Rule: Q[6, 9, 94]

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)
17.67702923508212481 - 1.8204296417179169033e-1045j 5.5e-491, 5.5e-491j
18.354060293922213777 + 3.9647506927527424261e-1047j 2.95e-492, 2.95e-492j
-11.34989147159540817 + 7.2044446126276673731e-1038j 2.21e-485, 2.21e-485j
16.001200358279347505 - 1.6912379526824561443e-1055j 2.56e-488, 2.56e-488j
-14.144004173934387912 + 4.4040394547992046985e-1055j 2.44e-486, 2.44e-486j
15.508495459423035005 + 1.727104472867971144e-1069j 1.15e-487, 1.15e-487j
-18.354060293922213777 + 7.2592630136949284235e-1074j 2.92e-492, 2.92e-492j
9.8961915530912014109 - 9.719535384334128618e-1068j 8.27e-486, 8.27e-486j
-9.8961915530912014109 - 7.8198021784083989982e-1066j 7.84e-486, 7.84e-486j
-7.8336337686959197363 - 1.290243764568662026e-1075j 1.14e-487, 1.14e-487j
-19.174644956486640665 - 7.9322720352497725672e-1078j 5.34e-494, 5.34e-494j
-15.508495459423035005 - 7.4778205113870413791e-1076j 1.12e-487, 1.12e-487j
-8.1695229757096022876 + 1.5406309573887547855e-1094j 2.75e-487, 2.75e-487j
-4.3418637687749014379 - 2.5423352225261443759e-1101j 1.6e-493, 1.6e-493j
-17.67702923508212481 + 1.2156948455386324884e-1091j 6.02e-491, 6.02e-491j
16.520535046149750781 - 1.5734184028613254529e-1097j 4.88e-489, 4.88e-489j
8.1695229757096022876 + 1.5518562059735652958e-1095j 2.8e-487, 2.8e-487j
12.896088504406621733 + 6.7882524421701642602e-1093j 1.26e-485, 1.26e-485j
-5.8716927614384833736 - 3.5626684908082686787e-1103j 1.12e-490, 1.12e-490j
-15.03706823713137249 + 1.901535070753113838e-1097j 3.62e-487, 3.62e-487j
3.8882912091011466435 - 1.1700289626409580455e-1119j 1.07e-494, 1.07e-494j
17.074626402236171621 - 1.4790640456763877656e-1114j 6.58e-490, 6.58e-490j
11.726390337672902605 - 1.4224485636777507656e-1109j 2.24e-485, 2.24e-485j
-6.1926395185711035801 - 2.4482710023928295982e-1114j 4.15e-490, 4.15e-490j
-17.074626402236171621 + 9.2936032521335310693e-1110j 6.81e-490, 6.81e-490j
-14.583159984582889207 - 8.1889280433674797851e-1117j 9.57e-487, 9.57e-487j
1.0719106606596820279 - 9.5613323849522130371e-1148j 9.68e-505, 9.68e-505j
-9.543817763509158045 + 5.9917951399885391908e-1128j 4.58e-486, 4.58e-486j
12.498781993917430931 + 1.3031567106432724821e-1128j 1.73e-485, 1.73e-485j
-16.001200358279347505 + 2.0920805456738078728e-1129j 2.62e-488, 2.62e-488j
7.1698635312426378058 + 9.3017924827030065888e-1141j 1.44e-488, 1.44e-488j
-8.508288589397451389 + 1.1916582424024365493e-1138j 6.46e-487, 6.46e-487j
9.1952137155035619771 + 7.2544532593392774109e-1139j 2.58e-486, 2.58e-486j
11.34989147159540817 - 2.2674413821056489443e-1138j 2.12e-485, 2.12e-485j
-16.520535046149750781 + 5.7055088383096628945e-1139j 4.51e-489, 4.51e-489j
2.7335445021588858596 + 3.2357627159645954569e-1157j 1.12e-498, 1.12e-498j
