Rule: Q[4, 9, 96]

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.

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)
-13.068404038136362584 + 5.0521704984777022679e-1382j 3.37e-492, 3.37e-492j
13.646956727986975951 - 1.4571772945581057781e-1384j 6.66e-494, 6.66e-494j
-8.9431803256739132964 - 2.6842633768866225702e-1374j 2.55e-485, 2.55e-485j
9.5086610378667984208 - 7.4231713143751206667e-1380j 1.12e-485, 1.12e-485j
-10.101653142605637749 - 1.4574604228369952031e-1378j 3.19e-486, 3.19e-486j
8.399517762004700005 + 6.0695537439139037366e-1386j 3.47e-485, 3.47e-485j
-11.41003110471815541 - 2.4475424070662009765e-1385j 2.97e-488, 2.97e-488j
-1.8597311085150166242 + 9.8292940877336943735e-1400j 3.26e-499, 3.26e-499j
-5.1951535449400162797 + 3.4533764861024532933e-1388j 2.97e-488, 2.97e-488j
4.5078764647525252421 - 6.7640742180376241774e-1390j 9.3e-490, 9.3e-490j
1.4460573018415706963 + 1.9761971044881230199e-1401j 2.97e-501, 2.97e-501j
12.591128975788745829 - 9.3965896904144651791e-1392j 6.24e-491, 6.24e-491j
10.410977008890801432 + 7.5798897689158544756e-1388j 1.26e-486, 1.26e-486j
11.41003110471815541 - 3.4151877895092094552e-1389j 3.02e-488, 3.02e-488j
-9.5086610378667984208 + 9.1516195179604110224e-1385j 1.17e-485, 1.17e-485j
-11.062864890738428579 - 1.0588236120128108485e-1394j 1.42e-487, 1.42e-487j
-12.166516521504373134 + 4.9843285625650364041e-1401j 7.52e-490, 7.52e-490j
-9.8012705049746591412 - 1.8100603407311194773e-1411j 6.69e-486, 6.69e-486j
-1.4460573018415706963 + 3.2469991233452960807e-1444j 2.81e-501, 2.81e-501j
9.8012705049746591412 + 1.4712430400109609004e-1428j 6.26e-486, 6.26e-486j
3.3950761742063986469 - 7.7558103525272806045e-1435j 1.09e-492, 1.09e-492j
4.7353888196157009852 + 4.0633835826442364759e-1432j 3.43e-489, 3.43e-489j
10.730730540994347892 - 7.9883330202276610906e-1432j 4.4e-487, 4.4e-487j
5.427551593035843152 + 1.1426465932901886688e-1430j 8.61e-488, 8.61e-488j
-12.591128975788745829 - 1.8473068850482822841e-1427j 6.38e-491, 6.38e-491j
-8.1345648919132201076 + 8.8747407791872676693e-1439j 3.47e-485, 3.47e-485j
1.8597311085150166242 - 1.0886740294355448265e-1472j 3.23e-499, 3.23e-499j
-11.776004215062928905 - 5.7867041042443688987e-1459j 5.43e-489, 5.43e-489j
8.6689032978387307126 - 1.0157712088832175075e-1473j 3.01e-485, 3.01e-485j
-0.71755046263783293307 - 6.0360651382211686546e-1494j 2.3e-505, 2.3e-505j
-9.2228868272158330214 + 2.9329510529859628747e-1473j 1.86e-485, 1.86e-485j
-7.1118958771970721814 + 1.0216283452129437851e-1493j 1.37e-485, 1.37e-485j
4.281883418172708875 - 8.3307284807041818741e-1513j 2.61e-490, 2.61e-490j
11.776004215062928905 - 5.1112598987497025746e-1512j 5.42e-489, 5.42e-489j
-3.8345325314433831864 + 2.1576681517516986757e-1513j 1.93e-491, 1.93e-491j
2.494412424107170401 + 5.3438447970550878777e-1518j 4.75e-496, 4.75e-496j
