Rule: Q[2, 99]

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)
313.34248565369918603 - 1.109745603073174265e-4341j 2.96e-2004, 2.96e-2004j
339.44805246149564491 + 1.9681583980611976425e-4347j 4.75e-2007, 4.75e-2007j
355.27426183231146874 - 7.5755500033886757152e-4352j 6.8e-2009, 6.8e-2009j
325.70421453805195485 - 3.0842605066085062109e-4350j 1.45e-2005, 1.45e-2005j
38.088789318586197755 - 8.1279346834904798515e-4371j 5.35e-2003, 5.35e-2003j
374.9970621078060582 - 4.3542054666039722003e-4365j 3.37e-2011, 3.37e-2011j
56.327440929728661907 + 6.1303661883745943514e-4361j 1.41e-1998, 1.41e-1998j
110.03671402715667066 - 5.0420322925462709684e-4395j 3.03e-1993, 3.03e-1993j
210.72893155374249141 + 9.0035014736795017734e-4475j 2.1e-1995, 2.1e-1995j
185.94532180030083849 - 2.6212788407540306562e-4530j 4.57e-1994, 4.57e-1994j
75.766926597209118574 + 2.2615957006955824401e-4554j 1.05e-1995, 1.05e-1995j
34.143106046470258247 + 1.0418607324826738586e-4576j 2.76e-2004, 2.76e-2004j
40.151179804260239818 + 1.3526466409973968872e-4575j 2.19e-2002, 2.19e-2002j
17.846187373005150637 - 7.998626336361008622e-4585j 6.67e-2012, 6.67e-2012j
106.22589138202836592 + 7.5152577651674227938e-4566j 2.01e-1993, 2.01e-1993j
22.150963900458203897 - 6.6024129968173752073e-4601j 1.95e-2009, 1.95e-2009j
4.0191941911874238578 - 3.0370839778883580504e-4615j 1.17e-2025, 1.17e-2025j
64.238718065501520335 + 6.3712452622550651596e-4583j 3.17e-1997, 3.17e-1997j
153.74965421901848838 - 6.3928440963551634103e-4602j 5.31e-1993, 5.31e-1993j
180.20035327866866464 + 1.9468470617866951438e-4634j 7.96e-1994, 7.96e-1994j
44.458484771433725647 + 5.0020686607044871094e-4659j 3.32e-2001, 3.32e-2001j
263.3411228639585381 - 7.6208443256400936657e-4653j 2.02e-1999, 2.02e-1999j
12.85776953455625921 + 1.1535399981031181502e-4673j 1.85e-2015, 1.85e-2015j
69.858932868390769531 - 1.0873548830416517189e-4653j 2.13e-1996, 2.13e-1996j
301.99880744424206933 - 6.5767318245130791644e-4659j 4.47e-2003, 4.47e-2003j
246.78919651618990333 - 8.913219082635911926e-4650j 5.26e-1998, 5.26e-1998j
148.86886903692502403 + 1.5352524612202862499e-4651j 6.1e-1993, 6.1e-1993j
16.519327072148207586 + 1.1521437965598403765e-4682j 9.51e-2013, 9.51e-2013j
49.014110278766975887 - 1.4052381220469249698e-4670j 4.23e-2000, 4.23e-2000j
102.50577637216561752 - 4.1873044901968422199e-4662j 1.39e-1993, 1.39e-1993j
58.896778373707392773 + 3.3401797193147126579e-4671j 4.07e-1998, 4.07e-1998j
19.226818128975172274 - 8.4337505964643655592e-4684j 4.52e-2011, 4.52e-2011j
217.43435130064988902 + 1.0844388703492540477e-4665j 7.39e-1996, 7.39e-1996j
130.54069512948305698 - 3.5401791286452670102e-4682j 7.7e-1993, 7.7e-1993j
11.742482179037598076 + 1.5906429233627043191e-4745j 2.14e-2016, 2.14e-2016j
254.88158422296545639 + 3.1620128261741805812e-4722j 1.03e-1998, 1.03e-1998j
191.86033018082720695 + 3.5794195320495840178e-4792j 2.3e-1994, 2.3e-1994j
14.025459779415004686 + 6.5793012256856179431e-4878j 1.52e-2014, 1.52e-2014j
53.82451063418978696 + 4.1439724356632625752e-4856j 4.52e-1999, 4.52e-1999j
9.6679401348144929163 - 9.7470234497134005212e-4936j 2.44e-2018, 2.44e-2018j
8.7081386176927051014 + 3.9548833268118415069e-4936j 2.31e-2019, 2.31e-2019j