12.109136947678033169 + 5.2871874382470014703e-1143j 2.17e-485, 2.17e-485j
2.1622432407445836276 - 7.9082993313042058662e-1161j 1.15e-500, 1.15e-500j
6.516004104212320361 + 1.4124646500030152739e-1149j 1.38e-489, 1.38e-489j
-6.8417366009545604973 + 1.9181966019053707627e-1149j 4.62e-489, 4.62e-489j
-2.7335445021588858596 - 2.4028514070543634826e-1159j 1.2e-498, 1.2e-498j
13.717490220739258895 - 2.0939871442026726245e-1144j 4.75e-486, 4.75e-486j
14.583159984582889207 - 3.0854410998450863124e-1146j 1.04e-486, 1.04e-486j
9.543817763509158045 + 1.2973468653189289798e-1145j 4.71e-486, 4.71e-486j
-10.252630887976094276 - 1.4283319606181157524e-1157j 1.12e-485, 1.12e-485j
-3.6165534267277441896 - 1.2701432159023334222e-1190j 1.22e-495, 1.22e-495j
-2.1622432407445836276 + 3.1796708455774737655e-1195j 1.24e-500, 1.24e-500j
7.8336337686959197363 - 3.2214186821672846708e-1179j 1.13e-487, 1.13e-487j
5.238103932311563875 - 2.1308530559539897808e-1200j 7.85e-492, 7.85e-492j
-1.3498952853218839149 + 5.0922746449399245672e-1222j 1.13e-503, 1.13e-503j
-12.109136947678033169 - 3.1667151337220865297e-1203j 2.12e-485, 2.12e-485j
-1.0719106606596820279 - 2.3419664243953201155e-1247j 1.01e-504, 1.01e-504j
-7.1698635312426378058 - 1.7041578340066427176e-1228j 1.38e-488, 1.38e-488j
4.3418637687749014379 + 1.262617588066803071e-1239j 1.69e-493, 1.69e-493j
-0.77437777109628731486 - 2.863055059017487799e-1252j 1.36e-505, 1.36e-505j
10.252630887976094276 + 9.5267727566553688593e-1231j 1.18e-485, 1.18e-485j
-13.717490220739258895 + 2.1584528420869444012e-1261j 4.96e-486, 4.96e-486j
-4.1104034562552220073 - 9.8259971863484315036e-1292j 5.29e-494, 5.29e-494j
4.6241694225337715441 + 1.5643711670505906435e-1289j 5.25e-493, 5.25e-493j
19.174644956486640665 + 9.4068548655794383156e-1291j 5.39e-494, 5.39e-494j
8.8501157234793962164 + 1.8227880309960999015e-1281j 1.27e-486, 1.27e-486j
14.144004173934387912 + 5.5809819353172427093e-1292j 2.33e-486, 2.33e-486j
0.58598752037437278873 - 1.3250030390610495032e-1361j 8.43e-506, 8.43e-506j
-10.613468441602452566 - 3.8512040542384300339e-1341j 1.53e-485, 1.53e-485j
-1.8891758777537106755 - 1.1478218757789230617e-1410j 1.25e-501, 1.25e-501j
4.1104034562552220073 + 6.5128716021499888344e-1393j 5.26e-494, 5.26e-494j
-12.896088504406621733 + 2.957143938849951905e-1402j 1.27e-485, 1.27e-485j
-4.9271768380957203172 - 5.2827916491591832479e-1448j 2.06e-492, 2.06e-492j
-5.238103932311563875 - 5.0365332566508856238e-1449j 7.35e-492, 7.35e-492j
3.6165534267277441896 + 5.694927989663967682e-1451j 1.24e-495, 1.24e-495j
1.8891758777537106755 - 1.8956323676089008528e-1457j 1.33e-501, 1.33e-501j
-3.3242574335521189524 - 1.9139950096286374923e-1452j 1.31e-496, 1.31e-496j
15.03706823713137249 + 7.6212284242417276944e-1440j 3.6e-487, 3.6e-487j
-11.726390337672902605 + 3.2039213756246086565e-1458j 2.29e-485, 2.29e-485j
