Rule: Q[1, 3, 83]

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)
316.52621150348662476 - 1.45244570921181997e-4685j 2.81e-2015, 2.81e-2015j
297.92304325824688863 + 7.6478521212817707218e-4694j 3.91e-2013, 3.91e-2013j
204.16320503761899965 + 1.1994069403030374987e-4739j 5.81e-2004, 5.81e-2004j
258.55057613808531529 - 4.396319791359866143e-4837j 6.65e-2009, 6.65e-2009j
270.13034517621675992 - 1.4476967237681163076e-4972j 4.26e-2010, 4.26e-2010j
116.7286608610741427 - 2.6609174959680989892e-5101j 5.86e-2000, 5.86e-2000j
283.03247992064303823 - 1.3702387453887072689e-5214j 1.85e-2011, 1.85e-2011j
130.91310414419264609 - 2.2677717975882341886e-5302j 4.15e-2000, 4.15e-2000j
67.676977941765357192 - 5.2230829669938817848e-5356j 5.53e-2002, 5.53e-2002j
47.942976448823916914 + 6.6425526977108397442e-5390j 9.35e-2005, 9.35e-2005j
7.0593572325302353609 + 3.2622403370208524636e-5433j 4.72e-2022, 4.72e-2022j
30.06876168268049784 + 4.3769697169431639488e-5416j 3.52e-2009, 3.52e-2009j
36.223976955845361193 + 3.3473782273254985667e-5422j 2.06e-2007, 2.06e-2007j
247.94665198597654811 - 3.086165586115082109e-5479j 8.35e-2008, 8.35e-2008j
28.157195442378860435 - 1.0196247580884906196e-5538j 7.31e-2010, 7.31e-2010j
11.546836695475976664 - 1.5235320533772594955e-5548j 3.86e-2018, 3.86e-2018j
24.539407276527417384 - 5.5611230760183854755e-5543j 3.2e-2011, 3.2e-2011j
45.448022787426861854 + 3.7104611262242597338e-5555j 3.03e-2005, 3.03e-2005j
112.27407312800446741 + 7.7472176968839347201e-5624j 5.83e-2000, 5.83e-2000j
64.603471413273722833 + 2.0968509521468801311e-5673j 2.43e-2002, 2.43e-2002j
6.2540205609881558815 - 6.230965703130624996e-5723j 3.76e-2023, 3.76e-2023j
43.029840543000792293 - 1.5578528476275475725e-5702j 9.13e-2006, 9.13e-2006j
141.11646310777846334 + 1.4210761631998983104e-5698j 2.22e-2000, 2.22e-2000j
21.190727398777671878 - 1.9973226487514403546e-5725j 1.35e-2012, 1.35e-2012j
238.10895433139986867 - 3.4245327093642608006e-5712j 6.82e-2007, 6.82e-2007j
50.516002566738903548 + 5.6733478006398194131e-5735j 2.57e-2004, 2.57e-2004j
40.687201293566113625 - 1.2989745597538990594e-5736j 2.79e-2006, 2.79e-2006j
10.445550355559114992 - 4.2145431787355915633e-5749j 6.25e-2019, 6.25e-2019j
58.717716548976395855 + 2.111522180225024213e-5733j 4.86e-2003, 4.86e-2003j
220.21629216234574552 + 1.1085537538378701641e-5729j 2.83e-2005, 2.83e-2005j
53.168479434515349654 + 8.8952349221353081531e-5761j 7.01e-2004, 7.01e-2004j
13.970759988920594402 - 6.2367361531754628738e-5774j 1.62e-2016, 1.62e-2016j
80.88951679591421162 + 1.1146043379899424438e-5756j 6.32e-2001, 6.32e-2001j
228.8983187667061523 + 3.0064194736026506906e-5821j 4.98e-2006, 4.98e-2006j
196.69194412467756639 - 2.6482762995203351356e-5909j 2.32e-2003, 2.32e-2003j
