Rule: Q[2, 4, 71]

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.

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)
256.55986045017809065 + 1.2119025609729549539e-2783j 3.87e-995, 3.87e-995j
219.2811297096255626 - 1.2462860221538438069e-2773j 3.43e-991, 3.43e-991j
230.2198616810137693 - 5.4567700479819500621e-2779j 2.72e-992, 2.72e-992j
274.25091726820898488 + 1.8816632615351136979e-2796j 3.84e-997, 3.84e-997j
200.0295481177935624 - 4.6090250690429944782e-2817j 2.3e-989, 2.3e-989j
19.792005915016098967 - 3.5986015471115153333e-2872j 1.85e-994, 1.85e-994j
92.222863149049019369 - 6.7995850454301231064e-2905j 5.38e-984, 5.38e-984j
130.70126230134405073 - 3.8047526214515308115e-2958j 1.31e-984, 1.31e-984j
62.771279656863614378 - 7.5052744327836110705e-2980j 2.2e-985, 2.2e-985j
26.976770789569045567 - 3.9798083677105682938e-3016j 8.77e-992, 8.77e-992j
21.473210553792172339 + 1.4547954028420249639e-3018j 8.67e-994, 8.67e-994j
6.9239565457104964806 + 1.4842063537780575035e-3026j 1.06e-1002, 1.06e-1002j
33.1954405296998864 + 5.9539891225215150746e-3013j 4.8e-990, 4.8e-990j
66.046730604994257454 - 3.8978148349080604611e-3007j 4.12e-985, 4.12e-985j
105.42184137332322333 + 5.9939125802396616307e-3048j 5.87e-984, 5.87e-984j
23.230308182255057244 - 2.4734062403239253898e-3084j 4.07e-993, 4.07e-993j
35.433315940541938267 - 5.1936524029142549854e-3081j 1.81e-989, 1.81e-989j
11.238299796934599835 - 8.4809624547468496578e-3091j 3.83e-999, 3.83e-999j
53.568864356874890963 + 1.09829418904606676e-3075j 2.46e-986, 2.46e-986j
45.249575853113048312 + 4.9199046561798881126e-3084j 1.6e-987, 1.6e-987j
209.28474492659645704 + 1.9953859599334175133e-3109j 3.19e-990, 3.19e-990j
148.29380151746947718 - 1.3645003875560943356e-3146j 1.84e-985, 1.84e-985j
80.270354300827786516 + 1.6549742780278798906e-3167j 2.66e-984, 2.66e-984j
175.55563525469061418 - 5.1166325071991170339e-3191j 2.76e-987, 2.76e-987j
12.486507079040894342 + 2.1498054287479526174e-3237j 2.55e-998, 2.55e-998j
120.04462608672711085 - 3.1878595640591224599e-3222j 3.05e-984, 3.05e-984j
13.804351333886423627 + 2.4642015345628712101e-3260j 1.71e-997, 1.71e-997j
10.058798621722378759 - 1.7496122688256295202e-3262j 5.11e-1000, 5.11e-1000j
242.4332962807959244 + 3.5116715873937211778e-3247j 1.46e-993, 1.46e-993j
56.53503614572984612 - 2.1163434112819301667e-3247j 5.44e-986, 5.44e-986j
47.928318419677678761 - 5.0377245845564648217e-3253j 3.99e-987, 3.99e-987j
191.38192803484327757 + 1.6443772682308386896e-3251j 1.38e-988, 1.38e-988j
1.9068679500385456545 - 9.0664383401795287205e-3300j 3.96e-1010, 3.96e-1010j
42.662505450956214576 - 5.2229921951899811532e-3276j 5.35e-988, 5.35e-988j
154.65338858809373684 - 1.1850209515383345946e-3273j 7.51e-986, 7.51e-986j
84.124982118652852849 - 1.5951628007101695699e-3286j 3.64e-984, 3.64e-984j
16.652872089049288866 + 1.4937457898842908834e-3301j 6.43e-996, 6.43e-996j
3.4142135623730950488 - 3.9591992517525937759e-3312j 5.04e-1006, 5.04e-1006j
3.044505322586287243 + 2.1481087354579889723e-3312j 4.77e-1007, 4.77e-1007j