-13.30196171276169788 + 4.9817425313781538686e-1484j 8.33e-486, 8.33e-486j
1.6208284466610963087 - 1.4435728873087267713e-1519j 1.22e-502, 1.22e-502j
5.5533529315903281928 - 1.8407967893241669241e-1508j 2.95e-491, 2.95e-491j
-10.979079848442242963 + 4.5117216876469063569e-1501j 1.85e-485, 1.85e-485j
10.613468441602452566 + 1.2514563865536201746e-1512j 1.65e-485, 1.65e-485j
8.508288589397451389 + 1.2079810885634338149e-1515j 6.24e-487, 6.24e-487j
7.5004595532644456776 - 4.5187886052408026592e-1517j 4.1e-488, 4.1e-488j
2.4440098084964929991 + 2.1507423093975687738e-1528j 1.14e-499, 1.14e-499j
1.6007107537571947367e-1638 - 4.3033491709079507419e-1638j 5e-1636, 5e-1636j
-8.8501157234793962164 + 6.4936541047342517686e-1514j 1.38e-486, 1.38e-486j
-7.5004595532644456776 - 4.891285550949223843e-1516j 3.96e-488, 3.96e-488j
4.9271768380957203172 - 1.3087836710174867615e-1520j 1.96e-492, 1.96e-492j
0.26949488839787767744 + 4.8612749639099310512e-1536j 1.56e-508, 1.56e-508j
6.1926395185711035801 - 3.877376379377315513e-1518j 3.99e-490, 3.99e-490j
-4.6241694225337715441 - 3.5134728673154235062e-1520j 5.28e-493, 5.28e-493j
-3.8882912091011466435 - 6.7206240484593899499e-1523j 1.11e-494, 1.11e-494j
-2.4440098084964929991 - 2.7239581544045403616e-1527j 1.2e-499, 1.2e-499j
1.3498952853218839149 + 1.9160684730125949627e-1531j 1.07e-503, 1.07e-503j
10.979079848442242963 - 1.1561152107639381374e-1512j 1.96e-485, 1.96e-485j
-1.6208284466610963087 + 9.9444243957585431819e-1531j 1.21e-502, 1.21e-502j
0.77437777109628731486 - 4.9886726406064362291e-1535j 1.39e-505, 1.39e-505j
-3.0280583169855816562 - 2.9515234857794712463e-1525j 1.21e-497, 1.21e-497j
-6.516004104212320361 + 5.6799222959513791286e-1517j 1.44e-489, 1.44e-489j
5.8716927614384833736 - 1.499706479490517621e-1518j 1.15e-490, 1.15e-490j
6.8417366009545604973 - 3.8827460285323118973e-1517j 4.56e-489, 4.56e-489j
-5.5533529315903281928 + 1.9330661008835398762e-1518j 2.82e-491, 2.82e-491j
-0.58598752037437278873 + 1.1618442328680722422e-1533j 7.42e-506, 7.42e-506j
-9.1952137155035619771 - 3.0312215743998626496e-1512j 2.58e-486, 2.58e-486j
3.0280583169855816562 - 1.8101820333922992851e-1527j 1.12e-497, 1.12e-497j
0.61670659019259415219 + 1.8715128785108206523e-1536j 1.31e-505, 1.31e-505j
3.3242574335521189524 + 3.0881733368566770564e-1527j 1.27e-496, 1.27e-496j
-0.61670659019259415219 - 3.1723466275898141382e-1535j 1.23e-505, 1.23e-505j
-0.26949488839787767744 + 6.2923584242586209728e-1538j 1.29e-508, 1.29e-508j
13.30196171276169788 - 1.1808016030327680472e-1517j 8.94e-486, 8.94e-486j
-12.498781993917430931 + 2.5262770507059207716e-1514j 1.73e-485, 1.73e-485j

Weights

Weight (ball center) Error (ball radius)
3.5407467241355467323e-69 + 2.404724585582515255e-1089j 1.42e-133, 4.85e-377j