4.9644598589149830822 + 1.7703159222662560007e-1510j 1.02e-488, 1.02e-488j
-5.6617503799029343685 + 6.6278474641648084541e-1507j 2.18e-487, 2.18e-487j
6.3763170792933649346 - 4.3593016884268831749e-1512j 2.57e-486, 2.57e-486j
9.2228868272158330214 + 1.3651613262305555154e-1511j 1.7e-485, 1.7e-485j
8.9431803256739132964 + 6.3828388893693286052e-1511j 2.37e-485, 2.37e-485j
7.1118958771970721814 + 1.4947828976290884255e-1511j 1.29e-485, 1.29e-485j
2.9899278943630500681 + 1.7524509485747890062e-1519j 1.12e-493, 1.12e-493j
-8.6689032978387307126 + 2.1581214290355195419e-1510j 3.26e-485, 3.26e-485j
6.8640847647154596363 - 1.0736831781515239521e-1524j 8.48e-486, 8.48e-486j
-1.2502344977390780677 - 4.9118309738751423607e-1542j 3.12e-502, 3.12e-502j
12.166516521504373134 + 1.4294246848595511112e-1530j 7.12e-490, 7.12e-490j
3.1820635469234418643 - 6.8197836463884925783e-1533j 3.04e-493, 3.04e-493j
5.8978597505550353874 - 6.7590193050250322261e-1526j 5.13e-487, 5.13e-487j
7.6164275015747542106 - 3.8664158694949427531e-1524j 2.63e-485, 2.63e-485j
-13.646956727986975951 - 2.1391826655496564027e-1533j 5.69e-494, 5.69e-494j
13.068404038136362584 - 4.0052588439917295986e-1532j 3.11e-492, 3.11e-492j
-3.1820635469234418643 - 3.5977130598162605738e-1534j 2.91e-493, 2.91e-493j
-10.730730540994347892 + 3.0628332422142108213e-1524j 4.43e-487, 4.43e-487j
11.062864890738428579 + 1.5042982806107927208e-1540j 1.27e-487, 1.27e-487j
-6.8640847647154596363 + 8.3302638279690860894e-1537j 8.2e-486, 8.2e-486j
-1.0693259078659559849 + 6.0007401251869670045e-1574j 3.56e-503, 3.56e-503j
-2.9899278943630500681 + 5.1170689253505740529e-1565j 1.05e-493, 1.05e-493j
-6.1360029167605153531 + 2.433673046601071309e-1555j 1.16e-486, 1.16e-486j
-2.0710493012196380732 - 2.2352293233553071062e-1591j 3.41e-498, 3.41e-498j
-7.8736493604189602801 - 4.5048312310297128979e-1576j 3.25e-485, 3.25e-485j
3.8345325314433831864 - 1.0770191973524452857e-1604j 1.83e-491, 1.83e-491j
-2.6976766507548633885 + 6.8384554192376460032e-1608j 6.04e-495, 6.04e-495j
-4.9644598589149830822 + 3.0971359408987071239e-1598j 1.07e-488, 1.07e-488j
2.6976766507548633885 + 3.5796950351617186602e-1609j 5.62e-495, 5.62e-495j
7.8736493604189602801 + 3.9344717486890606122e-1599j 3.1e-485, 3.1e-485j
-8.399517762004700005 + 2.0371432435899662119e-1597j 3.54e-485, 3.54e-485j
0.89811287352165339047 + 4.765743709406057636e-1635j 3.38e-504, 3.38e-504j
-2.8580170695898428779 + 1.5965112431185562747e-1624j 3.67e-494, 3.67e-494j
-4.0574100286463131221 + 8.383461797371573987e-1621j 6.61e-491, 6.61e-491j
8.1345648919132201076 + 2.232204244484980621e-1616j 3.46e-485, 3.46e-485j
5.6617503799029343685 + 3.730961535174597211e-1619j 2.27e-487, 2.27e-487j
-2.494412424107170401 + 4.5009245050107339174e-1627j 5.03e-496, 5.03e-496j