121.31621375382276133 + 8.7314440605142965018e-5966j 5.51e-2000, 5.51e-2000j
22.831748290133544681 - 6.3455644636474890136e-5999j 6.19e-2012, 6.19e-2012j
8.567771575364328415 - 2.6926599357908784882e-6007j 2.2e-2020, 2.2e-2020j
15.283901830357781014 - 2.733234862769329393e-6004j 9.05e-2016, 9.05e-2016j
2.7814037334895644843 + 2.8608266739877645267e-6016j 5.38e-2029, 5.38e-2029j
77.444114290658286589 - 5.1587053725227389479e-5986j 3.61e-2001, 3.61e-2001j
2.2498965104146485172 + 1.6676786354163133422e-6030j 3.1e-2030, 3.1e-2030j
84.433894594799021675 + 1.3442908694204360291e-5999j 1.02e-2000, 1.02e-2000j
0.69867220790096906176 + 6.9735269593255753087e-6072j 3.03e-2035, 3.03e-2035j
88.079989025709751674 + 7.333891695981414247e-6036j 1.51e-2000, 1.51e-2000j
182.67940960418428788 - 7.0134637479091909861e-6090j 2.05e-2002, 2.05e-2002j
135.93532814113053575 - 8.0524449986710092147e-6137j 3.2e-2000, 3.2e-2000j
169.73435305079315071 - 3.2886211474027986945e-6167j 1.26e-2001, 1.26e-2001j
3.369839231310923141 + 1.1137484861194401682e-6205j 8.45e-2028, 8.45e-2028j
95.689311109300540926 + 1.6620100470136382403e-6176j 3.02e-2000, 3.02e-2000j
19.61580007791513563 + 3.3826166135621499021e-6197j 2.22e-2013, 2.22e-2013j
211.98992111855510763 + 7.674272120369796242e-6184j 1.4e-2004, 1.4e-2004j
91.830740968922871363 + 4.3411447644324955537e-6196j 2.26e-2000, 2.26e-2000j
4.0144124351161850225 - 6.2722952744625818941e-6250j 1.29e-2026, 1.29e-2026j
1.7757084093252061829 + 1.9669131701436236943e-6255j 1.86e-2031, 1.86e-2031j
9.4388136618170019698 + 2.9101931722293635875e-6243j 1.1e-2019, 1.1e-2019j
151.98965792821375195 - 2.7335911397171282491e-6222j 8.97e-2001, 8.97e-2001j
16.662584802214783582 + 2.0154617301376246475e-6266j 5.71e-2015, 5.71e-2015j
107.9473438640636533 + 9.4672017677469133273e-6251j 5.23e-2000, 5.23e-2000j
5.463184561107291702 + 7.3202399088610099792e-6309j 2.72e-2024, 2.72e-2024j
38.418945114004554351 + 4.5419676250486416233e-6291j 8.21e-2007, 8.21e-2007j
157.70141122107474243 + 4.2604919866341831776e-6283j 5.15e-2001, 5.15e-2001j
126.04231775459740452 + 7.4566203642235897811e-6307j 4.82e-2000, 4.82e-2000j
99.659103040387795368 + 1.1503327877883421468e-6325j 4.07e-2000, 4.07e-2000j
1.3590390191452026245 + 1.06323457134056684e-6374j 1.07e-2032, 1.07e-2032j
0.056897625001077184683 + 1.3346148613535612657e-6381j 2.63e-2040, 2.63e-2040j
26.314326793252564405 - 4.9949761197255825604e-6352j 1.54e-2010, 1.54e-2010j
0.13909065093290862958 - 1.5508816827323191103e-6380j 5.7e-2039, 5.7e-2039j
70.840162566227863996 - 3.2463408550704252598e-6341j 1.1e-2001, 1.1e-2001j
7.8232631436879996743 + 8.5733859507187190822e-6381j 4.17e-2021, 4.17e-2021j
1 - 3.6791420106727788018e-6394j 5.56e-2034, 5.56e-2034j
