Rule: Q[4, 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.

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)
-16.973395399251414784 - 4.2714974121635332251e-1349j 3.83e-490, 3.83e-490j
15.404549522042985075 + 7.9625150639726044872e-1353j 6.32e-488, 6.32e-488j
-18.254933829521502531 + 6.2743809872016966546e-1354j 2.04e-492, 2.04e-492j
-14.477533209858567553 + 1.1489512794987246813e-1360j 5.96e-487, 5.96e-487j
16.418361529912424721 - 8.001536394096581436e-1382j 2.72e-489, 2.72e-489j
-17.576801360982593985 - 1.711887242178968689e-1378j 3.82e-491, 3.82e-491j
-15.404549522042985075 - 2.6708414415966126759e-1380j 5.97e-488, 5.97e-488j
19.076817836604987933 - 2.239324984886729296e-1400j 3.87e-494, 3.87e-494j
-4.2283965787258560516 + 5.9487611832954683799e-1401j 2.41e-493, 2.41e-493j
12.787237740521458813 + 1.1996725588815675575e-1390j 7.57e-486, 7.57e-486j
2.0493320500924562865 - 2.6671790076348185345e-1427j 3.83e-501, 3.83e-501j
-14.93227336475382485 - 7.4273483849238474448e-1412j 2.05e-487, 2.05e-487j
-15.898125691645699128 + 2.9522123217823322353e-1449j 1.53e-488, 1.53e-488j
-5.4228479113280690393 - 7.4683699184397851518e-1480j 1.41e-491, 1.41e-491j
-14.037558604811035728 - 6.1322026010207256907e-1474j 1.51e-486, 1.51e-486j
5.4228479113280690393 + 1.4985533787278898188e-1503j 1.4e-491, 1.4e-491j
-11.61517083364378436 + 8.2748709382009299955e-1496j 1.41e-485, 1.41e-485j
13.193906366370480655 + 2.2882535851401314232e-1508j 5.04e-486, 5.04e-486j
-1.5122552015009576337 - 3.2146491691698806149e-1534j 4.29e-503, 4.29e-503j
4.1385044402334930265 + 2.2494545757878623403e-1523j 1.34e-493, 1.34e-493j
-19.076817836604987933 + 1.2019089237030435289e-1518j 3.92e-494, 3.92e-494j
15.898125691645699128 + 3.3838568663256022086e-1517j 1.59e-488, 1.59e-488j
-13.610235936105720552 - 1.8753357986442617264e-1515j 2.91e-486, 2.91e-486j
-4.1385044402334930265 + 4.1614651734805756934e-1536j 1.46e-493, 1.46e-493j
18.254933829521502531 + 3.240306038948622365e-1535j 1.94e-492, 1.94e-492j
-16.418361529912424721 + 7.3212403790052564085e-1528j 2.77e-489, 2.77e-489j
1.775054015089716543 - 4.3459508538785203241e-1548j 4.38e-502, 4.38e-502j
9.0783779226529685322 - 7.8374022769764944698e-1532j 1.41e-486, 1.41e-486j
8.0500944905667764781 - 3.1436022518530921995e-1535j 1.37e-487, 1.37e-487j
-0.99948116724046459996 - 2.3576509049678922056e-1551j 3.24e-505, 3.24e-505j
3.8419528316907646175 + 2.6248010206248441366e-1540j 5.38e-495, 5.38e-495j
16.973395399251414784 - 3.5732073451953996963e-1536j 3.93e-490, 3.93e-490j
-10.138240569288621423 - 7.1966130431031725453e-1530j 6.43e-486, 6.43e-486j
14.037558604811035728 - 3.426463471783062882e-1539j 1.5e-486, 1.5e-486j
-7.3791316332603838679 + 8.4305950386016372444e-1543j 1.92e-488, 1.92e-488j
