Rule: Q[1, 4, 72]

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)
275.69602282660597135 + 4.3344774032680009592e-2425j 5.05e-997, 5.05e-997j
192.5952287737255196 + 4.0975114755941566546e-2412j 1.69e-988, 1.69e-988j
220.58021499007138544 + 5.178904668168648213e-2418j 4.52e-991, 4.52e-991j
210.55415711130543889 + 1.5191184577861543597e-2430j 4.21e-990, 4.21e-990j
257.96078740044740793 - 7.189709466997204349e-2443j 5.67e-995, 5.67e-995j
48.397366633591843812 - 1.8687781084155873104e-2444j 4.08e-987, 4.08e-987j
11.242378555161742866 - 1.8462282218220296581e-2476j 2.53e-999, 2.53e-999j
88.875503433043557979 - 1.1874869244432376468e-2459j 4.81e-984, 4.81e-984j
111.01603375602146145 + 4.0864521743962653469e-2486j 4.79e-984, 4.79e-984j
149.35252041664081617 + 1.4825580990218196045e-2501j 2.04e-985, 2.04e-985j
23.408942947150601149 + 1.3003640478284977098e-2524j 3.34e-993, 3.34e-993j
13.842036271113370496 - 2.145722414836514276e-2529j 1.11e-997, 1.11e-997j
169.38727938699145992 + 3.8482726029177442537e-2514j 1.08e-986, 1.08e-986j
38.120487786913660757 - 1.5826389568820233719e-2537j 5.47e-989, 5.47e-989j
101.71423959328062756 - 5.8620031900859294808e-2532j 6.01e-984, 6.01e-984j
97.292644115544344446 + 1.23749601550404498e-2552j 5.83e-984, 5.83e-984j
201.27045469161862499 - 8.0077891626072611469e-2567j 3.11e-989, 3.11e-989j
7.8836867930844304715 - 4.8723871069890344091e-2585j 6.36e-1002, 6.36e-1002j
93.015028370972727355 + 7.8553828176273301981e-2566j 5.43e-984, 5.43e-984j
63.367338450847074644 + 5.2869561706257362779e-2575j 2.21e-985, 2.21e-985j
2.8500082985710811872 + 1.3231115097906135594e-2599j 3.65e-1008, 3.65e-1008j
70.076765057939848751 + 3.0484232014086338668e-2575j 7.04e-985, 7.04e-985j
80.989745354791023555 - 2.2557035137039337889e-2600j 2.66e-984, 2.66e-984j
143.22877815150487713 - 2.8427481621311502867e-2649j 4.22e-985, 4.22e-985j
162.40582949352144251 + 5.1210790710522325124e-2697j 3.17e-986, 3.17e-986j
57.080787505854613553 + 3.5073112010798269787e-2723j 5.18e-986, 5.18e-986j
1.8047183625323194342 - 6.298549878851065556e-2775j 1.32e-1010, 1.32e-1010j
155.7369996056685763 - 3.9177852120869400814e-2748j 8.97e-986, 8.97e-986j
184.433728726645558 + 2.2296626516685479193e-2778j 7.75e-988, 7.75e-988j
243.79713353024342978 - 2.0548378367326267318e-2790j 1.96e-993, 1.96e-993j
54.089218636632777208 - 4.4214022559840316706e-2797j 2.18e-986, 2.18e-986j
60.172627489593627522 + 1.3443858667970516892e-2835j 1.08e-985, 1.08e-985j
3.994041081847372743 + 1.2089171681418810611e-2895j 5.98e-1006, 5.98e-1006j
29.226442385180252915 + 1.539569085947034042e-2876j 3.18e-991, 3.18e-991j
77.234128190142937744 - 1.5101405805928794665e-2922j 1.8e-984, 1.8e-984j
131.68643270687543098 - 6.2308968381834348936e-2987j 1.38e-984, 1.38e-984j
25.269266959690180876 - 3.3806020141022628802e-3035j 1.72e-992, 1.72e-992j
1.370198746592108722 - 2.3430303661138805588e-3055j 7.26e-1012, 7.26e-1012j
35.771213916304318364 - 5.8189485552887349526e-3028j 1.62e-989, 1.62e-989j