18.106521171082875047 + 2.2145638780467918279e-6373j 3.47e-2014, 3.47e-2014j
176.08428842619568219 + 5.4029691803183969841e-6360j 5.09e-2002, 5.09e-2002j
163.61184547453294838 - 2.9140422955316581877e-6409j 2.51e-2001, 2.51e-2001j
61.617669309096190874 + 1.1995449687869946215e-6436j 1.1e-2002, 1.1e-2002j
34.101263532195866719 - 2.8752377707075774099e-6473j 5.88e-2008, 5.88e-2008j
4.7134559094692264947 + 3.8656549171710950232e-6493j 1.83e-2025, 1.83e-2025j
103.74378971565421051 + 1.6879114448370198007e-6465j 4.98e-2000, 4.98e-2000j
189.54045919783800504 + 4.0661347780054483066e-6532j 7.05e-2003, 7.05e-2003j
74.095127444269431977 + 1.76672988395624197e-6595j 2.15e-2001, 2.15e-2001j
12.724184104001637914 - 1.5064800889769269946e-6655j 2.42e-2017, 2.42e-2017j
0.26919051050539195718 - 3.6651004152682371174e-6677j 1.06e-2037, 1.06e-2037j
32.049830739041327906 - 3.8672628048198235771e-6640j 1.38e-2008, 1.38e-2008j
146.46481436691792532 + 8.6866589514898149634e-6660j 1.61e-2000, 1.61e-2000j
0.011235695222698260473 + 3.5439342154159576165e-6732j 8.49e-2042, 8.49e-2042j
55.901867781920856109 + 7.4911583722947993854e-6694j 1.94e-2003, 1.94e-2003j
0.45511902958536072878 + 1.9620426770904067183e-6727j 1.57e-2036, 1.57e-2036j

Weights

Weight (ball center) Error (ball radius)
7.4912329206356905486e-137 + 5.4927386625265268081e-4822j 1.57e-384, 7.84e-1890j
6.6890090246909182781e-129 - 6.0648913300196110224e-4819j 2.18e-382, 1.09e-1887j
1.6454227319757110656e-88 + 2.8109466035872994028e-4799j 6.29e-370, 3.14e-1875j
5.7045708666390351772e-112 + 7.0569857818148994293e-4811j 3.84e-378, 1.92e-1883j
5.8753461866457665636e-117 - 2.6463929591004434373e-4813j 1.07e-379, 5.35e-1885j
9.1315091842071043567e-51 - 2.8105173151004787696e-4780j 2.37e-353, 1.18e-1858j
1.6541388965360520636e-122 + 5.7272760333686606448e-4816j 1.75e-381, 8.72e-1887j
6.9080570600741258941e-57 + 2.1978272132279667118e-4783j 2.89e-357, 1.44e-1862j
1.2651409480471315746e-29 + 2.01047575517497584e-4769j 2.28e-336, 1.14e-1841j
3.822931526230322651e-21 - 5.7497196755287504765e-4765j 2.37e-325, 1.18e-1830j
0.00068331508944130697544 + 1.4992002314220859814e-4754j 9.98e-264, 4.98e-1769j
1.7001430304080368612e-13 - 8.2199358072461522914e-4761j 7.44e-311, 3.72e-1816j
4.0023371742244393895e-16 + 2.9031401978550997612e-4762j 5.5e-317, 2.75e-1822j
2.1205263876394869332e-107 - 1.2264707730024971504e-4808j 5.08e-379, 2.53e-1884j
1.1090982128940425547e-12 + 2.3596484288826114537e-4760j 3.91e-309, 1.95e-1814j
1.1029959147330367031e-05 - 6.0664540171853487597e-4756j 9.69e-284, 4.84e-1789j
3.832784754684386367e-11 + 1.7884317986560345865e-4759j 1.02e-305, 5.09e-1811j
4.4922718636304297759e-20 + 2.139467956340865352e-4764j 9.67e-325, 4.83e-1830j