5.743579415689258763 + 5.6459352692795360319e-1546j 5.28e-491, 5.28e-491j
9.4278080593138556525 + 5.3057977423633325392e-1540j 2.65e-486, 2.65e-486j
12.389139733536447357 + 3.7556309287785913523e-1539j 1.06e-485, 1.06e-485j
2.9262379512396638103 - 9.1842872733547647185e-1564j 4.02e-498, 4.02e-498j
5.1041982567043265212 - 1.0016783568265950727e-1557j 3.53e-492, 3.53e-492j
-12.389139733536447357 - 5.2108843048010472979e-1549j 1.06e-485, 1.06e-485j
-6.3912143673685029419 + 7.3053684529400546514e-1567j 6.77e-490, 6.77e-490j
1.2559878171048571126 + 4.510998516307293893e-1582j 3.85e-504, 3.85e-504j
6.0663562390472352644 + 7.6483734860119914518e-1568j 2.12e-490, 2.12e-490j
1.5122552015009576337 - 3.2562775172344708584e-1581j 4.31e-503, 4.31e-503j
17.576801360982593985 + 3.5832160087365901992e-1569j 3.49e-491, 3.49e-491j
-11.237883435806211397 + 1.4785676152711040768e-1561j 1.37e-485, 1.37e-485j
-8.3897491246808042529 - 2.489799520509063257e-1571j 3.11e-487, 3.11e-487j
2.6275083508278204383 - 4.0798764135898325666e-1593j 3.72e-499, 3.72e-499j
-5.743579415689258763 + 5.9688177418663284273e-1584j 5.34e-491, 5.34e-491j
-3.2290040429144049805 - 2.5258470672133404792e-1590j 3.92e-497, 3.92e-497j
-1.2559878171048571126 - 3.7681439750050005053e-1597j 3.76e-504, 3.76e-504j
-7.7132801351214343748 + 1.1900280003203923511e-1578j 5.25e-488, 5.25e-488j
14.477533209858567553 - 1.0962091902291280026e-1581j 6.05e-487, 6.05e-487j
6.7182271371684016184 - 3.3927916440509443999e-1584j 2.17e-489, 2.17e-489j
-4.475457575362856296 - 6.9279383149491127797e-1588j 3.74e-493, 3.74e-493j
-2.6275083508278204383 - 1.2099881111396521663e-1593j 3.96e-499, 3.96e-499j
14.93227336475382485 - 6.427632950330212263e-1582j 2.02e-487, 2.02e-487j
13.610235936105720552 - 4.0770676918868876967e-1580j 3.04e-486, 3.04e-486j
0.99948116724046459996 + 1.0244848769922209878e-1599j 3.41e-505, 3.41e-505j
7.047493189352069405 + 1.6241251313400071303e-1583j 6.46e-489, 6.46e-489j
11.237883435806211397 + 3.009999910569332622e-1579j 1.33e-485, 1.33e-485j
-0.74196378430272585765 + 2.0726329366711069334e-1601j 2.22e-506, 2.22e-506j
11.998705579561558604 - 3.9899398559146082699e-1579j 1.27e-485, 1.27e-485j
4.2283965787258560516 - 2.2636848714251834308e-1600j 2.34e-493, 2.34e-493j
-9.4278080593138556525 - 9.5844744230713542878e-1592j 2.49e-486, 2.49e-486j
9.780996058089989437 + 2.0104073488757515825e-1607j 4.33e-486, 4.33e-486j
-8.7324382950217081707 - 1.3619487576312657763e-1625j 6.81e-487, 6.81e-487j
-11.998705579561558604 + 1.0884263789720486635e-1661j 1.27e-485, 1.27e-485j
10.499876543839432752 + 1.61701114565172004e-1687j 9.51e-486, 9.51e-486j
4.787881219930387608 - 6.0944478823253640811e-1728j 9.48e-493, 9.48e-493j
-10.86628150292416487 - 1.2734258183838389033e-1719j 1.15e-485, 1.15e-485j