2.0586788054686071094e-74 - 4.3351698332598385399e-1092j 1.92e-135, 6.56e-379j
1.5862248541011231132e-29 + 7.2240431752282928637e-1066j 9.04e-116, 3.09e-359j
5.0830456086843037333e-57 - 6.2292368301097732781e-1083j 9.71e-130, 3.32e-373j
6.2516858902171505099e-45 + 1.6404106527562890224e-1075j 1.57e-126, 5.35e-370j
1.1390108727929456249e-53 + 3.7571203376667189224e-1081j 1.34e-128, 4.57e-372j
2.0586788054686071094e-74 + 1.8385004543579659762e-1091j 3.36e-139, 1.15e-382j
7.6580482272058961922e-23 + 3.2570122670039115217e-1064j 1.97e-111, 6.73e-355j
7.6580482272058961922e-23 + 4.7601813934467525655e-1063j 1.19e-111, 4.05e-355j
6.3080764052344032463e-15 + 1.0610231697753343861e-1058j 3.51e-102, 1.2e-345j
5.5036145572411113228e-81 - 6.2336161657799466862e-1095j 1.09e-141, 3.71e-385j
1.1390108727929456249e-53 - 2.4265400617808022859e-1080j 3.33e-132, 1.14e-375j
4.3279034522809368108e-16 - 2.2162459056417127914e-1059j 5.58e-105, 1.9e-348j
8.4228259031129369381e-06 - 6.2269685562245950211e-1052j 4.02e-81, 1.37e-324j
3.5407467241355467323e-69 - 1.1032121075333719494e-1088j 7.23e-138, 2.47e-381j
1.15801094172332726e-60 + 7.342041362000983094e-1085j 4.83e-136, 1.65e-379j
4.3279034522809368108e-16 - 3.6110092730839951004e-1060j 5.61e-110, 1.92e-353j
1.2329710731203834271e-37 + 1.6370758861642924447e-1072j 8.33e-128, 2.85e-371j
4.1601076951350064672e-09 + 6.0354599652637692954e-1055j 7.58e-96, 2.59e-339j
1.4647936924541270007e-50 + 1.2248314650132453127e-1078j 5.73e-132, 1.96e-375j
5.1869022405501140412e-05 - 1.4786925547583293929e-1051j 1.83e-83, 6.24e-327j
1.1300080294562919506e-64 - 5.6181804368513033192e-1087j 5.42e-138, 1.85e-381j
2.0922553942157780587e-31 - 4.4782074765305771082e-1069j 1.21e-124, 4.13e-368j
6.0487548821241007748e-10 - 1.5301123651396821874e-1055j 3.01e-99, 1.03e-342j
1.1300080294562919506e-64 + 2.7895452310106591793e-1086j 1.98e-138, 6.76e-382j
1.1748580231361679398e-47 - 4.9308517591513990336e-1077j 2e-131, 6.82e-375j
0.063439758846306761804 - 2.6861739144572596532e-1048j 1.11e-42, 3.81e-286j
2.3269556847279854059e-21 - 2.770290693845461599e-1062j 2.22e-116, 7.57e-360j
1.8751297159709230359e-35 - 2.5762659193750926256e-1071j 6.58e-129, 2.25e-372j
5.0830456086843037333e-57 + 3.6629781577855372063e-1082j 1.2e-135, 4.08e-379j
9.0299722845215045093e-13 + 4.8655087779830373108e-1058j 1.51e-111, 5.17e-355j
2.5895544780693463125e-17 + 4.4368575961340901893e-1060j 5.2e-113, 1.78e-356j
6.0363902547447046877e-20 + 1.6413103416128052922e-1062j 1.66e-119, 5.67e-363j
1.5862248541011231132e-29 + 5.0343517086241243742e-1068j 2.65e-126, 9.07e-370j
1.15801094172332726e-60 - 3.9574536770798530234e-1084j 2.03e-138, 6.94e-382j
0.0027828773424695987115 - 2.0813677494132904661e-1050j 1.26e-83, 4.29e-327j
2.223443477238058041e-33 + 3.591716714440965775e-1070j 3.38e-128, 1.16e-371j
