Rule: Q[2, 6, 54]

Type

This rule is of Laguerre 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)
195.57664130011847413 - 9.000521557602023249e-430j 6.07e-428, 6.07e-428j
182.71966725539104716 + 5.5793039349782235777e-426j 3.54e-424, 3.54e-424j
211.75679139546915268 + 4.611313804332975135e-435j 1.3e-432, 1.3e-432j
152.8074980250073048 - 3.3875180844357472975e-425j 2.67e-423, 2.67e-423j
161.78624605597768247 + 4.9431715994570398224e-432j 3.09e-430, 3.09e-430j
31.822580116319373 - 3.3965870955768816972e-450j 5.37e-446, 5.37e-446j
52.139189796413913995 - 1.0958868111395597784e-438j 9.51e-437, 9.51e-437j
11.777678210306531347 - 2.7871967356870041815e-487j 1.79e-485, 1.79e-485j
93.802821683598180712 - 1.8001114437612401498e-455j 1.25e-453, 1.25e-453j
129.61922349476380607 + 6.768170838257511802e-476j 8.34e-474, 8.34e-474j
15.500943379346675441 - 2.7072030932244234603e-523j 1.83e-488, 1.83e-488j
45.701474066492827116 + 6.7706042549636885154e-488j 1.76e-482, 1.76e-482j
10.582738363032173373 + 9.0653013535638978367e-526j 8.89e-491, 8.89e-491j
6.2225187028629209116 + 1.3227994103045183125e-525j 1.63e-493, 1.63e-493j
22.788178638757229139 + 8.4725860921546938931e-506j 2.37e-486, 2.37e-486j
7.053870302093294924 - 2.2021277723816072987e-528j 3.74e-493, 3.74e-493j
29.399154797963218699 + 4.809775443587909702e-499j 8.68e-485, 8.68e-485j
24.883740740734678624 - 3.6427674422244474326e-502j 8.26e-486, 8.26e-486j
104.55743387922895512 - 3.5614753194332420028e-493j 9.47e-482, 9.47e-482j
171.65391707582182846 + 9.3600681353589330336e-505j 1.04e-486, 1.04e-486j
99.053514063971003138 + 5.8615505075919412349e-509j 1.66e-481, 1.66e-481j
8.1587850678157993965 + 2.1335826976512389845e-549j 1.84e-492, 1.84e-492j
14.023914954138327016 - 1.3160411064383428007e-546j 6.34e-489, 6.34e-489j
79.396888707290044792 + 2.7057517740257258889e-530j 3.84e-481, 3.84e-481j
136.83033660942937345 - 9.657826246776214855e-563j 1.13e-483, 1.13e-483j
110.33658160082774559 - 8.3175283794171963393e-595j 5.37e-482, 5.37e-482j
18.917861606125591519 - 1.291493685968706213e-638j 2.04e-487, 2.04e-487j
42.680215856431849377 + 4.359479401004935095e-609j 8.56e-483, 8.56e-483j
62.857224027046000478 - 1.1513493405390107915e-630j 2.28e-481, 2.28e-481j
144.53036642518738627 - 7.9919530695200219121e-671j 3.06e-484, 3.06e-484j
122.83162451167763441 + 3.1696973190736322284e-701j 1.04e-482, 1.04e-482j
1.6682880962583043051 - 1.0889184179412198889e-773j 3.15e-501, 3.15e-501j
2.7381921888659536321 + 1.6189352493671497335e-776j 5.2e-499, 5.2e-499j
3.4142135623730950488 + 2.4199383270793045023e-774j 7.09e-498, 7.09e-498j
12.825957359722200731 + 3.9004518315959899449e-755j 2.18e-489, 2.18e-489j
88.786742610843433882 - 6.6148165431539575389e-718j 2.95e-481, 2.95e-481j
27.086882242774857555 - 2.9172688811659870888e-741j 2.71e-485, 2.71e-485j
0.5857864376269049512 + 5.7198484495378940375e-800j 7.85e-505, 7.85e-505j
20.799370790425286883 + 1.3866644993018931814e-747j 7.25e-487, 7.25e-487j
39.785191956637590805 + 1.2436585921092684312e-732j 3.69e-483, 3.69e-483j
34.359541847452712207 - 2.5742997831786651547e-736j 6.1e-484, 6.1e-484j
2.1569301152897775303 + 4.9629318914451217004e-792j 4.03e-500, 4.03e-500j
48.852990282468635705 + 9.3975020409467010239e-728j 3.34e-482, 3.34e-482j
1.2542623721574744198 - 5.1156245886634705689e-799j 2.67e-502, 2.67e-502j
17.147383326155852173 + 9.2134124439046551883e-753j 6.27e-488, 6.27e-488j
70.780275002281295505 - 3.1100335816144120312e-728j 3.46e-481, 3.46e-481j
9.3459518428118469803 + 2.9669535855765230081e-770j 1.27e-491, 1.27e-491j
55.564946455318507613 - 1.246699533082346574e-741j 9.55e-482, 9.55e-482j
83.989350988141285823 + 1.0490444793627975519e-769j 3.58e-481, 3.58e-481j
74.997369841718594151 - 6.0973923008341394024e-808j 3.73e-481, 3.73e-481j
116.41730095631500806 - 9.871292861763627869e-833j 2.64e-482, 2.64e-482j
0.18754952395605534055 - 1.3326933620885956074e-910j 3.33e-507, 3.33e-507j
5.9184086721992864573 + 1.4356361122513271039e-889j 7.92e-494, 7.92e-494j
0.89322850384656798342 - 1.6623579413053476528e-907j 1.43e-503, 1.43e-503j
4.1813845726393364607 + 4.3019119248041089306e-892j 1.12e-496, 1.12e-496j
0.08837702141245734094 + 8.4098089738065167979e-909j 2.41e-508, 2.41e-508j
59.135639781149616031 + 6.3695673510358735217e-840j 1.63e-481, 1.63e-481j
5.0338021453153096712 - 3.8468201635560324743e-890j 2.12e-495, 2.12e-495j
37.012742396147762623 + 5.2852742239547021597e-851j 1.63e-483, 1.63e-483j
0.34625613278624417909 - 3.1504387043782707758e-903j 4.06e-506, 4.06e-506j
66.736311700163831996 + 8.9706892074681411269e-847j 2.86e-481, 2.86e-481j
0.018674481529260261175 + 6.1279173674996303525e-910j 4.81e-510, 4.81e-510j

