Rule: Q[3, 10, 92]

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)
-15.191825965413317461 + 2.8856178932484421591e-1403j 3.84e-488, 3.84e-488j
17.371877654590489591 - 3.190727718462225443e-1405j 2.17e-491, 2.17e-491j
18.052323834664075056 - 1.6638565613802740262e-1408j 1.16e-492, 1.16e-492j
15.191825965413317461 + 7.5262765751056252813e-1400j 3.78e-488, 3.78e-488j
-16.209352849121071932 + 2.7793625312759224189e-1410j 1.72e-489, 1.72e-489j
14.717774403625217707 + 2.0240703905785923667e-1405j 1.18e-487, 1.18e-487j
-16.766365010697578741 - 1.0384820917338427062e-1424j 2.56e-490, 2.56e-490j
-17.371877654590489591 + 6.6706209123002675949e-1427j 2.29e-491, 2.29e-491j
-4.6096758921816875609 + 1.9442029563649498022e-1427j 1.26e-492, 1.26e-492j
5.8238536767427603773 + 1.3948569530118208874e-1425j 1.13e-490, 1.13e-490j
12.972633458471051033 - 1.1579600169868066042e-1419j 2.64e-486, 2.64e-486j
15.687227150624048193 + 1.6232675524993652961e-1429j 9.06e-489, 9.06e-489j
-18.876937312632537721 + 5.0515193717141445724e-1438j 2.39e-494, 2.39e-494j
-3.5773982809904283695 - 3.5777700079469749528e-1438j 1.32e-494, 1.32e-494j
-10.267527885130341368 + 5.4985026489045926562e-1429j 4.06e-486, 4.06e-486j
8.1490171962050431755 + 2.774816413792236862e-1432j 1.49e-487, 1.49e-487j
-5.1908447913945880644 - 1.2130149982552346695e-1434j 1.04e-491, 1.04e-491j
-11.008607862927560911 - 1.1622143699416280809e-1428j 5.95e-486, 5.95e-486j
-1.1482061524327953557 + 9.9454068671499340391e-1452j 6.84e-505, 6.84e-505j
-11.387461254457926581 + 4.7402487113877899426e-1432j 6.36e-486, 6.36e-486j
-6.8031991685608756892 - 3.8321689009931825233e-1442j 3.26e-489, 3.26e-489j
-15.687227150624048193 - 7.1636249330064982493e-1439j 9.27e-489, 9.27e-489j
10.635458784422494282 + 1.1660488291088558246e-1439j 5.11e-486, 5.11e-486j
-12.56432934178607568 + 4.534259378912753703e-1448j 3.73e-486, 3.73e-486j
2.3283406218597398539 + 6.8353086364777249652e-1474j 3.59e-500, 3.59e-500j
-2.935875649128050707 - 4.7872776739376250462e-1471j 8.4e-498, 8.4e-498j
-18.052323834664075056 - 4.1291197524228864659e-1466j 1.34e-492, 1.34e-492j
9.9043906805315661724 - 3.2963279832906390394e-1459j 2.84e-486, 2.84e-486j
9.191051458263596644 - 2.3312789788771653944e-1472j 1.13e-486, 1.13e-486j
-1.7320508075688772935 + 3.6687766903756158011e-1502j 1.5e-502, 1.5e-502j
-8.4929613302143132181 + 7.4556508593405664979e-1486j 3.09e-487, 3.09e-487j
11.387461254457926581 - 2.2333551492540519509e-1494j 6.25e-486, 6.25e-486j
6.8031991685608756892 + 2.2600975433669706968e-1513j 3.3e-489, 3.3e-489j
-9.5456745890784812092 - 5.4791636532895634207e-1509j 1.8e-486, 1.8e-486j
6.1472200252288989832 - 2.6567673480512508511e-1519j 3.48e-490, 3.48e-490j