-13.193906366370480655 + 5.4696606756284073773e-1746j 4.77e-486, 4.77e-486j
-2.9262379512396638103 - 4.7128962557816956215e-1776j 3.88e-498, 3.88e-498j
8.7324382950217081707 + 2.1648658359473954896e-1765j 6.53e-487, 6.53e-487j
0.48768053669359689844 - 4.5816345065979154709e-1785j 1.39e-507, 1.39e-507j
0.74196378430272585765 - 4.92692728020107068e-1784j 2.04e-506, 2.04e-506j
-3.8419528316907646175 + 5.5215032968800511882e-1773j 5.51e-495, 5.51e-495j
-10.499876543839432752 - 2.4146794091265695439e-1762j 9.11e-486, 9.11e-486j
10.86628150292416487 + 7.4974715997213620336e-1770j 1.19e-485, 1.19e-485j
-7.047493189352069405 + 9.8616536080888507132e-1777j 7.04e-489, 7.04e-489j
2.3344142183389772393 - 5.5066631879488928425e-1789j 3.66e-500, 3.66e-500j
11.61517083364378436 + 5.9703611370711596416e-1772j 1.38e-485, 1.38e-485j
-5.1041982567043265212 + 4.45738060480609712e-1787j 3.9e-492, 3.9e-492j
-2.0493320500924562865 + 2.8372156450776159848e-1796j 3.91e-501, 3.91e-501j
-3.5346855695979391126 - 3.7931234149784698608e-1790j 4.29e-496, 4.29e-496j
3.2290040429144049805 + 4.2108037339157726402e-1791j 4.05e-497, 4.05e-497j
7.3791316332603838679 + 4.9604594410735644864e-1782j 1.9e-488, 1.9e-488j
-6.7182271371684016184 + 7.175646383398569311e-1781j 2.09e-489, 2.09e-489j
-1.775054015089716543 + 9.2834096524435882201e-1797j 4.07e-502, 4.07e-502j
10.138240569288621423 - 5.4766116379074926868e-1779j 6.8e-486, 6.8e-486j
4.475457575362856296 + 3.5174568310617938906e-1798j 3.95e-493, 3.95e-493j
3.5346855695979391126 + 1.983503435423282733e-1799j 4.57e-496, 4.57e-496j
-9.0783779226529685322 + 4.7827400544090639803e-1788j 1.36e-486, 1.36e-486j
-6.0663562390472352644 + 5.9624094191630491503e-1810j 1.97e-490, 1.97e-490j
-4.787881219930387608 + 1.0561490105732056594e-1813j 9.68e-493, 9.68e-493j
6.3912143673685029419 + 1.6157167558710220801e-1810j 6.85e-490, 6.85e-490j
-2.3344142183389772393 + 3.8650934899645230572e-1821j 3.98e-500, 3.98e-500j
8.3897491246808042529 + 4.1342174382029231037e-1807j 3.13e-487, 3.13e-487j
-0.24058448046302122344 + 8.6365425418164467979e-1835j 8.03e-509, 8.03e-509j
-2.4592750544622877266e-1876 + 8.846709546198345052e-1876j 9.82e-1874, 9.82e-1874j
-12.787237740521458813 + 3.5002694788401957841e-1810j 7.75e-486, 7.75e-486j
7.7132801351214343748 - 2.9706233207627698275e-1825j 5.35e-488, 5.35e-488j
0.24058448046302122344 - 1.0556262274002063275e-1896j 1.02e-508, 1.02e-508j
-8.0500944905667764781 + 2.7141421936266258471e-1822j 1.31e-487, 1.31e-487j
-0.48768053669359689844 - 5.7676373344281217437e-1850j 1.39e-507, 1.39e-507j
-9.780996058089989437 + 1.1842225128312079678e-1826j 4.58e-486, 4.58e-486j

Weights

Weight (ball center) Error (ball radius)
6.3424472924037727192e-64 - 2.1398375873961833238e-1411j 4.53e-134, 9.45e-375j
