 5.05e-346j
7.8262841867376479416e-36 + 1.9642354396963424602e-1251j 3.38e-126, 9.47e-370j

Download

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