-4.1096070615948672963 - 1.2768341656451264881e-1525j 1.23e-493, 1.23e-493j
1.7320508075688772935 + 3.1308735133891361588e-1534j 1.51e-502, 1.51e-502j
-12.972633458471051033 - 6.3577013337505693615e-1517j 2.65e-486, 2.65e-486j
13.390618388850402537 + 6.2176099134339908802e-1540j 1.5e-486, 1.5e-486j
5.1908447913945880644 - 1.0209845049182011165e-1567j 1.01e-491, 1.01e-491j
-14.261298034438102527 + 3.0399028270044308503e-1560j 3.34e-487, 3.34e-487j
-7.4703757752421840143 + 5.4894443528943734204e-1575j 2.36e-488, 2.36e-488j
-5.5044335790111064202 - 5.4765450859947225596e-1588j 3.26e-491, 3.26e-491j
12.56432934178607568 - 4.5035708094774748849e-1581j 3.74e-486, 3.74e-486j
-7.1353977778776009669 - 2.4342296510517680135e-1598j 8.99e-489, 8.99e-489j
18.876937312632537721 + 2.2803176569376469823e-1602j 2.37e-494, 2.37e-494j
16.766365010697578741 - 4.6394248308830213934e-1594j 2.46e-490, 2.46e-490j
-12.164613917843953773 - 2.5630164554538822553e-1599j 4.94e-486, 4.94e-486j
4.3645429200992042395 + 4.1525129491604879332e-1629j 4.5e-493, 4.5e-493j
4.8881853737411738491 - 5.43375495636486835e-1628j 3.51e-492, 3.51e-492j
14.261298034438102527 + 1.6869030036806907417e-1620j 3.35e-487, 3.35e-487j
16.209352849121071932 + 1.4414108685752009977e-1641j 1.76e-489, 1.76e-489j
-8.8402319211079820233 + 1.2863283813166476744e-1651j 5.97e-487, 5.97e-487j
-14.717774403625217707 - 5.9326893333626896259e-1671j 1.22e-487, 1.22e-487j
3.5773982809904283695 - 4.0564450573414270129e-1702j 1.36e-494, 1.36e-494j
5.5044335790111064202 + 1.2205461378873610283e-1692j 3.3e-491, 3.3e-491j
-0.85995874045067267595 - 3.138581419501473284e-1732j 3.63e-506, 3.63e-506j
13.819619014351087344 + 4.4881661723606692102e-1717j 7.38e-487, 7.38e-487j
7.1353977778776009669 + 1.2200373049590529903e-1751j 9.28e-489, 9.28e-489j
3.2440699910736954161 - 2.7161922140503909873e-1788j 1.66e-496, 1.66e-496j
-7.8082082744040940827 - 1.0926721465690530253e-1785j 6.29e-488, 6.29e-488j
-4.8881853737411738491 + 2.2694505680227893038e-1809j 3.47e-492, 3.47e-492j
-0.57297457152747560685 - 1.0813009903296557684e-1841j 1.88e-507, 1.88e-507j
11.772579440909368826 + 4.791732122296737915e-1829j 5.77e-486, 5.77e-486j
0.85995874045067267595 - 2.6370990997547074949e-1884j 3.51e-506, 3.51e-506j
12.164613917843953773 - 2.6851719627001478933e-1863j 5e-486, 5e-486j
9.5456745890784812092 + 2.255844637141936626e-1873j 1.84e-486, 1.84e-486j
-2.0286436164034340066 - 1.0781789110714412599e-1897j 2.29e-501, 2.29e-501j
11.008607862927560911 - 2.5840284048284604986e-1881j 6.08e-486, 6.08e-486j
8.8402319211079820233 + 2.4092541953165995812e-1890j 6.51e-487, 6.51e-487j
3.6663297561937948306 + 1.0851341497098573578e-1897j 3.99e-494, 3.99e-494j