5.2156669378862129718 - 1.9442083877466452811e-3066j 2.05e-1004, 2.05e-1004j
115.9114098182786959 - 3.0481275903283718572e-3048j 4.18e-984, 4.18e-984j
21.626062098229469848 + 1.3443066577009590154e-3099j 7.04e-994, 7.04e-994j
12.506067688224383884 + 2.4801377339838719611e-3104j 1.8e-998, 1.8e-998j
16.732796422858206358 + 2.9852955618819557508e-3103j 4.38e-996, 4.38e-996j
33.506718725043108401 - 6.3435777636891412036e-3096j 4.8e-990, 4.8e-990j
137.34578576563540829 + 1.0380821947433763555e-3090j 8.36e-985, 8.36e-985j
31.325574640112281691 + 1.0999420611849031659e-3124j 1.32e-990, 1.32e-990j
66.667714811766090584 + 6.6940877907924742147e-3118j 4.03e-985, 4.03e-985j
43.079559786209362451 - 1.5151024188487941519e-3137j 5.32e-988, 5.32e-988j
10.050672697017210215 - 3.2465728011187870762e-3150j 3.7e-1000, 3.7e-1000j
40.556062155549956957 + 1.791734072715770728e-3138j 1.75e-988, 1.75e-988j
51.195498417479513168 + 3.4149902520279328459e-3134j 8.97e-987, 8.97e-987j
6.0165843328122930598 - 2.315925788771281448e-3174j 1.22e-1003, 1.22e-1003j
18.28884872154551651 + 1.789843500480675585e-3166j 2.42e-995, 2.42e-995j
2.3004063783774552727 + 5.2734164609559155496e-3180j 2.26e-1009, 2.26e-1009j
27.208065736087283204 + 8.5913361946654328088e-3162j 7.27e-992, 7.27e-992j
126.23592566916823706 - 5.4422540979031377978e-3154j 2.15e-984, 2.15e-984j
84.868708127938572418 - 2.241562706069838955e-3204j 3.63e-984, 3.63e-984j
73.59773398727887791 - 1.6426897370911954623e-3256j 1.2e-984, 1.2e-984j
1 - 3.4946643404776618119e-3312j 4.56e-1013, 4.56e-1013j
45.692711906531931637 - 1.4249917860218323747e-3283j 1.44e-987, 1.44e-987j
106.28630723525510472 + 3.4111910298566231773e-3307j 5.78e-984, 5.78e-984j
0.064660314517071508809 + 5.1697005623046048054e-3377j 3.35e-1019, 3.35e-1019j
8.9309352875460485885 + 2.0201692219630368874e-3358j 4.84e-1001, 4.84e-1001j
0.6961520477625844758 - 2.0609898514509853717e-3371j 2.87e-1014, 2.87e-1014j
3.4322254873132868138 + 1.8590631910153555258e-3364j 5.53e-1007, 5.53e-1007j
0.012134222919125280029 - 3.5285212742482507491e-3425j 1.37e-1020, 1.37e-1020j
176.7157214156675451 + 3.8331173416244879887e-3342j 3.22e-987, 3.22e-987j
19.919662082945873246 - 1.3758112066064709112e-3374j 1.3e-994, 1.3e-994j
0.28618501123452146971 + 1.3160469396728721652e-3396j 1.77e-1016, 1.77e-1016j
6.91063405173990844 - 3.018376798892286377e-3382j 9.45e-1003, 9.45e-1003j
15.250750985692120556 - 4.3193630173742296723e-3377j 6.96e-997, 6.96e-997j
231.55019481328052453 - 6.1420502680670935158e-3364j 3.69e-992, 3.69e-992j
120.98136368252619187 - 2.1001697800572099939e-3383j 2.93e-984, 2.93e-984j
4.5435615435460229252 + 3.7961249961329883872e-3422j 3.95e-1005, 3.95e-1005j
0.45984232167445923681 + 1.3832744773512635586e-3432j 1.94e-1015, 1.94e-1015j
0.15769548012154955374 + 3.9824370523227154877e-3435j 9.84e-1018, 9.84e-1018j

Weights

Weight (ball center) Error (ball radius)
3.8604832767610711056e-119 - 6.4854518117818322828e-2515j 1.08e-144, 5.71e-888j