183.24732196928338721 + 1.4493513433924034109e-3289j 6.3e-988, 6.3e-988j
168.25304636849327882 + 1.1008316125700673804e-3311j 8.93e-987, 8.93e-987j
28.968527628200095829 + 5.9567484497403003499e-3341j 3.52e-991, 3.52e-991j
18.185586820714430903 - 8.5569455198415564931e-3346j 3.49e-995, 3.49e-995j
0.68194558862039863547 - 3.0384109770518766945e-3363j 1.81e-1013, 1.81e-1013j
72.927309087632371615 - 2.8669814479904446812e-3333j 1.15e-984, 1.15e-984j
161.29706568435600279 + 1.0264757686442956898e-3365j 2.88e-986, 2.88e-986j
37.756069264393559655 - 3.4917315379352825862e-3408j 6.49e-989, 6.49e-989j
114.99879093497830926 + 1.6069613918445070091e-3413j 4.26e-984, 4.26e-984j
0.47193845768537280597 - 7.0021483598747050646e-3499j 1.11e-1014, 1.11e-1014j
15.192804546561252503 + 9.0851720377229556366e-3481j 1.04e-996, 1.04e-996j
88.107523965009545652 - 3.1379166394531924052e-3467j 4.36e-984, 4.36e-984j
142.19473757440438185 - 3.8539076786510099112e-3516j 3.77e-985, 3.77e-985j
40.165251417067778274 - 2.2932634976628868486e-3555j 1.77e-988, 1.77e-988j
5.1621868255721773363 - 5.053517774215975228e-3574j 1.59e-1004, 1.59e-1004j
8.9471212919668647026 - 2.2432268868831810357e-3570j 7.03e-1001, 7.03e-1001j
96.476346310096399417 - 1.9927546338757846752e-3552j 5.83e-984, 5.83e-984j
136.33624977529986757 + 1.7884678356453319593e-3586j 7.68e-985, 7.68e-985j
69.430995569495565264 + 5.3220494448692082685e-3605j 7.46e-985, 7.46e-985j
110.12749869762819864 + 3.2687819079854187669e-3620j 5.09e-984, 5.09e-984j
7.9024371868127594172 + 1.6687637922768309317e-3662j 8.51e-1002, 8.51e-1002j
25.064436807985190912 - 6.7717219988400410801e-3653j 1.95e-992, 1.95e-992j
50.700710866620564595 + 2.0410354033692013045e-3644j 1.02e-986, 1.02e-986j
1.4425402026763935962 - 2.5724706141504132084e-3675j 2.12e-1011, 2.12e-1011j
1.0406748406401594478 + 1.5203714025252890948e-3676j 1.35e-1012, 1.35e-1012j
2.4365356063033129306 + 2.1476769218045049255e-3673j 9.52e-1009, 9.52e-1009j
3.6239863863396469522 - 6.265132247694807421e-3670j 8.72e-1006, 8.72e-1006j
59.601643572278379137 + 7.9529578869117377982e-3648j 1.1e-985, 1.1e-985j
0.018838346879704572148 - 3.0058678357919509316e-3744j 1.37e-1020, 1.37e-1020j
100.87384701138318167 - 9.9787952266618683642e-3686j 6e-984, 6e-984j
4.3755228402662420656 - 6.4168844365695430579e-3749j 2.44e-1005, 2.44e-1005j
0.5857864376269049512 + 2.5097083523237978453e-3757j 9.13e-1014, 9.13e-1014j
31.040975392106020544 + 8.8922562896845572376e-3728j 1.38e-990, 1.38e-990j
125.27501235557523945 - 2.8004437177125703937e-3732j 2.13e-984, 2.13e-984j
6.0108786995830601177 - 1.4666034689375468993e-3772j 1.36e-1003, 1.36e-1003j
76.539166692284585545 - 7.9041326066037612895e-3752j 1.93e-984, 1.93e-984j
0.24564089761650009396 + 8.3854536265464147828e-3796j 5.15e-1017, 5.15e-1017j
0.099430039245156716455 - 7.4152980150969544257e-3797j 1.07e-1018, 1.07e-1018j

Weights

Weight (ball center) Error (ball radius)
5.8447943293080226306e-111 + 1.3448525361869154715e-2877j 1.93e-148, 6.45e-891j