144.11193862318627494 + 1.5207310865796693322e-4938j 7.39e-1993, 7.39e-1993j
30.432006188867047393 - 1.1512299015570995709e-5012j 1.18e-2005, 1.18e-2005j
197.9550931829073778 + 3.0605191467512066343e-5041j 1.14e-1994, 1.14e-1994j
272.21412385805224566 + 1.8319389506651508695e-5152j 3.44e-2000, 3.44e-2000j
281.55928156543895503 + 1.8381953220755990689e-5291j 4.34e-2001, 4.34e-2001j
158.75921425113161968 - 6.7119569452538894614e-5401j 3.93e-1993, 3.93e-1993j
163.90291042481457195 - 5.2825091888943288928e-5456j 2.82e-1993, 2.82e-1993j
1.1388757760850387387 - 2.0972343675312336368e-5517j 1.07e-2032, 1.07e-2032j
291.4530863517203014 - 5.2839247791662004262e-5480j 4.89e-2002, 4.89e-2002j
239.0265858966708936 + 2.3586952894934319969e-5477j 2.01e-1997, 2.01e-1997j
134.95187582537619638 - 7.3648430324378601574e-5501j 7.83e-1993, 7.83e-1993j
85.191841686513221721 + 4.0736303001119558771e-5520j 9.23e-1995, 9.23e-1995j
1.4938945059174665541 + 8.8032489949225440492e-5599j 1.51e-2031, 1.51e-2031j
4.6743275098603147421 - 4.3046739467774313713e-5591j 1.47e-2024, 1.47e-2024j
42.274172476904506627 + 5.4272532698462247814e-5565j 8.49e-2002, 8.49e-2002j
32.258534823245461022 - 7.1983836185312252253e-5571j 5.78e-2005, 5.78e-2005j
15.2458680794577647 + 4.0138361510250965842e-5580j 1.14e-2013, 1.14e-2013j
46.70486823384505654 - 4.8292898952907781243e-5560j 1.26e-2000, 1.26e-2000j
1.8991010830379829104 - 4.8728481986144678705e-5627j 2.64e-2030, 2.64e-2030j
95.328842139612574138 + 1.18423228487754335e-5588j 5.37e-1994, 5.37e-1994j
113.94062818418358751 - 6.428447759896874993e-5759j 3.86e-1993, 3.86e-1993j
126.2372039540190782 + 2.5044437535493606743e-5928j 6.98e-1993, 6.98e-1993j
0.013860808009676030853 + 1.5723279715494315439e-6101j 1.31e-2041, 1.31e-2041j
139.47433424804242152 - 1.7843797295960081924e-6049j 7.63e-1993, 7.63e-1993j
2.3542377115956336307 + 4.7632850277626336326e-6194j 3.94e-2029, 3.94e-2029j
174.61672432588570257 + 2.1224255056626734535e-6157j 1.27e-1993, 1.27e-1993j
36.086316063952053977 - 6.788599756097457585e-6233j 1.22e-2003, 1.22e-2003j
204.24051894278541587 + 2.0919436232292587646e-6228j 4.74e-1995, 4.74e-1995j
3.4142135623730950488 - 7.4547554998599819458e-6297j 8.1e-2027, 8.1e-2027j
0.40864166117053488573 - 9.962143601395384014e-6306j 7.64e-2036, 7.64e-2036j
169.18660378753683359 + 3.3485374876830647191e-6261j 2.09e-1993, 2.09e-1993j
224.37285217275638601 + 5.8737124879409554097e-6274j 2.4e-1996, 2.4e-1996j
78.832086110635814612 + 1.8307194075819833471e-6282j 2.26e-1995, 2.26e-1995j
72.776325034249813562 - 1.0314554068092183291e-6283j 4.52e-1996, 4.52e-1996j
0.5857864376269049512 - 2.8166072384841502612e-6321j 6.43e-2035, 6.43e-2035j
7.7996457101207286734 - 1.9050051743546594253e-6306j 2.1e-2020, 2.1e-2020j
51.387036083911560829 - 4.299802906792509643e-6286j 1.36e-1999, 1.36e-1999j
23.695315510052800953 + 2.9920792793581592146e-6296j 1.27e-2008, 1.27e-2008j
28.662950951917795392 + 1.4402553713749454918e-6293j 2.17e-2006, 2.17e-2006j
6.942227913720655898 + 8.9816905621564772592e-6308j 2.17e-2021, 2.17e-2021j
0.17419771680869612785 - 9.607707670665399425e-6325j 3.36e-2038, 3.36e-2038j