-1.6506801238857845559 - 1.0943129015194008466e-1631j 2.9e-500, 2.9e-500j
-4.5078764647525252421 + 6.5576233631490956791e-1616j 9.73e-490, 9.73e-490j
6.6189546131776045999 + 1.7374204808767858351e-1626j 4.61e-486, 4.61e-486j
5.1951535449400162797 + 2.6355596573498882746e-1629j 3.12e-488, 3.12e-488j
6.1360029167605153531 - 6.1616232827933488589e-1628j 1.23e-486, 1.23e-486j
-5.8978597505550353874 + 2.8769532942120755865e-1625j 5.05e-487, 5.05e-487j
-10.410977008890801432 + 3.6393154547460276311e-1680j 1.22e-486, 1.22e-486j
3.6135018706346676917 + 2.4083097677717774721e-1730j 4.29e-492, 4.29e-492j
0.71755046263783293307 - 3.066673275781517747e-1757j 2.68e-505, 2.68e-505j
-6.6189546131776045999 + 2.9155713803136982563e-1736j 4.53e-486, 4.53e-486j
10.101653142605637749 + 2.1746949632258128727e-1769j 3.19e-486, 3.19e-486j
-4.7353888196157009852 + 4.7527708379872517001e-1771j 3.36e-489, 3.36e-489j
1.0693259078659559849 + 6.4462340030234582759e-1805j 3.7e-503, 3.7e-503j
4.0574100286463131221 + 3.4991008698141095428e-1793j 7.26e-491, 7.26e-491j
2.2832506552235534748 + 3.8343239334593305957e-1799j 3.9e-497, 3.9e-497j
2.0710493012196380732 - 1.8983112278665494871e-1799j 3.29e-498, 3.29e-498j
-0.32791032691154391444 - 1.4679811010554748845e-1809j 6.77e-508, 6.77e-508j
-3.6135018706346676917 - 5.3871811217054124498e-1786j 4.39e-492, 4.39e-492j
-7.3625982144413169604 + 3.2307589848729740127e-1805j 1.99e-485, 1.99e-485j
0.32791032691154391444 - 6.7174987369643500535e-1860j 6.26e-508, 6.26e-508j
-6.3763170792933649346 + 8.1222523063944654206e-1836j 2.47e-486, 2.47e-486j
0.14143992661572417524 + 2.9892704547953176385e-1878j 4.54e-509, 4.54e-509j
7.3625982144413169604 + 4.1314329048475672673e-1855j 1.88e-485, 1.88e-485j
-3.3950761742063986469 + 8.8529756726006648173e-1862j 1.04e-492, 1.04e-492j
-7.6164275015747542106 - 2.7403186775312910557e-1853j 2.54e-485, 2.54e-485j
1.6506801238857845559 + 5.6514943181932817034e-1879j 2.96e-500, 2.96e-500j
-0.89811287352165339047 + 5.2092360951214256598e-1882j 3.5e-504, 3.5e-504j
7.9591881170956730128e-1952 + 8.5706092589711978558e-1952j 1.27e-1949, 1.27e-1949j
-0.52464762327529031788 + 9.2118947567658029868e-1885j 1.3e-506, 1.3e-506j
1.2502344977390780677 + 2.717409277399936231e-1881j 2.97e-502, 2.97e-502j
0.52464762327529031788 - 3.0172986316535498348e-1884j 1.42e-506, 1.42e-506j
-5.427551593035843152 + 4.8290501057085478525e-1865j 8.72e-488, 8.72e-488j
-0.14143992661572417524 + 2.0459584506927663455e-1886j 4.54e-509, 4.54e-509j
-4.281883418172708875 - 2.2624240998364962938e-1868j 2.56e-490, 2.56e-490j
-2.2832506552235534748 + 4.7360616912233894448e-1875j 3.7e-497, 3.7e-497j
2.8580170695898428779 - 1.2693302185091452201e-1872j 3.79e-494, 3.79e-494j

Weights

Weight (ball center) Error (ball radius)
1.9625466824428441317e-75 + 4.9965157443766268795e-1431j 2.46e-137, 1.16e-377j
