Rule: Q[2, 74]

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)
261.06915578711749129 - 1.2965413763787528161e-2179j 8.4e-995, 8.4e-995j
213.4866003682986949 + 2.7146023264769626237e-2173j 7.26e-990, 7.26e-990j
234.56470671822387795 + 5.3300974944223005657e-2178j 6.22e-992, 6.22e-992j
278.86245722366736788 - 1.1190805116775964351e-2191j 7.66e-997, 7.66e-997j
246.85635555905321252 - 8.7171288642122029078e-2183j 3.15e-993, 3.15e-993j
32.806642809222985462 + 7.4136343194562901562e-2205j 3.53e-990, 3.53e-990j
91.095724987167653375 - 1.5384983498972547633e-2198j 1.2e-983, 1.2e-983j
87.052985388698986036 - 1.3294736760511449038e-2252j 9.74e-984, 9.74e-984j
139.91697340953710011 + 7.299644572355999561e-2298j 1.82e-984, 1.82e-984j
99.584117696554665909 + 3.7439690671122711855e-2324j 1.43e-983, 1.43e-983j
72.114728484319082362 - 1.3993289253124938597e-2348j 1.97e-984, 1.97e-984j
104.04105961992720478 + 1.5622258172737036597e-2377j 1.44e-983, 1.44e-983j
17.850513506845513241 - 1.4963021140772601377e-2423j 1.17e-995, 1.17e-995j
35.030474436740421827 - 8.2125115166834240422e-2412j 1.34e-989, 1.34e-989j
26.618936678335229828 - 1.7753011133530862266e-2422j 5.1e-992, 5.1e-992j
16.319709129583714865 + 4.8130594392341803152e-2434j 1.93e-996, 1.93e-996j
19.45444690630394304 + 8.8252319779000311286e-2433j 7e-995, 7e-995j
62.097730796591089542 - 1.6081546506790207205e-2421j 3.26e-985, 3.26e-985j
79.345789849197819197 + 1.4157711953523776759e-2493j 4.86e-984, 4.86e-984j
128.73757037178901411 + 1.4836990557442415406e-2565j 4.98e-984, 4.98e-984j
7.5918905138957018858 + 8.7868784420510044523e-2623j 1.11e-1002, 1.11e-1002j
10.912867508800772181 - 7.1782864741708005696e-2620j 7.37e-1000, 7.37e-1000j
134.22284495053401582 - 3.8336795289353886656e-2603j 3.07e-984, 3.07e-984j
50.167017675987897207 - 2.8339709675423765803e-2623j 1.2e-986, 1.2e-986j
8.6301049427671878104 + 2.6698226245970183234e-2638j 1.06e-1001, 1.06e-1001j
223.55275659843147951 + 2.0988288164531597197e-2620j 7.87e-991, 7.87e-991j
179.49838008204231249 - 1.9362185467555298838e-2624j 6.23e-987, 6.23e-987j
172.13404793791702663 - 1.9007152715930149796e-2655j 2.14e-986, 2.14e-986j
108.64831493527403697 - 1.2786884806291158976e-2714j 1.4e-983, 1.4e-983j
113.41309272556565378 - 6.3670444206768675691e-2796j 1.21e-983, 1.21e-983j
158.41297897070853751 + 7.8982612641302920252e-2868j 1.76e-985, 1.76e-985j
42.204847318882713845 - 1.1618718690508558181e-2908j 5.13e-988, 5.13e-988j
13.474410378977341738 - 1.4996416338355880352e-2940j 3.99e-998, 3.99e-998j
12.158496290956021528 + 1.300589025029031032e-2938j 5.64e-999, 5.64e-999j
204.16415367749320477 - 8.1935477591425942028e-2924j 5.46e-989, 5.46e-989j
145.83478807359849988 + 3.3081298489431459496e-2956j 9.7e-985, 9.7e-985j
47.422508317159559263 - 7.2152487419914253774e-2972j 4.17e-987, 4.17e-987j
21.132341570126247982 + 6.8510609495053610812e-2980j 4.14e-994, 4.14e-994j
3.4142135623730950488 - 6.9567148255116398994e-2993j 5.45e-1008, 5.45e-1008j