7.6284921566325016358e-49 + 2.6716732294877560746e-4779j 5.39e-355, 2.69e-1860j
2.6571510119392643434e-28 - 9.8215380479338074227e-4769j 4.12e-337, 2.06e-1842j
0.0015477002098770272972 - 1.6670067949536744617e-4754j 1.11e-270, 5.55e-1776j
4.8864482920430942558e-19 - 7.6842263069473652257e-4764j 1.19e-323, 5.95e-1829j
2.7236763326575900908e-61 + 1.2986828008620896336e-4785j 2.19e-363, 1.09e-1868j
1.0074895386015660448e-09 + 1.2228847296009949444e-4758j 6.01e-306, 3e-1811j
3.7029566423038815507e-103 + 1.5082328520774543604e-4806j 4.97e-380, 2.48e-1885j
3.0077216715887430067e-22 + 1.4902573871272217567e-4765j 1.35e-329, 6.76e-1835j
4.9259828131215965443e-18 + 2.666166351190669632e-4763j 2.9e-323, 1.45e-1828j
3.0785530815352225046e-05 + 1.4817894751399628159e-4755j 2.66e-291, 1.33e-1796j
9.0203622223505736777e-26 - 2.0702199566170851382e-4767j 2.5e-335, 1.25e-1840j
1.9400393747020843422e-95 + 1.0022258592000659567e-4802j 6.17e-379, 3.08e-1884j
2.1847806379790680444e-23 - 3.7220428680278923037e-4766j 3.34e-332, 1.67e-1837j
1.0960419025919807056e-06 - 1.0637251192015709235e-4756j 3.3e-302, 1.65e-1807j
2.5912416372931554044e-35 + 2.2752750677920753918e-4772j 5.47e-348, 2.73e-1853j
3.480902904923128566e-99 - 1.3903389074105700259e-4804j 5.59e-380, 2.79e-1885j
2.7634685316226708708e-85 - 1.144057178660341917e-4797j 2.4e-376, 1.2e-1881j
9.5727604678495274128e-53 + 2.7720090784144635128e-4781j 1.13e-360, 5.66e-1866j
2.0328998531931663968e-10 - 4.7336519263665319649e-4759j 1.96e-316, 9.81e-1822j
0.00015045003434799510088 + 7.9551209102213047822e-4755j 8.28e-298, 4.13e-1803j
3.0997901698230420016e-07 + 4.467768236876776645e-4757j 3.46e-309, 1.73e-1814j
0.034696556978359229212 + 4.5568974232983108758e-4754j 4.11e-279, 2.05e-1784j
7.8979837034105197079e-34 - 1.3280948005375984765e-4771j 7.65e-348, 3.82e-1853j
0.053009944631818895024 - 5.6973318618772869064e-4754j 2.31e-277, 1.16e-1782j
7.7000896664577732803e-37 - 3.7167544572743578353e-4773j 5.18e-351, 2.59e-1856j
0.13547306446803279147 - 1.2755192637389169067e-4753j 1.49e-280, 7.42e-1786j
2.066825334336433242e-38 + 5.7811487032701282716e-4774j 8.02e-353, 4e-1858j
3.0973509300217940812e-79 - 1.2155105507685682045e-4794j 3.1e-377, 1.55e-1882j
4.6950332185963606379e-59 - 1.7557938676370321595e-4784j 4.85e-367, 2.42e-1872j
1.2023684391193432677e-73 - 7.7374601721844337043e-4792j 1.55e-375, 7.76e-1881j
0.021211021180617039624 - 3.6317522039276139155e-4754j 8.7e-297, 4.34e-1802j
1.0845155546576175533e-41 + 1.2002009283898459712e-4775j 9.24e-358, 4.61e-1863j
4.6672553174702669296e-09 - 3.0891431637349067907e-4758j 4.75e-325, 2.37e-1830j
6.8870112058627763316e-92 - 5.8333902069731042272e-4801j 7.65e-382, 3.82e-1887j
4.9965420565418971108e-40 - 8.5494917051336958828e-4775j 2.35e-356, 1.17e-1861j