4.9491913764369367624e-82 + 3.5340856079499497917e-1435j 4.28e-140, 2.02e-380j
2.8751520901494870348e-36 - 7.4231160810404595055e-1409j 3.98e-120, 1.88e-360j
8.8272026674573866334e-41 - 1.6014754315990219479e-1413j 7.37e-124, 3.49e-364j
8.2855578643191581721e-46 + 5.4276887637342179044e-1415j 7.24e-126, 3.42e-366j
3.4498181550708751866e-32 - 7.1243460622376228021e-1409j 1.11e-118, 5.26e-359j
5.7858640416667090694e-58 + 1.0243518682116323461e-1421j 1.4e-131, 6.62e-372j
0.003736839802759964035 + 1.6540664767939088465e-1390j 3.29e-53, 1.56e-293j
2.4807954241547437179e-13 + 1.7509768585112307336e-1397j 6.37e-98, 3.01e-338j
1.9129049194011759862e-10 - 3.487729089564451716e-1396j 7.43e-93, 3.52e-333j
0.014026368678470761544 + 4.4352731619977576388e-1390j 2.31e-44, 1.09e-284j
3.5464943058885970074e-70 + 5.0871861930743224126e-1429j 1.08e-137, 5.09e-378j
1.5004066818407719013e-48 + 1.1533670362284645852e-1417j 2.93e-129, 1.39e-369j
5.7858640416667090694e-58 - 1.2417658710332841071e-1422j 2e-133, 9.47e-374j
8.8272026674573866334e-41 + 5.2244006716506714969e-1412j 4.54e-126, 2.15e-366j
1.3483596166569304918e-54 - 6.9285472607626795384e-1420j 4.67e-133, 2.21e-373j
1.1839797379340873727e-65 + 7.6279137555343211981e-1426j 3.55e-138, 1.68e-378j
3.1822393914581806464e-43 - 1.7222098126815491434e-1413j 1.94e-127, 9.2e-368j
0.014026368678470761544 + 6.1469499952989931664e-1390j 2.18e-55, 1.03e-295j
3.1822393914581806464e-43 + 7.8858584460132289399e-1415j 8.42e-130, 3.98e-370j
1.2052236308731562458e-06 + 3.0234515433091787234e-1393j 1.88e-90, 8.9e-331j
2.3513593234243307626e-11 + 8.616585689994861439e-1397j 7.29e-103, 3.45e-343j
1.8016819910132774964e-51 - 3.2779106689820096772e-1419j 4.74e-134, 2.24e-374j
2.116998830290558575e-14 - 1.002979914333160826e-1398j 6.67e-109, 3.16e-349j
3.5464943058885970074e-70 - 3.0025462720817619948e-1428j 1.24e-141, 5.87e-382j
2.7127353051655946965e-30 + 1.6448684163998651473e-1406j 1.89e-125, 8.95e-366j
0.003736839802759964035 + 1.0843956672495185476e-1390j 2.8e-73, 1.32e-313j
1.2657896247373583918e-61 - 1.0915498770755511753e-1423j 4.69e-138, 2.22e-378j
3.5351888138432666105e-34 + 5.8669180562336496222e-1410j 3.37e-128, 1.6e-368j
0.063338993352024703171 + 3.7531203387519252533e-1389j 1.28e-66, 6.07e-307j
1.8231950427772068852e-38 - 1.8245437186688621737e-1410j 3e-128, 1.42e-368j
1.5198455953905670495e-23 + 3.8970903444984352811e-1403j 2.77e-122, 1.31e-362j
1.3851062813695315701e-09 + 1.3737581628781066279e-1395j 6.19e-104, 2.93e-344j
1.2657896247373583918e-61 + 1.4926827844672101444e-1424j 1.26e-141, 5.96e-382j
5.1535578638156667806e-08 + 5.0224389910294897587e-1394j 4.86e-104, 2.3e-344j
0.00023444769681292288007 - 2.0018113883506728564e-1391j 2.31e-88, 1.09e-328j
2.5665265983970392346e-12 - 2.0401007629904562374e-1397j 2.8e-109, 1.32e-349j