-6.4737722356787530194 - 1.4167691875122639489e-1893j 1.1e-489, 1.1e-489j
-3.8050111444124697499 + 2.2284688357684311809e-1897j 5.39e-494, 5.39e-494j
-3.2440699910736954161 - 3.1646104399103911077e-1901j 1.54e-496, 1.54e-496j
-13.819619014351087344 - 3.7438428372728085623e-1891j 7.51e-487, 7.51e-487j
1.4386649849532411331 + 6.4169249972527516505e-1907j 1.1e-503, 1.1e-503j
3.8050111444124697499 - 3.1650312959629881012e-1898j 4.93e-494, 4.93e-494j
7.8082082744040940827 + 1.2143279600280509776e-1890j 5.81e-488, 5.81e-488j
4.6096758921816875609 - 6.8169036576431853011e-1896j 1.24e-492, 1.24e-492j
-4.3645429200992042395 - 1.1962024257673777551e-1896j 4.44e-493, 4.44e-493j
-1.4386649849532411331 + 8.2886990235239560437e-1908j 1e-503, 1e-503j
0.57297457152747560685 + 4.6921289286789231231e-1911j 1.85e-507, 1.85e-507j
-9.9043906805315661724 + 3.5850348772766576341e-1889j 2.88e-486, 2.88e-486j
-9.191051458263596644 + 3.1593077413596192783e-1890j 1.14e-486, 1.14e-486j
10.267527885130341368 - 2.9414696025974649428e-1888j 4.18e-486, 4.18e-486j
2.935875649128050707 - 4.6270153331471882959e-1902j 8.38e-498, 8.38e-498j
4.1096070615948672963 + 1.1873261798782195045e-1897j 1.32e-493, 1.32e-493j
7.4703757752421840143 + 2.2554251637786668981e-1892j 2.47e-488, 2.47e-488j
-6.1472200252288989832 + 7.3054841332420981549e-1894j 3.37e-490, 3.37e-490j
-13.390618388850402537 + 2.4965337734929228347e-1890j 1.43e-486, 1.43e-486j
-8.1490171962050431755 + 4.7105488835677300173e-1891j 1.42e-487, 1.42e-487j
-5.8238536767427603773 - 2.7641642987540811123e-1894j 1.03e-490, 1.03e-490j
0.28645353833861515066 - 8.3388045344176366728e-1912j 9.65e-509, 9.65e-509j
6.4737722356787530194 - 3.1630781981426651347e-1893j 1.06e-489, 1.06e-489j
-0.28645353833861515066 + 8.0969345187665238412e-1912j 9.65e-509, 9.65e-509j
-2.6308380841127442917 - 1.6906926262840160951e-1902j 5.12e-499, 5.12e-499j
7.8671935226764914395e-1980 + 1.159184488627429268e-1979j 1.47e-1977, 1.47e-1977j
2.6308380841127442917 - 1.768212965032480474e-1902j 5.55e-499, 5.55e-499j
8.4929613302143132181 + 4.638004516853800365e-1891j 3.01e-487, 3.01e-487j
-3.6663297561937948306 - 1.3155518520891541563e-1897j 3.7e-494, 3.7e-494j
-2.3283406218597398539 + 3.7089037749043740781e-1904j 3.46e-500, 3.46e-500j
-11.772579440909368826 + 3.7754545565372354896e-1889j 5.94e-486, 5.94e-486j
1.1482061524327953557 - 1.7288733799665244628e-1908j 6.45e-505, 6.45e-505j
2.0286436164034340066 - 3.6212494901534998097e-1905j 2.44e-501, 2.44e-501j
-10.635458784422494282 - 2.9067318281663324861e-1891j 5.16e-486, 5.16e-486j

Weights

Weight (ball center) Error (ball radius)
1.4790840799466030501e-51 - 3.3216574793189287547e-1452j 1.1e-125, 2.95e-367j
7.4773273543076519175e-67 + 4.9634872272191183578e-1459j 4.79e-132, 1.29e-373j