0.01213560283827611239 + 2.8997965936808844757e-4754j 1.26e-305, 6.28e-1811j
0.075443317094302572349 + 7.074144583139056392e-4754j 6e-296, 3e-1801j
7.5387001091217982471e-05 - 3.645595505192380679e-4755j 2.75e-316, 1.37e-1821j
5.5105216561220189815e-66 + 5.5473068008494303134e-4788j 1.37e-372, 6.84e-1878j
8.1875976670017322309e-08 - 1.8609701071301484843e-4757j 2.42e-326, 1.21e-1831j
5.6094662489277379986e-47 - 2.3870914677522737836e-4778j 5.83e-362, 2.91e-1867j
0.0032763405996287849826 + 1.9339279717795112962e-4754j 2.36e-314, 1.18e-1819j
4.6073197998339287374e-17 - 8.9438303755557409301e-4763j 5.27e-340, 2.63e-1845j
1.8847302555890466588e-68 - 3.1735326709240218587e-4789j 4.05e-374, 2.02e-1879j
8.7401825970082052436e-55 - 2.5563933709766105222e-4782j 3.63e-366, 1.81e-1871j
2.1063974377471042696e-43 - 1.5966800048962255291e-4776j 1.77e-360, 8.83e-1866j
0.099646436349009887924 - 8.7056487553902294615e-4754j 1.39e-311, 6.92e-1817j
0.059201934785854408875 - 1.1684175631172136077e-4753j 1.9e-311, 9.47e-1817j
6.7486581408557448933e-12 - 6.5848665427819068378e-4760j 1.02e-337, 5.11e-1843j
0.090560333014142847262 + 1.6621126471546668198e-4753j 6.67e-312, 3.33e-1817j
5.5060378782372293174e-31 - 3.9431120217249158193e-4770j 8.89e-354, 4.44e-1859j
0.00029301178731479417815 - 1.2522215520304557834e-4754j 1.51e-325, 7.55e-1831j
0.12147236567009760133 + 1.0603412548342860482e-4753j 1.94e-315, 9.67e-1821j
2.0215857627176903861e-08 + 7.6478296000458470473e-4758j 9.87e-334, 4.93e-1839j
2.1798434318529589874e-76 + 3.2530576084375550669e-4793j 1.31e-378, 6.53e-1884j
5.2899080890745817015e-71 + 1.6493020591178834585e-4790j 5.61e-376, 2.8e-1881j
5.1110975167674453445e-27 + 4.6019249773179882425e-4768j 8.19e-353, 4.09e-1858j
3.232319657052419631e-15 - 9.1261178487150395785e-4762j 5.57e-345, 2.78e-1850j
0.0065086913646639507011 - 2.3398474078537850868e-4754j 1.79e-330, 8.94e-1836j
3.6475795545840658159e-45 + 2.0092797405896364218e-4777j 1.08e-362, 5.41e-1868j
3.3793681940946693394e-82 + 3.9975265425285808459e-4796j 7.71e-382, 3.85e-1887j
2.18583893587301706e-32 + 7.4014788339322508543e-4771j 2.74e-356, 1.37e-1861j
3.6114575744402832041e-06 + 2.5296029920490938773e-4756j 2.34e-339, 1.17e-1844j
0.12025516918082006518 - 1.694032090763795288e-4753j 5.83e-335, 2.91e-1840j
2.4291147832778711433e-14 + 2.7807035328682125476e-4761j 5.14e-346, 2.56e-1851j
1.3376296506316049374e-63 - 8.8582736731904122613e-4787j 6.89e-373, 3.44e-1878j
0.028132857488477386345 + 3.9015538662788542057e-4754j 1.27e-337, 6.32e-1843j
1.4631504056594259861e-24 + 8.9501323817446004242e-4767j 2.64e-352, 1.32e-1857j
0.1361795592491166566 + 1.5047161671374349085e-4753j 1.79e-337, 8.92e-1843j

Download

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