5.6892938154513240558e-53 - 3.6701255120788618409e-1404j 3.91e-131, 8.15e-372j
1.2655984017346415051e-73 + 4.1502622720787675075e-1417j 9.02e-138, 1.88e-378j
5.4618522823554293744e-47 - 1.326090720805225317e-1403j 4.33e-128, 9.02e-369j
6.2411364773694834267e-60 + 1.0006197207252607143e-1408j 1.07e-135, 2.22e-376j
2.0753013561878539835e-68 - 3.239393811251622736e-1414j 4.43e-136, 9.25e-377j
5.6892938154513240558e-53 - 5.3169248636711439573e-1407j 5.1e-131, 1.06e-371j
3.5801125201743218914e-80 + 8.3639998648288441447e-1420j 1.27e-144, 2.66e-385j
3.9725984757488008709e-06 + 6.4261447439801395624e-1378j 5.59e-80, 1.17e-320j
4.9989384734163383009e-37 - 5.1385903231667845946e-1397j 3.59e-127, 7.49e-368j
0.013685669157889135161 + 2.7857954558575715419e-1376j 6.19e-51, 1.29e-291j
7.0557744186878641711e-50 + 3.2964804474490623541e-1405j 6.37e-130, 1.33e-370j
2.635524576620035909e-56 + 1.3689441323617016045e-1409j 9.53e-133, 1.99e-373j
5.2474888510921980645e-08 + 7.7697238498860418588e-1381j 1.23e-93, 2.56e-334j
2.8068024652545031421e-44 + 4.0876617109331655078e-1402j 1.27e-128, 2.66e-369j
5.2474888510921980645e-08 + 1.6972660524912311341e-1380j 4.97e-97, 1.04e-337j
7.6778186007238940471e-31 + 9.4588240139032370782e-1395j 8.03e-124, 1.67e-364j
2.5957199838445905781e-39 + 3.6073904649518754118e-1398j 5.52e-132, 1.15e-372j
0.032834902011675526701 + 7.4478859795790361917e-1376j 3.34e-48, 6.98e-289j
1.9138852459833852433e-05 - 1.4252330792625834447e-1377j 2.05e-87, 4.27e-328j
3.5801125201743218914e-80 - 1.3612526758573882325e-1420j 7.07e-144, 1.48e-384j
2.635524576620035909e-56 - 1.6273219393382793837e-1406j 1.78e-139, 3.71e-380j
1.0040522570313242429e-41 - 1.0154109694425683709e-1400j 1.23e-128, 2.57e-369j
1.9138852459833852433e-05 - 7.9470235036378904259e-1378j 8.38e-88, 1.75e-328j
1.2655984017346415051e-73 - 2.6499171890971221858e-1416j 6.83e-147, 1.42e-387j
6.2411364773694834267e-60 + 2.753539645796512718e-1410j 4.49e-135, 9.37e-376j
0.022143987559460078548 - 5.2793003524023131518e-1376j 2.41e-61, 5.02e-302j
1.7596683924535270716e-19 - 1.1178998410786482492e-1387j 4.51e-121, 9.4e-362j
1.1430734763589340536e-15 + 1.7235961689872007893e-1385j 8.12e-117, 1.69e-357j
0.062335518201361008122 + 1.7481677349492151604e-1375j 1.73e-59, 3.61e-300j
7.6368110095523807815e-05 + 8.7651414840653486361e-1378j 3.16e-90, 6.59e-331j
6.3424472924037727192e-64 - 5.3173923499353269142e-1411j 1.47e-143, 3.06e-384j
6.8741698954818802727e-24 + 7.4798550113378395528e-1391j 1.09e-124, 2.28e-365j
2.8068024652545031421e-44 + 1.3059363927690684334e-1400j 2.33e-136, 4.86e-377j
1.9914632088913184136e-13 + 1.2447309763908187339e-1384j 3.3e-115, 6.88e-356j
8.8110085445006012435e-09 - 4.3621075574518177121e-1381j 1.9e-106, 3.97e-347j
7.0100389889135773349e-21 + 1.8458848346501452462e-1388j 2.05e-123, 4.27e-364j