39.728082673983784153 + 1.0224040143818194761e-2973j 1.6e-988, 1.6e-988j
24.713614337975222595 + 3.4549070213468751071e-2978j 1.03e-992, 1.03e-992j
58.9675914220243821 + 2.8718826412015250096e-2971j 1.57e-985, 1.57e-985j
1.7052773486091572778 - 2.8224273932866087398e-2997j 1.55e-1011, 1.55e-1011j
14.861252403269218809 + 6.6004655188992497453e-2983j 3.08e-997, 3.08e-997j
5.7193777303360611292 - 5.9029027107398994001e-2991j 1.05e-1004, 1.05e-1004j
95.270975741009977189 - 2.1151415495578455356e-2967j 1.37e-983, 1.37e-983j
123.448213990731038 + 2.285529943821181152e-2979j 7.4e-984, 7.4e-984j
1.2668843681339582692 + 4.1646451078121336836e-3023j 8.38e-1013, 8.38e-1013j
0.89377465019017410715 + 8.1879904277376152816e-3024j 5.3e-1014, 5.3e-1014j
6.6217971113119087705 + 4.9678087005251021315e-3014j 1.11e-1003, 1.11e-1003j
37.337138565607375082 + 1.149925074421124907e-2998j 4.75e-989, 4.75e-989j
68.668382349903048033 - 6.7594689529147725448e-2995j 1.13e-984, 1.13e-984j
30.664283008161076244 + 1.0760854868066768085e-3000j 9.34e-991, 9.34e-991j
2.2091445191849165668 + 4.1200160792880301839e-3020j 2.56e-1010, 2.56e-1010j
44.769073088045836155 + 2.3998304361218504469e-2997j 1.58e-987, 1.58e-987j
118.34340766437300646 + 8.6131872515673931435e-2993j 9.85e-984, 9.85e-984j
195.4511974999346064 + 3.0703925400505828882e-3001j 3.1e-988, 3.1e-988j
187.25274261004889822 + 6.5631450103029894267e-3015j 1.49e-987, 1.49e-987j
9.7369236648845383681 + 1.0567844526929951864e-3061j 8.72e-1001, 8.72e-1001j
0.5857864376269049512 + 4.1503445783033813516e-3076j 2.35e-1015, 2.35e-1015j
2.7787063884951352354 - 5.7488087587887838518e-3071j 4.12e-1009, 4.12e-1009j
83.137841780951561501 - 2.356201201928882715e-3044j 7.17e-984, 7.17e-984j
151.99344387087608422 + 4.9966408623758015633e-3089j 4.13e-985, 4.13e-985j
4.1159473485417607081 - 1.5194877331550307031e-3132j 8.01e-1007, 8.01e-1007j
65.330391142119146869 - 5.8611904432496543649e-3109j 6.17e-985, 6.17e-985j
4.8842204473155191943 - 7.3005371794346265322e-3146j 9.53e-1006, 9.53e-1006j
75.672690109270534456 + 5.5651959551299121646e-3120j 3.18e-984, 3.18e-984j
0.0028704695436498995252 + 1.70277585717381964e-3173j 1.74e-1021, 1.74e-1021j
22.885083289874908664 + 1.9298584496325821971e-3145j 2.07e-993, 2.07e-993j
0.051373226153329005846 + 7.4321969219734036764e-3172j 9.45e-1020, 9.45e-1020j
0.34278691433017923467 + 1.5776024493879731588e-3169j 8.2e-1017, 8.2e-1017j
28.602115485797237375 + 5.6123531425300552819e-3144j 2.12e-991, 2.12e-991j
55.937357719501365197 + 4.9586324110127846452e-3136j 6.79e-986, 6.79e-986j
165.11706689994030256 - 3.1373645526662033563e-3146j 6.75e-986, 6.75e-986j
53.004591744331474119 - 1.0324458983180628388e-3163j 3.22e-986, 3.22e-986j
0.1646725575802100936 + 4.0581819284895052563e-3195j 3.23e-1018, 3.23e-1018j

Weights

Weight (ball center) Error (ball radius)
6.4712076134812398474e-113 - 2.1868068731184473227e-2270j 3.27e-137, 1.52e-882j