1.9120124664241602207e-83 - 3.9997007268308725685e-2495j 2.68e-133, 1.42e-876j
1.6696216019064567191e-95 - 1.9876156585680723289e-2502j 6.8e-138, 3.61e-881j
3.4756648556168906475e-91 + 4.909909263496633763e-2500j 2.17e-136, 1.15e-879j
1.4436684903138517828e-111 + 5.7664504107704333202e-2511j 1.82e-143, 9.65e-887j
2.635055169450327682e-21 - 8.1575235267358582834e-2465j 2.43e-94, 1.29e-837j
1.6090791384428544611e-05 + 1.7896969273324477003e-2455j 1.29e-50, 6.85e-794j
1.0273059794429536576e-38 - 8.5143691293317684968e-2474j 7.9e-113, 4.19e-856j
2.9416953890997763052e-48 + 1.1577216621390952157e-2478j 1.19e-119, 6.32e-863j
8.5691888801270372683e-65 - 6.4290241451180186732e-2487j 1.47e-128, 7.8e-872j
1.2417645147671594246e-10 + 9.3426347066780535384e-2459j 1.3e-76, 6.9e-820j
1.3363314031725586022e-06 + 3.1061448685578653785e-2456j 1.5e-61, 7.96e-805j
1.9510182268113903651e-73 + 4.4249428727449848993e-2491j 4.58e-132, 2.43e-875j
6.6569171171890957516e-17 - 2.5338151914071202988e-2462j 4.05e-91, 2.15e-834j
3.0120615884360797006e-44 + 1.2589082772638510501e-2476j 9.26e-118, 4.92e-861j
2.4248710784547109312e-42 - 1.1805346078373572073e-2475j 1.06e-116, 5.62e-860j
3.4810572303274340559e-87 - 1.1144683963483096533e-2497j 4.76e-138, 2.53e-881j
0.00038083298043731805886 - 2.302604742087159977e-2454j 3.79e-55, 2.01e-798j
1.6909256718342174007e-40 + 1.0353473294496661517e-2474j 1.06e-115, 5.62e-859j
9.804038221213853924e-28 + 4.3194581961952678651e-2468j 1.78e-108, 9.44e-852j
0.033064427635966566884 + 1.4989886458824331928e-2452j 3.13e-35, 1.66e-778j
1.2755035093842256016e-30 + 1.3222685787658178659e-2469j 6.21e-111, 3.3e-854j
2.5602016875225553106e-35 - 4.793257077656115152e-2472j 4.42e-114, 2.35e-857j
3.7558199152568293244e-62 + 1.2839490133616919468e-2485j 1.46e-130, 7.76e-874j
2.0036751717701380802e-70 - 1.1874516237163671689e-2489j 2.65e-134, 1.41e-877j
4.9338539378972851545e-25 + 1.172479884969823174e-2466j 1.64e-109, 8.7e-853j
0.076636072647963186002 + 2.2303976611456144547e-2452j 1.74e-37, 9.26e-781j
1.5089885329444126616e-67 + 2.9066752047318732953e-2488j 4.32e-133, 2.29e-876j
6.3197701517598995406e-80 + 6.0252669333525260902e-2494j 8.69e-139, 4.62e-882j
1.7221151061096936341e-105 - 9.0118511900401665774e-2508j 4.25e-150, 2.26e-893j
9.5067285826441753493e-24 - 5.7808196527328887038e-2466j 2.46e-110, 1.31e-853j
2.3156895401738372079e-26 - 2.298961143786674289e-2467j 5.4e-112, 2.87e-855j
0.0098824454450727118363 + 1.1716611621621006426e-2452j 4.1e-64, 2.18e-807j
4.1752178291695813239e-13 - 3.4282556374734427108e-2460j 1.02e-101, 5.44e-845j
1.0599845194367653058e-33 + 3.2958613174315433431e-2471j 1.62e-117, 8.62e-861j
3.5793817803511802706e-57 + 3.8132262986192791905e-2483j 1.58e-131, 8.4e-875j
2.01515974823738658e-11 - 3.2088204266710481363e-2459j 5.14e-100, 2.73e-843j
0.10231894243203936081 - 2.947372402134136992e-2452j 4.34e-53, 2.3e-796j
6.7257203861137539813e-16 + 9.1628829406084172612e-2462j 7.03e-106, 3.74e-849j