1.5894645726497154494e-15 + 9.1775049866610539626e-1399j 7.44e-117, 3.52e-357j
2.9988706917573391653e-19 - 1.2831146058634513847e-1401j 5.8e-120, 2.74e-360j
1.8231950427772068852e-38 + 2.8100161090593755908e-1412j 2.21e-131, 1.05e-371j
2.8751520901494870348e-36 - 4.3160234645932894463e-1411j 2.09e-130, 9.91e-371j
1.5198455953905670495e-23 + 4.4472130844690928521e-1404j 4.45e-125, 2.1e-365j
1.2232845821226032012e-05 + 5.7200608078420650757e-1392j 9.21e-100, 4.36e-340j
3.5351888138432666105e-34 + 3.7662051125137802081e-1408j 1.83e-133, 8.66e-374j
4.7980071694432176353e-22 - 3.1549631135004373109e-1403j 5.7e-124, 2.7e-364j
0.02236082186436172423 - 1.2144573616954283668e-1389j 3.99e-80, 1.89e-320j
1.1839797379340873727e-65 - 1.1649383342078755104e-1426j 1.46e-146, 6.93e-387j
4.6919870142819609757e-06 - 1.3000767621177763133e-1392j 6.98e-103, 3.3e-343j
1.0460205534805121893e-16 - 4.026823236857860869e-1400j 5.78e-120, 2.74e-360j
9.2335895373206191306e-27 + 6.9927907884073188633e-1406j 6.33e-128, 3e-368j
4.9491913764369367624e-82 - 1.6970171780575723256e-1434j 1.58e-157, 7.46e-398j
1.9625466824428441317e-75 - 9.3654831018849495111e-1432j 9.17e-152, 4.34e-392j
4.6919870142819609757e-06 - 2.7373705700516782634e-1392j 8.26e-113, 3.91e-353j
1.8016819910132774964e-51 + 3.6069584744206985081e-1418j 3.03e-144, 1.44e-384j
1.3483596166569304918e-54 + 7.3423752724265993479e-1421j 5.74e-142, 2.72e-382j
4.7980071694432176353e-22 - 2.397446206017750776e-1402j 1.15e-132, 5.44e-373j
0.031141852865151431742 + 2.1564705600979872301e-1389j 4.74e-88, 2.24e-328j
1.2232845821226032012e-05 + 1.1469778043470497438e-1391j 1.07e-112, 5.08e-353j
6.0086423916045465066e-18 + 3.9779610488861415922e-1400j 1.95e-130, 9.23e-371j
0.0016403214854135560925 - 9.17137296404815925e-1391j 8.12e-105, 3.84e-345j
1.7415839134377535535e-28 - 1.2144694904672341664e-1405j 5.29e-136, 2.5e-376j
5.1535578638156667806e-08 + 2.006388096834614414e-1394j 5.7e-116, 2.7e-356j
7.4913085503852683663e-05 + 2.8301707119896620713e-1391j 8.52e-112, 4.03e-352j
2.5665265983970392346e-12 - 7.1399419996245236116e-1397j 5.71e-126, 2.7e-366j
7.4913085503852683663e-05 + 1.5179948712743171867e-1391j 5.75e-110, 2.72e-350j
1.7415839134377535535e-28 - 7.726670285335747057e-1407j 8.71e-134, 4.12e-374j
3.4498181550708751866e-32 - 2.2719377301085219436e-1407j 1.86e-137, 8.81e-378j
0.043664496687070125524 - 2.5193449753752672794e-1389j 4.26e-98, 2.01e-338j
1.9728339310769967869e-05 - 2.2778156664757609148e-1391j 7e-114, 3.31e-354j
8.9429425697377100729e-09 - 1.4077940647997140786e-1394j 1.8e-122, 8.5e-363j
2.7127353051655946965e-30 + 7.7909081888238786551e-1408j 7.27e-135, 3.44e-375j
1.5894645726497154494e-15 + 2.0649996804687256292e-1399j 1.18e-126, 5.58e-367j
0.00023444769681292288007 - 3.5513144644412521338e-1391j 1.11e-113, 5.24e-354j