1.8589402663464708607e-92 - 4.9088786421230377665e-2260j 3.2e-131, 1.49e-876j
1.5614909603683287827e-101 - 1.2470189066239732953e-2264j 3.4e-134, 1.58e-879j
1.6324978029593709368e-120 + 3.1691938961795334564e-2274j 1.33e-140, 6.19e-886j
8.1096840278708946118e-107 + 2.646453055074178979e-2267j 7.21e-136, 3.36e-881j
1.2339145899402757949e-14 - 4.5891488762791967415e-2219j 2.3e-78, 1.07e-823j
1.1253159202728953501e-39 - 4.3364957713896067894e-2233j 5.17e-109, 2.41e-854j
6.2094176741025492466e-38 + 3.481079728693428062e-2232j 8.15e-108, 3.8e-853j
9.965685962671677409e-61 - 6.588211111898239209e-2244j 7.23e-123, 3.37e-868j
2.4719443378556430352e-43 - 5.54500754335374811e-2235j 2.03e-112, 9.46e-858j
1.6797188260258301832e-31 + 8.0734523701888555707e-2229j 6.85e-105, 3.19e-850j
2.9630023095240557377e-45 + 5.6567122633947226866e-2236j 5.87e-114, 2.73e-859j
2.7717526397368172098e-08 - 9.4045855582235690255e-2217j 3.8e-69, 1.77e-814j
1.3852531828189393442e-15 - 1.3731940986423911496e-2219j 1.84e-86, 8.57e-832j
5.3487715173876852325e-12 + 3.1102730590532078399e-2218j 8.58e-80, 4e-825j
1.2216240873745998431e-07 + 1.7958901252464516083e-2216j 9.89e-68, 4.61e-813j
5.8356470853820213209e-09 + 4.8200877843589241802e-2217j 6.03e-72, 2.81e-817j
3.4186512321920299656e-27 - 1.5690098913972112724e-2226j 5.16e-103, 2.4e-848j
1.2956657033029409914e-34 + 1.8739970983682037032e-2230j 1.73e-108, 8.09e-854j
6.625115577030514336e-56 - 1.9232364285290188583e-2241j 8.41e-124, 3.92e-869j
0.00050658300624995856177 - 7.6807550020811878842e-2215j 3.16e-56, 1.48e-801j
2.2061482936356284631e-05 + 1.834959298283605917e-2215j 4.18e-64, 1.95e-809j
2.8508137646868315317e-58 + 1.1851749151957055869e-2242j 5.2e-125, 2.43e-870j
4.5546398082370137159e-22 - 9.8428250574775878319e-2224j 1.3e-100, 6.04e-846j
0.00019158574520790641704 + 4.9170436048100161991e-2215j 4.19e-61, 1.95e-806j
8.5774097848247176644e-97 + 3.1259137861585989958e-2262j 1.71e-141, 7.97e-887j
8.3728304761610079367e-78 - 1.3311245253322179027e-2252j 4.17e-136, 1.95e-881j
1.2575291107607603677e-74 + 5.4767389787757930697e-2251j 6.91e-135, 3.22e-880j
3.0571936882932309861e-47 - 5.3636631354930472439e-2237j 7.39e-121, 3.44e-866j
2.6959718936633188955e-49 + 4.7093245449261475716e-2238j 1.96e-122, 9.12e-868j
1.0443758159923118431e-68 + 5.6248327848199528498e-2248j 2.49e-133, 1.16e-878j
1.180605926388255995e-18 + 9.3751838977859051688e-2222j 7.34e-104, 3.42e-849j
1.900549586191192508e-06 + 6.071528317450915461e-2216j 9.46e-82, 4.41e-827j
6.7153504299189626859e-06 - 1.0710593100204436289e-2215j 6.32e-80, 2.95e-825j
1.9357115016637449103e-88 + 5.3337110216265968049e-2258j 9.35e-142, 4.36e-887j
2.7889765097522625231e-63 + 3.2790333652692294003e-2245j 1.54e-130, 7.18e-876j
6.8519329002584023568e-21 + 4.5542923791629838918e-2223j 2.99e-107, 1.39e-852j
1.1393228670822564034e-09 - 2.428779603360327224e-2217j 1.08e-92, 5.04e-838j
0.021997505095386011925 + 4.3750772842426029147e-2214j 1.08e-68, 5.02e-814j