0.0040429046522360544178 + 3.3477379052842941911e-2453j 1.01e-75, 5.34e-819j
2.278446396987339291e-50 - 9.9210316623143889066e-2480j 2.67e-128, 1.42e-871j
7.0727448114409947306e-10 - 2.636252451228554725e-2458j 2.02e-98, 1.07e-841j
4.8144640445456901487e-06 - 7.5185116075625638092e-2456j 1.99e-90, 1.05e-833j
8.2144109344897354945e-08 + 4.977550498520412406e-2457j 2.18e-95, 1.16e-838j
6.2384422798587269231e-15 - 3.1821338678151135689e-2461j 1.64e-105, 8.73e-849j
1.2958307930955375161e-59 - 2.3212111686761406926e-2484j 1.68e-133, 8.94e-877j
5.3195358910100430933e-14 + 1.0637178624693920376e-2460j 1.09e-104, 5.79e-848j
3.7339404111239801619e-29 - 7.7458694215058392346e-2469j 6.16e-117, 3.27e-860j
5.0163111809840457766e-19 - 1.6780950688039698115e-2463j 6.05e-111, 3.21e-854j
4.9878431067817191484e-05 - 4.2081677268461082515e-2455j 3.6e-94, 1.91e-837j
6.0401469566429814773e-18 + 6.7018920125570507798e-2463j 7.79e-110, 4.13e-853j
1.6605257333905442481e-22 + 2.8581014005456966232e-2465j 2.06e-113, 1.09e-856j
0.0020752673991132255367 - 1.3359111275937953651e-2453j 1.37e-91, 7.26e-835j
1.8178236891901581888e-08 - 1.9212746151482281155e-2457j 5.01e-102, 2.66e-845j
0.052563050290975029903 - 1.7697333052608153709e-2452j 1.86e-84, 9.85e-828j
3.0199572770468464387e-12 + 1.0667461633838070618e-2459j 2.86e-105, 1.52e-848j
8.0321240017641968527e-55 - 5.7160275811854979878e-2482j 1.97e-134, 1.04e-877j
5.4665819907452464195e-37 + 6.5816816928108547009e-2473j 3.43e-124, 1.82e-867j
3.8954672510640569692e-32 - 2.144090295153532705e-2470j 2.94e-121, 1.56e-864j
0.12409646152881247116 + 4.0337011247983430041e-2452j 5.95e-91, 3.16e-834j
3.8067814123954568325e-20 + 3.7795426263773383307e-2464j 6.87e-114, 3.65e-857j
3.2200472934664828406e-46 - 1.2520132710407012123e-2477j 4.3e-130, 2.28e-873j
0.069032846687033611448 - 4.2121470696793756175e-2452j 3.74e-95, 1.98e-838j
0.00014329513746297542065 + 9.8330138478533246998e-2455j 1.65e-103, 8.75e-847j
0.13464589630673996743 - 5.6185098033820494862e-2452j 2.02e-95, 1.07e-838j
0.018850073494929114727 - 1.3633253517850275858e-2452j 8.13e-99, 4.32e-842j
0.030912549228056314946 + 1.2939002574498986144e-2452j 1.83e-95, 9.74e-839j
1.3467416200758646274e-76 - 1.559084933093988277e-2492j 1.97e-146, 1.05e-889j
3.7266391440759507694e-09 + 7.2190886929784696241e-2458j 1.13e-108, 6.02e-852j
0.11091016379814083169 - 8.493207015449587779e-2452j 5.15e-99, 2.73e-842j
0.0009321090230911359504 + 5.468076901588766551e-2454j 6.51e-104, 3.45e-847j
3.4405931103596889445e-07 - 1.2576886410590918036e-2456j 2.36e-107, 1.25e-850j
3.1703261615978667935e-100 + 5.6403243413498935122e-2505j 8.81e-159, 4.68e-902j
1.4830365426578211834e-52 + 7.8511719010490446993e-2481j 4.07e-134, 2.16e-877j
0.0063340526022264571751 - 7.5072244196051951431e-2453j 1.26e-104, 6.69e-848j
0.1282198954240546499 + 7.5254672621523302884e-2452j 1.32e-103, 7.03e-847j
0.09488614430435244719 + 7.161180499646438394e-2452j 1.53e-103, 8.05e-847j

Download

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