Rule: Q[2, 88]

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)
313.24669117191372272 - 2.930722584567015558e-4153j 5.66e-2012, 5.66e-2012j
298.09592108072846645 - 5.2769912247667483639e-4150j 2.86e-2010, 2.86e-2010j
262.35190137502580574 + 2.5573507435554201227e-4144j 1.65e-2006, 1.65e-2006j
273.16198412866920142 + 2.6752118003407857485e-4146j 1.21e-2007, 1.21e-2007j
242.91550148810872046 - 3.8721871675243680912e-4139j 1.08e-2004, 1.08e-2004j
14.605261153695391307 - 8.0637022614303472488e-4168j 7.55e-2016, 7.55e-2016j
40.982943339699320066 - 6.3943186220654425726e-4157j 3.73e-2005, 3.73e-2005j
195.64045193958396286 + 1.7792637278673801466e-4150j 6.48e-2001, 6.48e-2001j
284.95953121071308049 - 1.3741432814867120822e-4175j 7.2e-2009, 7.2e-2009j
48.068118055553278548 - 8.9649698948015979554e-4180j 1.28e-2003, 1.28e-2003j
23.428986562370317002 + 1.7081539707102267844e-4187j 5.14e-2011, 5.14e-2011j
25.11745088731158364 + 2.2968885128593352508e-4187j 2.99e-2010, 2.99e-2010j
142.41959165583134516 + 7.152292604221274224e-4174j 2.43e-1998, 2.43e-1998j
86.913576463111042413 - 6.5022940066868575027e-4188j 5.78e-1999, 5.78e-1999j
58.550809456163284185 + 1.9298709844571577702e-4194j 8.07e-2002, 8.07e-2002j
36.612736486608564803 + 1.7905089247201258137e-4200j 2.73e-2006, 2.73e-2006j
15.922900130491216813 + 1.2600108370681228633e-4208j 5.42e-2015, 5.42e-2015j
105.94251126293689795 - 6.9302047284323499191e-4190j 3.22e-1998, 3.22e-1998j
101.92756300606651548 - 1.4109627230827082582e-4206j 2.74e-1998, 2.74e-1998j
332.16096993328416643 - 1.4631915959791903308e-4238j 3.77e-2014, 3.77e-2014j
26.869716716183902518 + 1.8609847502710185146e-4231j 1.57e-2009, 1.57e-2009j
30.568354510113664537 - 1.1049241384008005722e-4231j 3.57e-2008, 3.57e-2008j
90.516193623445271901 - 1.278620145077341453e-4219j 9.04e-1999, 9.04e-1999j
21.803694517815880158 - 1.8593404283304496018e-4248j 9.28e-2012, 9.28e-2012j
252.316763422425209 + 3.9467786660450960143e-4235j 1.59e-2005, 1.59e-2005j
127.76370487667790309 - 3.3224317228025025966e-4257j 4.56e-1998, 4.56e-1998j
20.240981208507239556 - 2.5550590222398181275e-4300j 1.42e-2012, 1.42e-2012j
53.157425193253334822 - 8.494026618603412621e-4290j 1.15e-2002, 1.15e-2002j
38.763180282147593196 + 4.2926287515684949403e-4293j 1.03e-2005, 1.03e-2005j
12.150002319904907314 + 3.8597403235109955429e-4305j 1.37e-2017, 1.37e-2017j
209.99271992210634419 - 7.5220141093598623166e-4285j 5.93e-2002, 5.93e-2002j
28.686449966987626855 - 1.7678791706993620005e-4316j 7.21e-2009, 7.21e-2009j
64.259314949459866331 - 2.031246827485133853e-4305j 4.88e-2001, 4.88e-2001j
234.04832860101748631 - 1.3615381327214662328e-4315j 6.79e-2004, 6.79e-2004j
225.64131166018694862 - 4.743898185405478594e-4354j 3.43e-2003, 3.43e-2003j
76.672663883070950191 - 2.9654170259131441985e-4384j 1.09e-1999, 1.09e-1999j
61.36493245420658742 + 1.8909168395970667447e-4421j 1.97e-2001, 1.97e-2001j
132.50806251081956838 + 3.1593140633488373575e-4464j 3.89e-1998, 3.89e-1998j