5.0250295934383499774e-72 - 7.7247421234427226314e-1462j 7.22e-134, 1.94e-375j
1.4790840799466030501e-51 - 8.9169598403695427341e-1450j 7.75e-127, 2.08e-368j
1.8951972455297898697e-58 - 8.5493786852471763422e-1456j 5.35e-131, 1.44e-372j
1.703032580872223166e-48 + 9.7275623024726181891e-1449j 5.34e-126, 1.43e-367j
2.0921564284425257015e-62 + 7.1186082566263072262e-1458j 7.37e-133, 1.98e-374j
7.4773273543076519175e-67 - 3.3418176615450392234e-1460j 6.86e-135, 1.84e-376j
2.5227635098265545901e-06 + 3.8412678385159524502e-1425j 1.49e-81, 4.01e-323j
5.5354822275160836714e-09 + 2.2557914307630992264e-1427j 1.43e-91, 3.85e-333j
4.7126184427346409557e-38 + 7.7149620066714661448e-1444j 1.86e-123, 5.01e-365j
7.3950348542424013021e-55 - 4.1070598230742007459e-1452j 5.96e-130, 1.6e-371j
1.5945618851930601179e-78 - 2.7804264454453112812e-1466j 2.42e-140, 6.51e-382j
0.0003112973227944945527 - 4.3912994443587740698e-1423j 1.57e-74, 4.22e-316j
1.8691101638085165064e-24 - 1.9530103316133519443e-1437j 1.05e-116, 2.81e-358j
5.192694274782159921e-16 - 5.8794175631688999085e-1432j 2.51e-108, 6.74e-350j
1.7397453000446917278e-07 + 1.9867829718261471656e-1426j 2.91e-90, 7.83e-332j
7.2451115300085621456e-28 - 2.3494244783432763525e-1439j 1.3e-119, 3.49e-361j
0.059680292610012625074 - 5.0295181244680232521e-1423j 1.68e-37, 4.51e-279j
1.0578701581398278733e-29 + 2.2395685526320248809e-1440j 4.14e-121, 1.11e-362j
1.1753350422071737042e-11 - 1.1259344718722725224e-1429j 3.2e-103, 8.59e-345j
7.3950348542424013021e-55 + 6.7462523570017426347e-1454j 4.49e-133, 1.21e-374j
4.0502733671719102702e-26 + 1.2722884612171509775e-1437j 6.95e-123, 1.87e-364j
8.4673203628954465816e-36 - 1.0114402593991713708e-1443j 5.53e-126, 1.48e-367j
0.0079892670216821052178 - 2.4524130836605145124e-1423j 5.28e-70, 1.42e-311j
0.001642198553942867843 - 1.1969959132407167138e-1423j 4.4e-76, 1.18e-317j
5.0250295934383499774e-72 + 6.6760866278380043119e-1463j 4.59e-140, 1.23e-381j
7.1907788683785936683e-23 + 7.4484674267933945645e-1436j 9.49e-121, 2.55e-362j
6.3779370200057494948e-20 + 3.2603745638578738791e-1434j 2.22e-118, 5.95e-360j
0.026257919811995209565 - 3.1083532698211886877e-1423j 4.6e-63, 1.24e-304j
2.9959466709202567606e-17 + 3.1146530155743649604e-1433j 1.1e-114, 2.95e-356j
1.0578701581398278733e-29 + 1.568782366864018779e-1439j 3.63e-126, 9.74e-368j
1.1753350422071737042e-11 - 2.9547379712642999689e-1429j 1.35e-109, 3.63e-351j
2.3263662844329242197e-21 - 1.1621256448293906351e-1435j 1.19e-118, 3.2e-360j
8.0763328956859346501e-10 - 5.395307355883231938e-1428j 2.29e-106, 6.16e-348j
2.3614666066564058179e-05 + 3.2037037346167646798e-1424j 2.79e-92, 7.5e-334j