6.1029549284835603774e-95 + 3.8903591940327491181e-2868j 1.2e-143, 4.02e-886j
1.1957636836719427788e-99 + 2.7227802901373057621e-2871j 3.27e-145, 1.09e-887j
1.6337613903901675534e-118 - 1.289342714196606867e-2881j 1.22e-151, 4.06e-894j
1.2002451992822970675e-86 + 6.983510064773379459e-2865j 1.3e-141, 4.33e-884j
4.1710461745469379481e-09 + 1.2781971729576282644e-2824j 2.51e-73, 8.37e-816j
3.7124188232904369534e-40 + 1.3138296992606709071e-2841j 3.51e-120, 1.17e-862j
9.5445796009082233531e-57 + 3.9591982450075861448e-2850j 1.84e-130, 6.13e-873j
1.7656862293031380269e-27 + 6.1484775705149735067e-2835j 2.94e-109, 9.81e-852j
3.7547514564302165852e-12 + 1.891671187704180622e-2826j 6.63e-85, 2.21e-827j
8.1202607624676378938e-10 - 4.6864351642920834743e-2825j 4.14e-78, 1.38e-820j
0.00093044234611609369801 + 6.9391438908754970539e-2821j 2.58e-48, 8.63e-791j
8.4143829966940186155e-15 - 5.5637045314649455143e-2828j 1.89e-91, 6.3e-834j
6.8964787926395030008e-29 - 1.0915668343530095507e-2835j 2.25e-111, 7.52e-854j
7.6039822898615006142e-46 - 1.4963591255705141275e-2844j 1.33e-125, 4.43e-868j
1.4634286654091983654e-10 + 1.662940102870036345e-2825j 8.62e-82, 2.88e-824j
9.3208019384822652109e-16 + 1.5947804971716062533e-2828j 4.78e-94, 1.6e-836j
1.5972790981133394456e-05 + 2.8267818004161671079e-2822j 2.98e-66, 9.95e-809j
1.585771198276468229e-23 - 8.2065875043251288499e-2833j 1.51e-106, 5.04e-849j
5.871400367347960038e-20 + 7.2657444179940670468e-2831j 5.81e-102, 1.94e-844j
1.2331755897483283461e-90 - 1.2164406768766999225e-2866j 8.19e-147, 2.73e-889j
2.4604268362697228635e-64 - 5.7669659282900334008e-2854j 4.4e-138, 1.47e-880j
5.2229827236850964494e-35 - 6.3974281837398852081e-2839j 3.36e-120, 1.12e-862j
4.2814814932058201879e-76 - 8.0689488581051975045e-2860j 3.28e-143, 1.1e-885j
4.8457442058870791757e-06 - 1.2275742836361647795e-2822j 5.03e-77, 1.68e-819j
3.7664759986764103472e-52 + 8.7025585799439525364e-2848j 3.28e-132, 1.1e-874j
1.3681665221225090419e-06 + 5.2076893199502787432e-2823j 1.23e-79, 4.11e-822j
4.9033635075072005904e-05 - 6.3811586940062223897e-2822j 1.36e-73, 4.53e-816j
6.7174412315959057028e-105 - 2.6770582754375605497e-2874j 2.95e-153, 9.86e-896j
8.4444848967211705486e-25 + 1.683547108549920122e-2833j 5.58e-112, 1.86e-854j
4.1725206362303114586e-21 - 1.7028973190418304833e-2831j 2.98e-108, 9.97e-851j
6.4122668171089464017e-83 - 3.9371379079699028148e-2863j 1.01e-145, 3.37e-888j
0.073747060735876300901 + 3.8452998550760987993e-2819j 3.63e-52, 1.21e-794j
7.5346200761402967612e-19 - 2.9720000644053177141e-2830j 9.68e-107, 3.23e-849j
4.4424592998921799345e-67 + 2.4210358274574382575e-2855j 1.72e-140, 5.75e-883j
1.1429506598786625473e-36 + 8.6453989133464741311e-2840j 1.49e-124, 4.98e-867j
8.7648422258257010575e-08 + 8.6527819603666951629e-2824j 3.55e-91, 1.19e-833j
-0.0080879263250517519892 - 1.3575701757101499443e-2818j 5.44e-68, 1.82e-810j
0.032247010643218090412 + 7.5530385827739845827e-2819j 3.34e-66, 1.11e-808j