73.440379415665338422 - 1.5997924705927259897e-4489j 5.36e-2000, 5.36e-2000j
43.272995882709790745 + 7.0904623937199756256e-4524j 1.31e-2004, 1.31e-2004j
79.994172383933765572 - 1.9751571241932731546e-4549j 1.94e-1999, 1.94e-1999j
94.217504767898720316 + 6.0614804411155448248e-4681j 1.36e-1998, 1.36e-1998j
8.9121066537022287339 + 1.4468246479966459286e-4768j 2.35e-2020, 2.35e-2020j
5.4173109957453856998 - 4.5501199246065415377e-4779j 2.64e-2024, 2.64e-2024j
176.07767969097416134 - 7.6817230153068253183e-4865j 1.02e-1999, 1.02e-1999j
137.39128622969405384 - 6.8466375216371943136e-5042j 3.06e-1998, 3.06e-1998j
110.06859978335328312 + 1.6202999407920289668e-5206j 3.96e-1998, 3.96e-1998j
18.740288024537213784 - 1.4154161725484885892e-5299j 2.35e-2013, 2.35e-2013j
1.5232479528146776883 + 1.7501940215022825919e-5332j 7.94e-2032, 7.94e-2032j
7.0474496868562880299 - 7.8873194143939032754e-5316j 2.69e-2022, 2.69e-2022j
164.13219144651811557 - 1.4689861905850489902e-5378j 3.97e-1999, 3.97e-1999j
0.36696183346286860873 - 2.5118922013137823418e-5517j 5.17e-2037, 5.17e-2037j
217.63770376608458795 - 9.5472751295044024827e-5535j 1.58e-2002, 1.58e-2002j
13.347755371417581233 + 1.8707449912040223904e-5635j 1.02e-2016, 1.02e-2016j
32.516173649628036023 - 3.0040858185303333341e-5619j 1.51e-2007, 1.51e-2007j
188.8786151715100847 + 5.6406737408943030368e-5695j 1.86e-2000, 1.86e-2000j
9.9324441310341553163 + 1.2178039408426663982e-5790j 2.03e-2019, 2.03e-2019j
7.9504746376547846054 + 3.2973577422350862864e-5794j 2.69e-2021, 2.69e-2021j
158.44721827272579811 + 5.3894250249129030937e-5772j 7.46e-1999, 7.46e-1999j
67.235544821707781313 - 3.2600888838536510243e-5814j 1.17e-2000, 1.17e-2000j
2.8636728402319014351 + 1.5666048671928327837e-5905j 1.93e-2028, 1.93e-2028j
114.30955775296884675 - 2.1239532050759222282e-5873j 4.58e-1998, 4.58e-1998j
170.00503675522486306 + 1.5252404616163122994e-5940j 2.16e-1999, 2.16e-1999j
6.2030273429995091811 + 4.0218261086916197661e-6012j 2.65e-2023, 2.65e-2023j
4.6905038320141040447 + 7.3088134205135856572e-6014j 2.82e-2025, 2.82e-2025j
98.020298033110028492 - 8.5877432946644925087e-5986j 1.91e-1998, 1.91e-1998j
55.815446226953924676 + 1.3259978433543308773e-6011j 3.41e-2002, 3.41e-2002j
182.36368758636539995 + 3.8357532111608768884e-6014j 4.72e-2000, 4.72e-2000j
70.295304724784450687 - 1.5523073281229341195e-6033j 2.38e-2000, 2.38e-2000j
2.3683058710466299637 + 2.2295819766901568262e-6064j 1.47e-2029, 1.47e-2029j
1.9231662298139847947 + 1.6481452313443917568e-6064j 1.12e-2030, 1.12e-2030j
1.1662435642709123717 + 8.1083933043599988791e-6067j 4.89e-2033, 4.89e-2033j
0.080831819535479177651 - 4.8661016981101665247e-6074j 5.21e-2040, 5.21e-2040j
4.0228235480768591416 + 1.5011341904225507456e-6060j 2.53e-2026, 2.53e-2026j
3.4142135623730950488 - 3.6870469701687057823e-6061j 2.18e-2027, 2.18e-2027j
45.634361059947611258 + 8.5691296524060717058e-6038j 4.38e-2004, 4.38e-2004j
0.5857864376269049512 - 2.3644565901547046669e-6069j 1.14e-2035, 1.14e-2035j
83.407048514305235086 - 3.0322119238643324973e-6031j 3.42e-1999, 3.42e-1999j