0.026257919811995209565 - 3.9090311082752128555e-1423j 1.08e-69, 2.9e-311j
4.7126184427346409557e-38 + 6.0496484683280697957e-1445j 2.48e-129, 6.66e-371j
1.9548900781037107382e-40 - 4.9977649786844533235e-1445j 2.52e-133, 6.78e-375j
1.7397453000446917278e-07 + 4.0515915807423133888e-1426j 2.57e-103, 6.89e-345j
1.2258446717421757214e-45 - 5.0654089398467700605e-1449j 3.86e-133, 1.04e-374j
1.0221636898067861202e-13 - 4.8860935450580138118e-1431j 7.36e-113, 1.98e-354j
3.3314866868526035273e-08 - 4.4273237597410043911e-1427j 5.58e-104, 1.5e-345j
8.4673203628954465816e-36 - 1.0727480832920464082e-1442j 8.57e-132, 2.3e-373j
1.1703006438986184959e-12 + 2.3918741851890136946e-1430j 1.48e-111, 3.98e-353j
1.5945618851930601179e-78 + 2.5615484041828457318e-1465j 2.52e-151, 6.76e-393j
2.0921564284425257015e-62 - 1.4337494001564382382e-1456j 1.31e-144, 3.51e-386j
1.1623543511497201756e-33 + 1.4824807390261843972e-1442j 1.39e-129, 3.73e-371j
6.9795482480075191472e-06 - 2.1495959393784111322e-1424j 2.11e-105, 5.67e-347j
7.5902638992426153931e-07 - 1.7738986508734221097e-1425j 1.52e-107, 4.07e-349j
1.2258446717421757214e-45 - 1.622860218298051704e-1447j 8e-138, 2.15e-379j
1.8951972455297898697e-58 + 2.6076064228875495812e-1454j 3.4e-143, 9.12e-385j
1.4919364985748438304e-18 - 5.1580732553546405307e-1434j 6.28e-123, 1.69e-364j
1.703032580872223166e-48 + 1.5047789776773160935e-1450j 9.87e-139, 2.65e-380j
0.0003112973227944945527 - 7.0991622042112149495e-1423j 9.67e-105, 2.6e-346j
3.3314866868526035273e-08 - 9.4646128703409462378e-1427j 1.86e-112, 4.99e-354j
0.079231216321168947286 + 6.0347910590242499859e-1423j 1.12e-82, 3e-324j
5.8646636182772424032e-43 + 2.9391380066696062943e-1446j 4.15e-137, 1.11e-378j
1.1703006438986184959e-12 + 6.6348478506050723487e-1430j 2.63e-120, 7.06e-362j
0.00064330394928592436375 + 1.9061074918661218226e-1423j 2.08e-104, 5.58e-346j
7.8060610088339769333e-15 + 9.5416348526451639386e-1432j 4.32e-122, 1.16e-363j
7.5902638992426153931e-07 - 9.0973994787835864677e-1426j 5.95e-112, 1.6e-353j
0.097044710293510735742 - 6.9069986735692430609e-1423j 1.15e-87, 3.09e-329j
1.2446057141712728296e-31 - 1.5235042149492348862e-1440j 1.91e-133, 5.14e-375j
0.079231216321168947286 + 6.7595922406198612515e-1423j 5.04e-91, 1.35e-332j
1.1623543511497201756e-33 + 1.3442789785715838338e-1441j 2.94e-134, 7.89e-376j
2.3263662844329242197e-21 - 5.0997195008204678153e-1435j 3.04e-129, 8.16e-371j
0.015196727871725513801 + 2.3631412090300159826e-1423j 1.12e-103, 3e-345j
7.2451115300085621456e-28 - 1.4749374170909803432e-1438j 2.36e-132, 6.34e-374j
1.4919364985748438304e-18 - 1.9542509765205508924e-1433j 4.55e-128, 1.22e-369j
-0.00013426751337785002791 + 9.0375666186880959947e-1423j 1.77e-112, 4.77e-354j