1.3569387521972839804e-17 - 4.3331332449290531976e-2221j 4.3e-104, 2e-849j
3.4522392421484388444e-11 - 6.0611322280970135988e-2218j 5.07e-96, 2.36e-841j
7.5721315575584027269e-26 + 8.3073889712316009519e-2226j 3.24e-112, 1.51e-857j
0.085608461880561106898 - 8.1816168125722379999e-2214j 3.86e-64, 1.8e-809j
4.999215616603518843e-07 - 3.3463284604073119534e-2216j 2.37e-88, 1.1e-833j
0.0028509323025657328211 - 1.7019233774493214038e-2214j 2.73e-79, 1.27e-824j
1.7866536947736726448e-41 + 5.0695917823417721674e-2234j 1.28e-120, 5.99e-866j
1.2668721171664768664e-53 + 2.8337108008514021909e-2240j 1.79e-127, 8.36e-873j
0.11429510625245076257 + 9.3289993464689834859e-2214j 1.16e-67, 5.42e-813j
0.13931146651729017981 - 1.0184794423804893037e-2213j 1.16e-67, 5.41e-813j
0.0012460964648833037293 + 1.1620486136208425379e-2214j 4.51e-83, 2.1e-828j
1.4304989658672379821e-16 + 2.1578212813533639498e-2220j 2.13e-104, 9.91e-850j
5.1063543461904228962e-30 - 4.9041660586863235251e-2228j 5.24e-116, 2.44e-861j
1.0123147514996079021e-13 + 1.227427954074172132e-2218j 2.3e-102, 1.07e-847j
0.058924012969717700673 + 6.8934539733591488867e-2214j 1.1e-78, 5.12e-824j
9.4066370348786601157e-20 - 2.0705074654402654362e-2222j 9.05e-108, 4.22e-853j
2.0158911492475387079e-51 - 3.8128972819544738406e-2239j 9.01e-127, 4.2e-872j
1.1042891181371814865e-84 - 4.2841743011593970577e-2256j 1.43e-144, 6.69e-890j
3.7880931609974349984e-81 + 2.6661388076464237308e-2254j 4.6e-143, 2.14e-888j
6.7406888459388530649e-05 - 3.0504116074390824666e-2215j 2.31e-96, 1.08e-841j
0.15334761405799232747 + 1.0587023830498790141e-2213j 3.42e-86, 1.59e-831j
0.037425977148440919778 - 5.5923570442822924509e-2214j 3.86e-90, 1.8e-835j
3.0163340210249083184e-36 - 2.6295297496257533986e-2231j 2.45e-121, 1.14e-866j
6.1436237694487276128e-66 - 1.4487006893059209425e-2246j 3.33e-136, 1.55e-881j
0.011987366632273982765 - 3.3044653115439792329e-2214j 7.57e-96, 3.53e-841j
1.3927907947571814084e-28 + 2.8382692143563435677e-2227j 3.14e-118, 1.46e-863j
0.0060645350615925563181 + 2.4116717375830928423e-2214j 8.15e-98, 3.8e-843j
4.9415931495821318131e-33 - 1.26321243408586345e-2229j 3.13e-120, 1.46e-865j
0.016274695283226863106 + 3.0013764379936766212e-2214j 1.58e-97, 7.36e-843j
2.0611174666875958167e-10 + 1.2118551055348610404e-2217j 2.84e-107, 1.33e-852j
0.076851363501331636716 - 7.3281447199825472876e-2214j 1.05e-97, 4.91e-843j
0.14944062551971189926 - 1.0372758778818694161e-2213j 7.41e-98, 3.46e-843j
7.65848775140495686e-13 - 1.7262122303230626316e-2218j 3.44e-109, 1.6e-854j
1.5173712378223346053e-24 - 4.225652795517874328e-2225j 3.06e-117, 1.43e-862j
1.3384407288768380981e-71 - 1.8967186916499051849e-2249j 2.75e-141, 1.28e-886j
2.7574937088597153531e-23 + 2.0723727404956895355e-2224j 1.38e-116, 6.42e-862j
0.12357733126637467541 + 9.3724248552579134337e-2214j 7.38e-104, 3.44e-849j

Download

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