0.0076689363980895182235 - 3.1277948575740219347e-1390j 1.02e-107, 4.81e-348j
1.9129049194011759862e-10 - 1.0607948192509748666e-1395j 4.69e-126, 2.22e-366j
1.2938104133936180479e-20 + 2.082050027041054287e-1402j 1.52e-130, 7.21e-371j
2.4807954241547437179e-13 + 4.6306341557011969351e-1398j 1.18e-125, 5.58e-366j
6.0086423916045465066e-18 + 7.4115963061401569284e-1401j 6.5e-129, 3.07e-369j
1.0460205534805121893e-16 - 1.9603797860525688309e-1399j 1.31e-133, 6.18e-374j
1.5004066818407719013e-48 - 1.5204886056829093912e-1416j 3.75e-149, 1.78e-389j
2.6482479163782028024e-07 - 7.6545394948752476393e-1394j 2.22e-122, 1.05e-362j
0.063338993352024703171 + 3.195423827364575702e-1389j 2.13e-112, 1.01e-352j
1.2938104133936180479e-20 + 1.3932329505822939488e-1401j 1.21e-136, 5.71e-377j
8.2855578643191581721e-46 - 3.3023343213482688828e-1416j 3.78e-146, 1.79e-386j
2.3513593234243307626e-11 + 2.7992402450735957416e-1396j 6.81e-130, 3.22e-370j
0.031141852865151431742 + 1.6957137742590983444e-1389j 2.05e-114, 9.71e-355j
8.9429425697377100729e-09 - 5.2845326944612629615e-1395j 2.52e-124, 1.19e-364j
0.00065159457074090669534 + 3.2118595252613511823e-1391j 1.94e-120, 9.17e-361j
0.0016403214854135560925 - 5.7212539774074179006e-1391j 4.85e-120, 2.3e-360j
0.09888653335318958056 + 6.4139296123623000075e-1389j 6.48e-117, 3.07e-357j
2.6482479163782028024e-07 - 1.8045274690183634218e-1393j 2.95e-127, 1.4e-367j
4.0835757043346381862e-25 - 5.9882722286608182779e-1404j 4.31e-140, 2.04e-380j
0.09888653335318958056 + 5.9600765545276872085e-1389j 2.87e-119, 1.36e-359j
2.9988706917573391653e-19 - 7.6525747725219784365e-1401j 6.82e-137, 3.23e-377j
0.094444038660777708135 - 1.0352584025061575445e-1388j 1.61e-119, 7.6e-360j
4.0835757043346381862e-25 - 5.807138109028593548e-1405j 2.94e-138, 1.39e-378j
1.2052236308731562458e-06 + 6.727131755501396152e-1393j 3.66e-128, 1.73e-368j
9.2335895373206191306e-27 + 8.7245091822886669197e-1405j 4.88e-141, 2.31e-381j
0.0076689363980895182235 - 2.1527881729036557491e-1390j 5.29e-124, 2.5e-364j
0.043664496687070125524 - 3.0820490247646890617e-1389j 8.27e-123, 3.91e-363j
0.067893856503428293133 + 1.3554100154770353346e-1388j 2.09e-122, 9.87e-363j
0.084144727946081258024 - 4.5879311384490794908e-1389j 1.12e-122, 5.28e-363j
0.02236082186436172423 - 9.1645860731992145488e-1390j 9.74e-124, 4.61e-364j
0.084144727946081258024 - 4.0793047278473289505e-1389j 5.86e-123, 2.77e-363j
2.116998830290558575e-14 - 4.0892067444729335636e-1398j 5.84e-135, 2.76e-375j
0.094444038660777708135 - 1.0685416696309511445e-1388j 3.01e-124, 1.44e-364j
1.3851062813695315701e-09 + 3.9057617521164405181e-1395j 6.53e-132, 3.09e-372j
0.00065159457074090669534 + 5.4152923026481552151e-1391j 2.39e-127, 1.12e-367j
1.9728339310769967869e-05 - 1.1741521624011880439e-1391j 4.89e-128, 2.4e-368j

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