7.3527060965467908408e-35 + 6.5905990244983044816e-1396j 3.06e-132, 6.37e-373j
0.0016596534801504642878 - 3.7480302340586416927e-1377j 4.67e-87, 9.74e-328j
2.7889020013586291794e-07 - 6.7927855103281016491e-1380j 4.27e-103, 8.9e-344j
7.3527060965467908408e-35 + 5.758656740239630289e-1397j 2.83e-132, 5.9e-373j
1.7541795217379253897e-10 - 1.1067606620785461783e-1382j 1.57e-113, 3.27e-354j
0.046338225454857423664 - 1.4220385319173783003e-1375j 1e-66, 2.09e-307j
1.3183527621384841371e-09 + 1.1207118742051270177e-1381j 9.93e-110, 2.07e-350j
0.032834902011675526701 + 9.1742142499400392867e-1376j 3.69e-72, 7.7e-313j
2.0753013561878539835e-68 + 1.7741940731148041785e-1413j 9.35e-147, 1.95e-387j
5.6320492855764147843e-29 - 1.0281055136044417151e-1393j 8.07e-130, 1.68e-370j
7.0681166551963211288e-17 - 9.2131651511036464836e-1387j 1.01e-122, 2.12e-363j
0.0037446250540343988376 + 7.2070858022267192094e-1377j 2.79e-89, 5.82e-330j
8.8110085445006012435e-09 - 1.8968593636059332482e-1381j 8.39e-112, 1.75e-352j
0.00066109659742917311446 + 1.2973269862954872236e-1377j 3.03e-98, 6.32e-339j
0.046338225454857423664 - 1.1961894197775068554e-1375j 1.45e-75, 3.03e-316j
1.6122600079612296661e-14 - 2.5569868686511540771e-1385j 5.15e-120, 1.07e-360j
5.4618522823554293744e-47 - 7.0193854672081159218e-1402j 9.57e-141, 2e-381j
2.0705975402264147567e-11 + 6.9704742048362683246e-1383j 2.42e-118, 5.04e-359j
5.4992911412984073286e-06 - 9.2298802738216894611e-1379j 4.75e-107, 9.9e-348j
0.0037446250540343988376 + 5.0040324027153849721e-1377j 3.44e-96, 7.18e-337j
7.0557744186878641711e-50 + 4.0919060249759539762e-1403j 5.67e-142, 1.18e-382j
1.0040522570313242429e-41 - 2.2790573344366559237e-1399j 8.08e-139, 1.68e-379j
0.062335518201361008122 + 2.0058643680580208918e-1375j 3.61e-83, 7.54e-324j
2.1622394898330236742e-12 - 1.6577715102574392088e-1383j 1.73e-121, 3.61e-362j
5.6320492855764147843e-29 - 7.7073600516032709071e-1393j 1.01e-135, 2.1e-376j
0.077780925525534640723 - 2.4181054706579191378e-1375j 2e-85, 4.18e-326j
8.4336368201324822925e-33 - 7.6376008994944488753e-1395j 1.14e-136, 2.37e-377j
3.9725984757488008709e-06 + 1.1680520611209401189e-1377j 4.69e-110, 9.78e-351j
7.0100389889135773349e-21 + 3.9964273816004509971e-1389j 1.33e-133, 2.77e-374j
2.3840838777671737191e-22 - 2.8510783526449781867e-1389j 2.66e-132, 5.54e-373j
3.7944659308575067985e-18 + 1.6029675384644636223e-1387j 2.36e-131, 4.92e-372j
8.4336368201324822925e-33 - 7.8206833510934074002e-1396j 5.5e-140, 1.15e-380j
1.6673845806266408794e-25 - 5.4843373563714162507e-1391j 1.94e-135, 4.04e-376j
1.3220760208934673584e-06 + 2.9767300637399711005e-1379j 1.75e-116, 3.65e-357j
3.3725423171185040232e-27 + 1.0120815197687663365e-1392j 1.15e-137, 2.4e-378j