0.010679612363336330258 - 1.1018623914387758111e-1049j 4.08e-77, 1.39e-320j
7.8070296473304200653e-11 + 1.0286330641121850224e-1056j 4.77e-111, 1.63e-354j
8.9295406951524944152e-12 - 9.1974158006731200925e-1057j 7.47e-111, 2.55e-354j
0.0027828773424695987115 - 3.4019996572417624877e-1050j 2.2e-86, 7.51e-330j
2.3145403739715962038e-42 + 4.387969131416891369e-1075j 1.64e-134, 5.61e-378j
1.1748580231361679398e-47 + 6.1476636338046287006e-1078j 3.55e-137, 1.21e-380j
2.3269556847279854059e-21 - 2.3946677584198052488e-1063j 2.3e-122, 7.85e-366j
2.1367354187681663505e-24 - 8.0949030076381462301e-1064j 1.36e-125, 4.64e-369j
0.00016521989295475242442 + 4.6924275352717294534e-1051j 1.04e-97, 3.54e-341j
0.010679612363336330258 - 1.6204922841504004588e-1049j 1.25e-84, 4.27e-328j
6.3080764052344032463e-15 + 1.9448098547817760087e-1059j 7.31e-118, 2.5e-361j
1.377147850660677243e-07 + 3.387272145693454199e-1054j 5.75e-109, 1.97e-352j
0.043961157045965695336 + 1.3817652793335133231e-1048j 2.12e-74, 7.24e-318j
2.223443477238058041e-33 - 1.1097620879189886473e-1068j 9.79e-133, 3.34e-376j
0.063439758846306761804 - 3.2464665455213460943e-1048j 1.26e-70, 4.3e-314j
9.0299722845215045093e-13 + 2.1556801011430364318e-1057j 2.24e-115, 7.66e-359j
8.4228259031129369381e-06 - 2.7809997975461886645e-1052j 3.21e-105, 1.1e-348j
0.10426001608320439349 + 1.8419586141559395296e-1047j 5.1e-72, 1.74e-315j
2.1367354187681663505e-24 - 4.1116578197023818387e-1065j 7.53e-126, 2.57e-369j
2.3145403739715962038e-42 - 4.6458419996709651947e-1074j 1.17e-136, 3.98e-380j
1.7764461320642941298e-05 + 1.7229421306593676135e-1051j 7.83e-104, 2.67e-347j
2.6877828012919228322e-06 + 6.3810024993486646598e-1053j 1.74e-107, 5.96e-351j
5.5036145572411113228e-81 + 1.5979443269050733257e-1095j 2.42e-154, 8.27e-398j
1.3451885200221133996e-18 - 1.0530285800643624032e-1061j 2.19e-122, 7.48e-366j
6.2516858902171505099e-45 - 1.7978783257168516421e-1076j 2.02e-137, 6.91e-381j
0.31121103468609892954 + 1.0236962948901594811e-1046j 1.33e-81, 4.56e-325j
5.0153351852417675238e-26 + 1.4301000263826474186e-1064j 1.84e-129, 6.29e-373j
0.018054050924069682486 + 3.4152411557744630843e-1049j 1.9e-92, 6.48e-336j
1.7764461320642941298e-05 + 8.067904890716899207e-1052j 1.63e-107, 5.58e-351j
1.2329710731203834271e-37 - 2.5671055054974717555e-1071j 1.78e-136, 6.08e-380j
6.5716686791458615231e-07 - 3.6602607810678234602e-1053j 1.22e-112, 4.18e-356j
1.377147850660677243e-07 + 9.1933913643747219197e-1054j 6.96e-114, 2.38e-357j
0.00016521989295475242442 + 2.4246324780420771042e-1051j 5.97e-108, 2.04e-351j
0.018054050924069682486 + 2.4405514683595830316e-1049j 8.43e-98, 2.88e-341j
0.0004698881717357316137 - 8.2513834799714678286e-1051j 3.38e-106, 1.16e-349j
1.4647936924541270007e-50 - 1.7115159038199509239e-1079j 2.17e-142, 7.4e-386j