147.59982583486103875 - 2.0992663635859716699e-6042j 1.75e-1998, 1.75e-1998j
17.301090869182389318 + 1.5990530697909482124e-6085j 3.72e-2014, 3.72e-2014j
0.85298429688199709727 + 1.1754955872408864271e-6104j 2.65e-2034, 2.65e-2034j
0.19825760443360258461 + 1.1333729990367471502e-6108j 1.75e-2038, 1.75e-2038j
118.66941737996125326 + 3.8102293813600032219e-6067j 4.87e-1998, 4.87e-1998j
123.15254949383129886 - 8.6317301645490096102e-6097j 4.6e-1998, 4.6e-1998j
152.93956267737175769 + 1.3840981901799272886e-6117j 1.28e-1998, 1.28e-1998j
0.0153574985837129863 - 1.0881736079324899645e-6173j 9.36e-2042, 9.36e-2042j
50.575405497471694779 - 6.5719519520440329051e-6134j 4.12e-2003, 4.12e-2003j
11.011662869529294648 + 2.4758503226719092101e-6150j 1.79e-2018, 1.79e-2018j
34.530691818640076386 + 1.3176401598310747099e-6137j 6.93e-2007, 6.93e-2007j
202.67021110510049255 + 2.5125683725887764168e-6130j 2.07e-2001, 2.07e-2001j

Weights

Weight (ball center) Error (ball radius)
1.5057818242865752471e-135 - 6.0194018455579885083e-4236j 1.74e-372, 3.48e-1879j
4.8336816283729924089e-129 + 1.1710159226291772186e-4232j 1.07e-370, 2.13e-1877j
1.1990062580196756541e-113 - 7.2263149015436367092e-4225j 9.12e-367, 1.82e-1873j
2.6230039816354164229e-118 + 3.1573256371230376932e-4227j 3.35e-368, 6.67e-1875j
2.9049466816735379191e-105 - 1.2821133927906914402e-4220j 4.41e-365, 8.79e-1872j
5.8447351690844706925e-07 - 6.3274648006206312771e-4170j 3.65e-266, 7.27e-1773j
3.5845172001381912978e-18 + 1.176310244603823828e-4174j 8.26e-304, 1.65e-1810j
7.460657120180010298e-85 - 2.9944541804236357495e-4210j 6.14e-359, 1.22e-1865j
2.1714854389854174653e-123 - 8.4621219103648525476e-4230j 6.48e-370, 1.29e-1876j
3.2887894688413942019e-21 + 8.9927669694212938775e-4177j 1.78e-310, 3.55e-1817j
1.1070934905277621813e-10 - 9.8988330437085023705e-4172j 5.27e-286, 1.05e-1792j
2.1243352763556526249e-11 + 4.6112143862667084114e-4172j 2.08e-288, 4.14e-1795j
7.1744544948513600537e-62 + 1.6647968156510002978e-4198j 9.96e-350, 1.98e-1856j
6.3774849702171646472e-38 - 4.4714666521654357954e-4186j 3.16e-333, 6.31e-1840j
1.0348831169508882741e-25 + 1.8317226004877643425e-4179j 1.55e-319, 3.09e-1826j
2.6596575423827404755e-16 + 4.8034639582171071989e-4174j 1.88e-303, 3.76e-1810j
1.6383675407901836671e-07 + 3.3461514029216310048e-4170j 1.35e-277, 2.69e-1784j
3.9750068847956282038e-46 + 2.2528391910334750269e-4190j 1.58e-340, 3.14e-1847j
2.1437667133481419149e-44 - 1.7989651665454013622e-4189j 3.5e-339, 6.97e-1846j
1.2345239016363020105e-143 + 4.9475172148036702278e-4240j 1.71e-381, 3.4e-1888j
3.8204891434584120858e-12 - 2.1161398297553538906e-4172j 2.74e-296, 5.46e-1803j
1.0149412372651507434e-13 - 4.3488898887746108211e-4173j 1.13e-300, 2.26e-1807j
1.7856227570320306643e-39 + 6.7930840236501313755e-4187j 9.91e-336, 1.97e-1842j
5.4105158994379936034e-10 + 2.0873164930122413977e-4171j 2.03e-291, 4.05e-1798j
2.5523497332869970256e-109 + 1.1264334136717104394e-4222j 6.84e-370, 1.36e-1876j