Weights

Weight (ball center) Error (ball radius)
1.627535433643532713e-84 + 6.0322656236388946824e-496j 1.54e-174, 2.14e-352j
5.2310258912042167102e-79 - 4.8024848238668672469e-493j 5.95e-173, 8.31e-351j
2.0718961595149004926e-91 - 1.4523687364417024315e-499j 3.62e-177, 5.06e-355j
3.7256747979352012585e-66 + 3.1801617095018370461e-486j 1.4e-169, 1.96e-347j
5.1232534703195964993e-70 - 2.7818516408750247148e-488j 9.74e-171, 1.36e-348j
3.7500777231824322045e-14 - 7.1477126455423055555e-457j 2.21e-134, 3.09e-312j
7.6198492543715800908e-23 + 4.8121089291161777913e-461j 2.79e-146, 3.9e-324j
8.5717237429721608094e-06 + 1.5681300251835461207e-450j 2.79e-112, 3.89e-290j
9.3780847769598428167e-41 - 2.3282836522063523469e-472j 2.89e-160, 4.04e-338j
3.5608858663458626292e-56 - 7.3700619960431146155e-481j 4.17e-167, 5.82e-345j
2.9183768059331397067e-07 - 5.6231858860459664646e-452j 3.69e-120, 5.15e-298j
4.3797923691731981383e-20 + 5.2809779052439383167e-460j 7.36e-144, 1.03e-321j
3.1444550733001564042e-05 - 2.7868686041937293453e-450j 3.1e-112, 4.33e-290j
0.00061331251447316731745 - 2.6175297954588224306e-448j 1.68e-102, 2.34e-280j
2.5900197489236132208e-10 - 1.9947291665679468102e-454j 2.69e-129, 3.75e-307j
0.00090850582191628265787 + 5.4476139082963461235e-449j 1.15e-105, 1.61e-283j
4.0401319675632264842e-13 + 2.990385238016852967e-456j 7.25e-135, 1.01e-312j
3.3526922595166992703e-11 + 4.9793456482911495149e-455j 2.38e-131, 3.32e-309j
2.1997495532773737245e-45 - 5.981704382527554101e-475j 1.06e-164, 1.48e-342j
2.9422783886222993786e-74 + 1.5602407081391770694e-490j 9.84e-176, 1.37e-353j
5.151087443677488397e-43 + 1.2505394818246419599e-473j 1.49e-163, 2.08e-341j
0.00032924457618537916684 - 1.4742540094050585132e-449j 2.28e-115, 3.18e-293j
1.1024825938704771018e-06 + 2.421093072726860804e-451j 1.36e-124, 1.89e-302j
1.4825672858129548401e-34 + 8.3804386080970390161e-469j 2.15e-160, 3e-338j
2.7995838495133772499e-59 + 1.5504729616722132365e-482j 2.55e-171, 3.55e-349j
7.1470816323428278642e-48 + 2.5158943826139779767e-476j 1.16e-166, 1.62e-344j
1.1112933161151411197e-08 - 3.1997319562878754251e-453j 4.07e-134, 5.68e-312j
8.6127689038338461787e-19 - 2.1081259139372178591e-459j 2.48e-149, 3.47e-327j
1.9104851859500725743e-27 + 1.8726287479565156849e-464j 1.51e-157, 2.11e-335j
1.3576777140843087608e-62 - 2.5624315918280829684e-484j 4.44e-173, 6.2e-351j
2.9786882896462180766e-53 + 2.8465174307755035493e-479j 1.68e-169, 2.35e-347j