1.0380734103033403063e-10 + 5.1323819691395372553e-1429j 6.92e-124, 1.86e-365j
0.00010833946859919088625 - 2.0304221444621560756e-1423j 1.51e-114, 4.06e-356j
0.00064330394928592436375 + 1.2348690786178997407e-1423j 9.07e-113, 2.44e-354j
5.8646636182772424032e-43 + 1.3789853555360540106e-1447j 1.07e-144, 2.87e-386j
0.041362712495176856695 + 4.8593566316304969792e-1423j 1.93e-104, 5.19e-346j
0.00010833946859919088625 - 3.3887756298694504619e-1423j 1.18e-114, 3.16e-356j
7.8060610088339769333e-15 + 2.9754056857047744828e-1431j 1.76e-127, 4.72e-369j
2.5227635098265545901e-06 + 7.1915193592872117758e-1425j 1.51e-117, 4.06e-359j
6.9795482480075191472e-06 - 1.1895431904971680442e-1424j 3.3e-118, 8.87e-360j
0.041362712495176856695 + 4.0180263028304402298e-1423j 6.56e-108, 1.76e-349j
0.097044710293510735742 - 7.4488577805514457449e-1423j 4.24e-108, 1.14e-349j
7.1907788683785936683e-23 + 1.5665715571539543356e-1436j 1.46e-135, 3.91e-377j
6.3779370200057494948e-20 + 8.0122733285132854031e-1435j 1.69e-133, 4.54e-375j
1.8691101638085165064e-24 - 1.0116595442184181811e-1436j 5.61e-134, 1.51e-375j
0.001642198553942867843 - 1.7710128934132007671e-1423j 2.76e-117, 7.4e-359j
2.3614666066564058179e-05 + 5.5822458992347220138e-1424j 8.11e-119, 2.18e-360j
1.0221636898067861202e-13 - 1.4354760596448689564e-1430j 3.29e-128, 8.84e-370j
8.0763328956859346501e-10 - 2.285119680403069461e-1428j 1.47e-127, 3.96e-369j
1.9548900781037107382e-40 - 3.1304818424311550096e-1446j 1.55e-146, 4.17e-388j
5.192694274782159921e-16 - 1.7719981746605374055e-1432j 1.91e-132, 5.13e-374j
5.5354822275160836714e-09 + 1.0048546137676554321e-1427j 4.6e-127, 1.23e-368j
0.10968601623439407994 + 7.8275722001359812683e-1423j 1.54e-117, 4.14e-359j
1.0380734103033403063e-10 + 1.2764865327141382313e-1428j 5.29e-128, 1.42e-369j
0.10968601623439407994 + 7.5376280587279298473e-1423j 1.01e-117, 2.71e-359j
0.0038066199777038835954 + 1.4122275572536283358e-1423j 1.7e-122, 4.57e-364j
0.11427911165563427536 - 7.8561673933682925505e-1423j 5.47e-119, 1.47e-360j
0.0038066199777038835954 + 2.0043430490507184567e-1423j 4.06e-122, 1.09e-363j
2.9959466709202567606e-17 + 1.1026007506699887617e-1432j 1.2e-132, 3.22e-374j
-0.00013426751337785002791 + 5.5213054299259079216e-1423j 1.43e-122, 3.85e-364j
0.0079892670216821052178 - 1.8001547021109376852e-1423j 1.43e-122, 3.83e-364j
1.2446057141712728296e-31 - 1.9261661467587009378e-1441j 4.19e-143, 1.12e-384j
0.059680292610012625074 - 5.8526249852431610013e-1423j 1.37e-123, 2.86e-365j
0.015196727871725513801 + 3.0921748859254296062e-1423j 2.93e-124, 5.82e-366j
4.0502733671719102702e-26 + 2.2398199227070801481e-1438j 4.96e-140, 1.34e-381j

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