0.83494972980458189776 - 5.7529610968424127126e-6321j 7.22e-2034, 7.22e-2034j
25.295112210125528307 - 1.9116157956612593248e-6294j 7.29e-2008, 7.29e-2008j
88.489519299970506792 + 4.3665171302951777924e-6280j 1.74e-1994, 1.74e-1994j
26.950825794709710237 + 1.6600372767497721655e-6293j 4.08e-2007, 4.08e-2007j
2.8592597087934068869 + 2.1163997223719671828e-6314j 5.77e-2028, 5.77e-2028j
6.1356674751498783276 + 1.0579756772916606312e-6308j 1.94e-2022, 1.94e-2022j
0.072499839628019165357 - 1.0614684137771876339e-6326j 7.12e-2040, 7.12e-2040j
231.5630247817283493 + 1.4886751293155282066e-6278j 7.59e-1997, 7.59e-1997j
117.94017477467858648 - 4.7749378207250578106e-6288j 4.94e-1993, 4.94e-1993j
81.973224794558143929 - 1.0255060244105452875e-6298j 4.69e-1995, 4.69e-1995j
67.013469515011737235 + 1.8895814823937659413e-6300j 8.14e-1997, 8.14e-1997j
98.874129126380457317 + 4.62440832346566941e-6296j 8.76e-1994, 8.76e-1994j
10.679299560637807307 - 1.0639089228002595617e-6324j 2.4e-2017, 2.4e-2017j
91.867929853035505868 + 7.545675266931655258e-6300j 3.36e-1994, 3.36e-1994j
5.3797625224664782226 - 1.1527470157012142467e-6345j 1.65e-2023, 1.65e-2023j
0.29733821814745128241 - 4.2677186597601905705e-6359j 9.93e-2037, 9.93e-2037j
61.533521357839034929 + 2.1426988906733071386e-6315j 1.19e-1997, 1.19e-1997j
20.66160761867456211 - 1.6206161729788894067e-6335j 3.3e-2010, 3.3e-2010j
122.0380664184170835 - 1.221144259088253742e-6317j 6.09e-1993, 6.09e-1993j

Weights

Weight (ball center) Error (ball radius)
9.7553248472493572089e-136 - 2.9378099986964732322e-4443j 3.18e-337, 5.28e-1839j
5.553646626107713852e-147 - 6.1131495690662578295e-4449j 5.41e-341, 8.97e-1843j
8.7904549132217227276e-154 + 2.2513558362856271425e-4452j 2.17e-343, 3.59e-1845j
4.5870688537674801554e-141 + 5.9614042098792123464e-4446j 1.72e-339, 2.86e-1841j
5.8376914971823651334e-17 - 2.9280887173436281019e-4382j 3.1e-254, 5.14e-1756j
3.2047954270049570753e-162 - 1.2411879150540334723e-4456j 1.93e-346, 3.2e-1848j
8.7387152666593999954e-25 - 2.7267185734585290215e-4385j 4.44e-271, 7.38e-1773j
6.279242461075743874e-48 - 1.9071979974361714077e-4398j 8.57e-299, 1.42e-1800j
1.9987780367303299405e-91 - 8.5403157512551577179e-4421j 5.62e-325, 9.32e-1827j
1.0245344533224661212e-80 - 2.4524846745895893207e-4415j 3.72e-320, 6.17e-1822j
3.7665828157342162279e-33 - 1.5575080203205599305e-4390j 4.57e-285, 7.59e-1787j
2.8427030130714827134e-15 - 1.7761714963296867977e-4381j 2.42e-254, 4.01e-1756j
7.6426707957420377917e-18 + 1.1629265127329273774e-4382j 4.25e-260, 7.05e-1762j
2.404451897013958239e-08 - 4.1580031959189862961e-4378j 5.32e-232, 8.83e-1734j
2.7698496688751569783e-46 + 1.3878268981407628867e-4397j 1.36e-298, 2.25e-1800j
3.6381569118998984866e-10 + 5.1493244232638716411e-4379j 2.52e-240, 4.18e-1742j
0.011320094496539293754 - 4.7442190362526209513e-4375j 2.17e-180, 3.6e-1682j
3.4609542914650868254e-28 - 1.2609335894754205653e-4387j 2.85e-279, 4.73e-1781j
8.3460299715856532332e-67 - 3.2400020493277346431e-4408j 2.15e-314, 3.57e-1816j
3.1118724000707486539e-78 + 4.5434226282066486416e-4414j 4.63e-320, 7.69e-1822j
1.0897884316734425087e-19 + 1.7970909032176455548e-4383j 3.13e-267, 5.2e-1769j