0.084273590972724504058 + 6.0809598017464673554e-448j 3.74e-110, 5.22e-288j
0.040693286958754916662 + 2.8249590260140998268e-448j 5.77e-116, 8.05e-294j
0.023765612371861901271 - 1.9333339906250282206e-448j 1.39e-118, 1.95e-296j
2.8283978057037912162e-06 - 7.7290656189386999568e-451j 4.33e-132, 6.05e-310j
1.352018327699497033e-38 + 3.9049243261927825515e-471j 7.14e-164, 9.97e-342j
3.8897869178339909928e-12 - 1.2295812884499086506e-455j 1.04e-143, 1.46e-321j
0.15369611266338943484 - 9.647774280615180555e-448j 1.39e-116, 1.94e-294j
1.7935907528374303435e-09 + 7.9611685162843939809e-454j 4.42e-140, 6.17e-318j
1.4920420902483261259e-17 + 8.9887612757795117138e-459j 4.23e-151, 5.9e-329j
3.1039294457864678432e-15 + 1.6796293090967551317e-457j 1.15e-148, 1.6e-326j
0.061720302430759381986 - 4.2598574379538867475e-448j 6.55e-124, 9.15e-302j
1.9543995823434995255e-21 - 1.6693305131029307423e-460j 7.2e-155, 1.01e-332j
0.10996030947475618507 - 7.678857230370342961e-448j 3.43e-123, 4.79e-301j
6.1164291617201186043e-08 + 1.3152721392432795792e-452j 3.53e-140, 4.93e-318j
7.5226287932014133378e-31 + 1.3520722501072450439e-466j 6.11e-163, 8.53e-341j
0.00010649118570373359387 + 5.7416904691239507652e-450j 2.83e-137, 3.95e-315j
2.5833374992576289931e-24 + 3.4888426375995036366e-462j 2.09e-158, 2.91e-336j
1.5679049609599046172e-36 - 5.9633065269179756701e-470j 8.67e-166, 1.21e-343j
1.1566367912125178872e-32 - 1.0961050150992907668e-467j 4.36e-164, 6.09e-342j
1.7214967176381942829e-50 - 9.1696816960667133131e-478j 3.63e-173, 5.07e-351j
0.099443723862411128465 - 1.1070513682572537654e-447j 1.48e-137, 2.07e-315j
0.0020040281702550718868 + 2.9394983872808129671e-448j 2.03e-141, 2.83e-319j
0.13761262886991930345 + 8.7153527794269146936e-448j 5.5e-138, 7.68e-316j
0.012393108111314404642 + 1.4716821144849004885e-448j 3.08e-141, 4.3e-319j
0.078863736303672551367 + 7.0049354073103346181e-448j 8.42e-139, 1.18e-316j
7.575769708904792433e-26 - 2.2910739548574575655e-463j 9.04e-161, 1.26e-338j
0.0058008268231239361736 - 1.4248066739718086142e-448j 8.33e-143, 1.16e-320j
2.2851123211664214471e-16 - 3.8941776348974213443e-458j 5.41e-155, 7.56e-333j
0.14175594552935110122 + 1.1014144189985879539e-447j 1.35e-142, 1.88e-320j
4.1163116108043985533e-29 - 1.6011350700031617703e-465j 1.13e-162, 1.58e-340j
0.046014919999192397024 - 1.8556597277666827175e-448j 2.84e-143, 3.96e-321j

Download

All rules of Laguerre type can be downloaded here packed into a single file.