2.5957199838445905781e-39 + 2.1066538940088041322e-1399j 1.14e-143, 2.38e-384j
0.0016596534801504642878 - 2.4939493869135050466e-1377j 2.78e-113, 5.8e-354j
3.7944659308575067985e-18 + 6.3556162140886076791e-1387j 4.5e-132, 9.39e-373j
0.08893933240630260196 + 3.4257806494858693702e-1375j 1.41e-99, 2.94e-340j
0.077780925525534640723 - 2.6777909494585345851e-1375j 8.76e-100, 1.83e-340j
7.6368110095523807815e-05 + 5.1069608751155364013e-1378j 9.9e-118, 2.07e-358j
1.6673845806266408794e-25 - 9.0845449000732653846e-1392j 4.25e-137, 8.85e-378j
3.3725423171185040232e-27 + 6.7761201656619400058e-1392j 1.75e-137, 3.66e-378j
2.1622394898330236742e-12 - 5.7818308003441963885e-1384j 5.88e-130, 1.23e-370j
0.0075735078760643029586 - 1.4169317983392319489e-1376j 2.7e-112, 5.64e-353j
7.6778186007238940471e-31 + 8.0337672868334314617e-1394j 3.56e-139, 7.42e-380j
2.7889020013586291794e-07 - 3.2694480065757607381e-1380j 1.76e-124, 3.67e-365j
0.013685669157889135161 + 2.0984340737556388599e-1376j 2.66e-114, 5.55e-355j
0.00023697831399886534006 - 7.3426908497910234778e-1378j 4.99e-119, 1.04e-359j
0.00066109659742917311446 + 2.0363311277153392722e-1377j 1.57e-118, 3.28e-359j
1.9914632088913184136e-13 + 3.7885605486156683401e-1384j 4.95e-131, 1.03e-371j
2.0705975402264147567e-11 + 2.5755170408042855569e-1383j 6.72e-130, 1.4e-370j
0.022143987559460078548 - 4.1320460816911575828e-1376j 5.19e-115, 1.08e-355j
6.8741698954818802727e-24 + 4.104019629238736923e-1390j 1.48e-136, 3.08e-377j
5.4992911412984073286e-06 - 1.741195985744437254e-1378j 1.65e-122, 3.45e-363j
0.00023697831399886534006 - 1.2047603130254562538e-1377j 1.59e-120, 3.33e-361j
1.7596683924535270716e-19 - 2.6177689498292950112e-1388j 8.15e-137, 1.7e-377j
1.3183527621384841371e-09 + 4.6230017196738191439e-1382j 4.28e-129, 8.92e-370j
1.3220760208934673584e-06 + 1.5045883616614972869e-1379j 8.78e-126, 1.83e-366j
1.7541795217379253897e-10 - 2.8325692117412768593e-1382j 9.41e-130, 1.96e-370j
0.0075735078760643029586 - 1.025424309026273278e-1376j 5.69e-122, 1.19e-362j
7.0681166551963211288e-17 - 3.404031149502390808e-1386j 8.06e-135, 1.68e-375j
0.094244821680817899891 - 3.9464570311294764416e-1375j 2.36e-120, 4.95e-361j
0.095428228118557150427 + 4.3097358036356903764e-1375j 2.8e-120, 5.86e-361j
4.9989384734163383009e-37 - 3.7356169656104887378e-1398j 2.46e-147, 5.16e-388j
1.6122600079612296661e-14 - 8.2803005805574412437e-1385j 1.39e-133, 2.9e-374j
0.094244821680817899891 - 4.0790726507171904958e-1375j 2.85e-123, 4.9e-364j
1.1430734763589340536e-15 + 4.990014947467050504e-1386j 1.18e-135, 2.44e-376j
0.08893933240630260196 + 3.2037226141175438625e-1375j 9.17e-124, 1.21e-364j
2.3840838777671737191e-22 - 5.679508883958230518e-1390j 1.17e-139, 2.47e-380j

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