3.7136756743015696545e-114 + 2.4553076837577712158e-4432j 1.3e-336, 2.17e-1838j
2.9743622188223456047e-06 - 4.8603645995473461206e-4377j 4.41e-229, 7.31e-1731j
1.3189469562975927467e-30 - 4.3622133127509331612e-4389j 5.2e-285, 8.62e-1787j
7.614347163352435561e-131 + 8.7467812855489230422e-4441j 1.3e-341, 2.15e-1843j
5.2437546375100528353e-107 + 1.035979194695740148e-4428j 2.84e-334, 4.71e-1836j
1.0713834402923667475e-64 + 3.9276869529600435643e-4407j 7.14e-315, 1.18e-1816j
8.7041037923046963812e-08 + 7.9612824632770378541e-4378j 1.02e-241, 1.69e-1743j
1.2101333708316318187e-21 + 2.9249093438286037026e-4384j 3.36e-275, 5.58e-1777j
1.115900971369271847e-44 - 9.6908398412147885234e-4397j 2.14e-301, 3.55e-1803j
6.8692067627440827286e-26 - 5.7153042096700429015e-4386j 2.83e-281, 4.69e-1783j
6.2862514506055123148e-09 + 2.1215026816712975386e-4378j 2.15e-248, 3.57e-1750j
2.5303897511681576923e-94 + 2.8668080708145066314e-4422j 8.9e-330, 1.48e-1831j
8.83202027007657976e-57 + 4.7502931416570334005e-4403j 1.16e-311, 1.92e-1813j
8.65779128460233013e-06 + 8.4823728399589482588e-4377j 4.47e-239, 7.41e-1741j
1.6741396243504578579e-110 - 1.7471451020328925455e-4430j 3.31e-336, 5.49e-1838j
2.8477261139378116176e-83 + 1.2172713083503516786e-4416j 5.13e-325, 8.51e-1827j
9.6788293038397604593e-07 + 2.7216689213231299968e-4377j 6.13e-246, 1.02e-1747j
1.03996175876449001e-23 + 7.5555334299261013106e-4385j 4e-282, 6.63e-1784j
6.2364887746077850606e-05 + 2.413123483857742232e-4376j 2.18e-238, 3.61e-1740j
0.00015434766708238645093 - 3.9354798853138354333e-4376j 2.72e-236, 4.51e-1738j
1.2155101238292847768e-62 - 4.4827804548275178232e-4406j 1.01e-315, 1.68e-1817j
1.0921057139663872162e-13 - 1.0002409715780785113e-4380j 3.44e-269, 5.7e-1771j
6.6184663515175168568e-86 - 5.5283898568335316533e-4418j 1.4e-326, 2.32e-1828j
5.4683446011583130449e-118 - 2.8098972074971881142e-4434j 1.28e-340, 2.12e-1842j
5.0448675293658367787e-122 + 2.5435218756588982753e-4436j 1.67e-342, 2.77e-1844j
5.7180087891156268765e-69 + 2.5099072654334023486e-4409j 7.97e-321, 1.32e-1822j
3.4271326781043375625e-71 - 1.8208261999017425858e-4410j 3.32e-322, 5.51e-1824j
0.10557072836534182919 - 3.361464484582202895e-4374j 2.89e-210, 4.8e-1712j
2.7047041350055498099e-126 - 1.7534068147854740484e-4438j 7.26e-345, 1.2e-1846j
1.184043871333594675e-103 - 5.2148859837024921142e-4427j 1.53e-336, 2.53e-1838j
1.099216132811751387e-58 - 4.9192805046278536838e-4404j 9.14e-318, 1.52e-1819j
3.2703018126808110757e-37 + 9.2128255262854889887e-4393j 3.77e-307, 6.25e-1809j
0.085350295787534468406 + 2.4164494282068181699e-4374j 6.51e-225, 1.08e-1726j
0.0063480272815021933172 + 3.2929444007298010106e-4375j 2.37e-246, 3.93e-1748j
9.4126328215923004456e-19 - 4.5762130413527088674e-4383j 1.29e-287, 2.13e-1789j
1.8144552226810164919e-14 + 4.2576709779462282263e-4381j 6.28e-283, 1.04e-1784j
2.9828206422359717106e-07 - 1.4892089954965761554e-4377j 6.34e-268, 1.05e-1769j
1.1852933784037010336e-20 - 7.1296008032088881556e-4384j 4.85e-290, 8.04e-1792j
0.064400853703702390031 - 1.7651799065657794475e-4374j 2.96e-237, 4.91e-1739j
1.3919465343422868372e-41 - 4.2033044077630773622e-4395j 7.32e-311, 1.21e-1812j