2.0922553942157780587e-31 + 2.74477261526523275e-1067j 7.35e-134, 2.51e-377j
6.190383308809421402e-40 + 1.1510257874396199496e-1072j 3.77e-138, 1.29e-381j
0.028800444992622077365 - 5.140131765136620069e-1049j 1.85e-99, 6.3e-343j
2.5414924145064968385e-08 - 8.0724826517247983232e-1055j 2.83e-119, 9.67e-363j
9.8162919472633168796e-28 - 3.094850444032457373e-1065j 7.54e-132, 2.58e-375j
5.0153351852417675238e-26 + 4.7950705119068245695e-1066j 2.77e-132, 9.47e-376j
2.5895544780693463125e-17 + 6.3489137948959512118e-1061j 6.66e-127, 2.27e-370j
8.0508479538866723215e-14 - 9.9569010574576801601e-1059j 4.93e-125, 1.68e-368j
0.0057583938021478296133 + 4.7873204239095425906e-1050j 2.24e-109, 7.66e-353j
0.10656767488670411119 + 8.933159658537990071e-1048j 2.38e-101, 8.14e-345j
1.3451885200221133996e-18 - 8.5092372425609883264e-1061j 1.87e-129, 6.38e-373j
8.0508479538866723215e-14 - 4.8758124324550902053e-1058j 5.85e-126, 2e-369j
6.5716686791458615231e-07 - 1.4442902145340573961e-1053j 2.62e-119, 8.96e-363j
0.1056270306491162206 - 1.0105662268789134247e-1047j 4.98e-105, 1.7e-348j
6.0487548821241007748e-10 - 4.4983104136379591359e-1056j 1.68e-123, 5.74e-367j
2.6877828012919228322e-06 + 1.5155327821554455293e-1052j 6.72e-120, 2.29e-363j
5.1869022405501140412e-05 - 3.0198062728250642514e-1051j 7.18e-118, 2.45e-361j
0.0057583938021478296133 + 7.4148554653709528851e-1050j 1.43e-114, 4.88e-358j
0.043961157045965695336 + 1.088022010773853201e-1048j 1.05e-110, 3.57e-354j
9.8162919472633168796e-28 - 5.1395404657003898922e-1067j 5.51e-136, 1.88e-379j
0.028800444992622077365 - 6.852788320689357406e-1049j 1.73e-112, 5.91e-356j
0.10426001608320439349 + 1.6066666097423167362e-1047j 1.6e-110, 5.46e-354j
0.0012053508836907283151 + 1.6194243780836446567e-1050j 1.27e-116, 4.35e-360j
7.8070296473304200653e-11 + 3.8017954314066690349e-1056j 8.59e-126, 2.93e-369j
4.1601076951350064672e-09 + 1.9198842887804996313e-1055j 7.18e-125, 2.45e-368j
8.9295406951524944152e-12 - 2.2792558573511769863e-1057j 5.36e-127, 1.83e-370j
2.5414924145064968385e-08 - 2.354010868052670032e-1054j 3e-124, 1.02e-367j
0.31121103468609892954 + 1.1351564595623031528e-1046j 1.99e-115, 6.8e-359j
6.0363902547447046877e-20 + 1.5650086662736693608e-1061j 6.32e-133, 2.16e-376j
0.0012053508836907283151 + 9.3730884299116221883e-1051j 3.22e-121, 1.1e-364j
-0.2497802423690517562 - 1.1080223263030306028e-1046j 6.56e-116, 2.24e-359j
0.0004698881717357316137 - 4.5128739353719491307e-1051j 1.15e-121, 3.92e-365j
-0.2497802423690517562 - 1.2353516657790684439e-1046j 5.41e-117, 1.85e-360j
0.1056270306491162206 - 1.0597237512484618952e-1047j 5.63e-118, 1.92e-361j
6.190383308809421402e-40 - 9.1144595486299694223e-1074j 9.6e-146, 3.3e-389j
1.8751297159709230359e-35 + 5.3478136931035308424e-1070j 2.3e-143, 7.8e-387j

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