2.0629684719647442449e-79 + 1.9290531794749172633e-2861j 4.18e-145, 1.4e-887j
6.04354063232544474e-73 + 2.8914617151194230516e-2858j 3.4e-143, 1.13e-885j
5.3336893375275397753e-13 - 6.0546067070738186315e-2827j 5.12e-104, 1.71e-846j
1.9853200534764214454e-08 - 3.377135376221931632e-2824j 5.92e-96, 1.98e-838j
0.21405220158164103773 - 3.1184449028631806285e-2818j 1.78e-68, 5.94e-811j
7.5635544373151928943e-32 - 2.9467654084964933097e-2837j 2.68e-123, 8.96e-866j
6.0498300283558979509e-70 - 8.9555032062529877119e-2857j 2.59e-142, 8.64e-885j
9.4777985679808654848e-17 - 4.3989717427067034693e-2829j 3.69e-110, 1.23e-852j
5.6477831398215327894e-50 - 1.1302957804756455752e-2846j 4.38e-135, 1.46e-877j
0.19797785529641037143 - 2.0832998762446887489e-2818j 3.39e-76, 1.13e-818j
3.5924139207861806846e-07 - 2.1526075232738728561e-2823j 5.73e-98, 1.91e-840j
2.2010944730628367612e-38 - 1.0997697913362096213e-2840j 2.08e-128, 6.93e-871j
1.0519613144568716713e-61 + 1.2208924064797178818e-2852j 2.05e-140, 6.85e-883j
8.8336295601683136782e-18 + 1.1666304395375526301e-2829j 1.65e-113, 5.52e-856j
0.0046808446211970139138 + 3.814170484951260334e-2820j 8.81e-94, 2.94e-836j
0.00014026588498175438009 + 1.4191065032873445986e-2821j 1.09e-97, 3.63e-840j
5.4549101791358462933e-42 - 1.4702574279087303083e-2842j 1.71e-131, 5.72e-874j
3.5411234431320788693e-59 - 2.3150521737676976158e-2851j 9.02e-140, 3.01e-882j
2.4156055495903505797e-30 + 1.8413823275123132578e-2836j 4.14e-125, 1.38e-867j
7.1171326774440985494e-48 + 1.352299528208710798e-2845j 7.52e-135, 2.51e-877j
0.00037407675858491147214 - 3.1319311508625549533e-2821j 6.6e-103, 2.2e-845j
2.4389261530292977887e-11 - 5.7059537141856219325e-2826j 2.13e-111, 7.11e-854j
2.6989584180773301507e-22 + 3.8221859784539279691e-2832j 3.92e-120, 1.31e-862j
0.10222605048815651442 - 4.6156944560136971544e-2819j 8.86e-98, 2.96e-840j
0.13148981144852776839 + 6.9237892710481936575e-2819j 3.84e-97, 1.28e-839j
0.049322387062458453399 - 3.9513929631376045565e-2819j 1.11e-99, 3.71e-842j
0.022548446060001296173 + 8.9719045880848577444e-2819j 3.8e-101, 1.27e-843j
4.06598526097282504e-26 - 3.2957448279885710871e-2834j 6.01e-123, 2.01e-865j
0.047459551380798293546 + 3.157541626957204176e-2820j 2.41e-102, 8.03e-845j
6.9423923509205854653e-44 + 1.5369620522027263771e-2843j 1.76e-133, 5.88e-876j
0.009534661110886623082 - 1.1026239328211411047e-2819j 1.38e-105, 4.59e-848j
-0.12423874341012829943 + 4.5101236527510137947e-2818j 5.57e-102, 1.86e-844j
6.9826852218514854904e-14 + 1.8694224327805499347e-2827j 6.23e-116, 2.08e-858j
2.0901623938835214104e-54 - 6.1447256896440620116e-2849j 3.96e-139, 1.32e-881j
0.0021593549081312231091 - 1.5748303188531384602e-2820j 3.74e-109, 1.25e-851j
2.1097488800372684701e-33 + 4.4658299946147445895e-2838j 6.51e-128, 2.17e-870j
0.14104691651410180072 + 3.5559169031985922924e-2819j 7.12e-108, 2.38e-850j
0.10231804065612164101 - 1.2758618436266189913e-2819j 2.91e-108, 9.69e-851j

Download

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