1.2970393757906453644e-49 + 2.5108953429104161064e-4399j 3.22e-315, 5.34e-1817j
6.373050361325300496e-55 - 4.3563862986891307727e-4402j 4.13e-318, 6.85e-1820j
0.035031020829072191662 + 4.804450791575134397e-4375j 2.36e-238, 3.92e-1740j
1.2242531499807836435e-60 + 4.8285110831124973007e-4405j 3.08e-320, 5.1e-1822j
0.045590934502492601934 + 1.2906573559666871858e-4374j 1.43e-251, 2.37e-1753j
8.0487352856544188141e-76 - 7.7737160314738304791e-4413j 2.29e-328, 3.79e-1830j
4.1974046854373524832e-16 + 7.2721082306531850477e-4382j 1.11e-291, 1.85e-1793j
1.2723672143201268592e-88 + 2.2848444923078468682e-4419j 1.06e-334, 1.77e-1836j
0.019081622508676820539 + 6.7177920685661143119e-4375j 5.67e-263, 9.41e-1765j
0.087193175157379226311 + 1.203049808000642419e-4373j 6.73e-250, 1.12e-1751j
1.7865477036749521942e-73 + 1.2332990092033977567e-4411j 1.89e-327, 3.14e-1829j
2.5408246172108489182e-97 - 8.57308741011447374e-4424j 2.08e-339, 3.46e-1841j
1.8006471323932477915e-34 + 2.8833289981254085886e-4391j 1.05e-311, 1.74e-1813j
7.3117521929825901457e-32 + 8.276416873326885128e-4390j 1.12e-309, 1.86e-1811j
0.12150244043671635939 - 7.8588206256164978487e-4374j 1.1e-259, 1.82e-1761j
0.00036189047589938536879 + 6.2783719687226806598e-4376j 2.13e-280, 3.53e-1782j
1.1588263569682610283e-22 - 1.3081231106988384226e-4384j 4.76e-302, 7.9e-1804j
8.0483535629100627862e-11 - 2.4499713665948290293e-4379j 1.58e-293, 2.63e-1795j
6.2017324991829800275e-13 + 2.3006094272185097311e-4380j 7.6e-296, 1.26e-1797j
0.00080376318880855865586 - 9.8015309610788646948e-4376j 3.71e-283, 6.16e-1785j
0.10033581308175660383 + 5.0175848157631497401e-4374j 3.69e-268, 6.12e-1770j
0.12047212809395783513 + 4.8951242178302422095e-4374j 5.25e-269, 8.71e-1771j
1.6828288268365900272e-11 + 1.1391066451421222521e-4379j 6.53e-295, 1.08e-1796j
1.2386392894954425822e-38 - 1.5786170736619343941e-4393j 1.11e-316, 1.84e-1818j
3.324333601256816101e-12 - 5.1769207531371317863e-4380j 7.51e-296, 1.25e-1797j
0.030373506084189274032 - 9.3683405606395796965e-4375j 7.02e-280, 1.16e-1781j
0.0016907364819768634472 + 1.4981144250973883744e-4375j 3.1e-285, 5.15e-1787j
0.075635191080712868008 - 1.9229192512507675396e-4374j 1.96e-274, 3.26e-1776j
1.9867453539069671844e-100 + 2.2628463103027936277e-4425j 6.75e-345, 1.12e-1846j
2.4350082135285902641e-51 - 3.1616745991683454112e-4400j 4.68e-323, 7.76e-1825j
7.9773048807578560924e-36 - 5.221631545626282167e-4392j 3.34e-315, 5.54e-1817j
2.2136672401853139347e-29 + 2.3110034700445714778e-4388j 1e-311, 1.66e-1813j
4.115087231255413853e-43 + 6.50425503981366103e-4396j 1.12e-319, 1.85e-1821j
2.3873291462034690267e-05 - 1.4469607572805702332e-4376j 9.49e-297, 1.57e-1798j
4.3272262209315450753e-40 + 2.6201795766221856459e-4394j 3.68e-318, 6.11e-1820j
0.0033674607158613651315 - 2.2431690674578315098e-4375j 1.01e-295, 1.67e-1797j
0.085316714171095500522 - 1.0678138179971968367e-4373j 1.28e-291, 2.13e-1793j
5.0462771862754810019e-27 + 7.4775901009083310011e-4387j 2.15e-311, 3.56e-1813j
1.5549847897144293909e-09 - 1.0574477509800333084e-4378j 6.07e-302, 1e-1803j
4.1436345158775183761e-53 + 3.8013058377543017402e-4401j 6.99e-325, 1.16e-1826j

Download

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