1.5236383261809306735e-55 - 2.9981801141175899138e-4195j 1.19e-348, 2.38e-1855j
2.4808619889001538649e-09 - 4.3149808672668103157e-4171j 2.76e-291, 5.5e-1798j
2.1492760830034462258e-23 + 4.0095468288215873973e-4178j 4.27e-320, 8.51e-1827j
3.1974621180804694031e-17 - 3.178547394816498819e-4174j 1.49e-309, 2.96e-1816j
6.1767698677731849869e-06 - 2.1100626653035100065e-4169j 3.28e-282, 6.54e-1789j
4.7328676637102926067e-91 - 2.1053217816720550768e-4213j 8.15e-366, 1.62e-1872j
6.4360079470561778109e-13 + 9.6095199647006114577e-4173j 8.26e-302, 1.65e-1808j
3.6320115762535587707e-28 + 7.7977026252408251507e-4181j 1.26e-327, 2.52e-1834j
1.9495440927391174445e-101 + 1.1194801495131174126e-4218j 6.18e-369, 1.23e-1875j
8.2961706623856852701e-98 - 7.7783184875082532106e-4217j 4.17e-368, 8.3e-1875j
1.6477905538793687893e-33 + 9.8741083777252586537e-4184j 4.91e-335, 9.78e-1842j
6.382660735024540175e-27 - 3.8248462112158622678e-4180j 6.74e-328, 1.34e-1834j
1.3641990484278042167e-57 + 2.6400584502568303165e-4196j 3.24e-353, 6.46e-1860j
4.0627025134556420369e-32 - 5.5139321604595064432e-4183j 4.25e-334, 8.46e-1841j
3.7436852122393209227e-19 + 3.1408953977599770845e-4175j 6.79e-320, 1.35e-1826j
6.1121320544896802457e-35 - 1.7017141524059620113e-4184j 1.13e-336, 2.26e-1843j
4.529714117440944021e-41 - 9.8602130937390970396e-4188j 5.53e-342, 1.1e-1848j
0.00013352973491576524435 + 1.0790017475291442556e-4168j 2.34e-295, 4.65e-1802j
0.0033572747441055399319 + 6.8791711868873697033e-4168j 2.27e-287, 4.52e-1794j
2.0951094090282742565e-76 + 6.0612695867460535304e-4206j 2.61e-365, 5.19e-1872j
1.0635013460577528597e-59 - 2.1722608715682259244e-4197j 6.51e-356, 1.3e-1862j
6.5961365225617001659e-48 - 2.6754839358483551615e-4191j 8.11e-349, 1.62e-1855j
1.0677571694701277623e-08 + 8.7332495120678303341e-4171j 5.17e-310, 1.03e-1816j
0.082486958254647427866 - 3.8068497057955391209e-4167j 2.69e-274, 5.36e-1781j
0.00075981790009447225359 + 2.8544875550553858524e-4168j 1.11e-297, 2.21e-1804j
3.0199560272089383071e-71 + 2.6165506808331525341e-4203j 1.71e-363, 3.4e-1870j
0.13441236320437181004 - 1.8468566915648681384e-4167j 1.82e-278, 3.62e-1785j
2.3671286011583641066e-94 + 4.4234858008366953636e-4215j 3.83e-372, 7.64e-1879j
1.959699680628291925e-06 + 1.1690360686602271151e-4169j 4.79e-309, 9.55e-1816j
1.4972600177255627818e-14 + 1.9855265306160008422e-4173j 6.04e-322, 1.2e-1828j
6.2074140691830163806e-82 + 9.1954660093573533677e-4209j 3.6e-368, 7.17e-1875j
5.0989100815558961769e-05 - 6.4096203620145438323e-4169j 5.51e-308, 1.1e-1814j
0.0003286377351077699072 - 1.775200334148090875e-4168j 1.42e-305, 2.83e-1812j
8.6103533431656149882e-69 - 4.7160895207387689447e-4202j 5.66e-363, 1.13e-1869j
1.9039294448236251449e-29 - 1.5456811576446961545e-4181j 3.33e-339, 6.63e-1846j
0.029800381814956171377 + 2.723684567989018921e-4167j 1.76e-300, 3.5e-1807j
9.7595318529608452058e-50 + 3.0070370223183740698e-4192j 5.33e-353, 1.06e-1859j
8.78558709106207914e-74 - 1.3230972182987397745e-4204j 3.48e-365, 6.94e-1872j
0.0016491803127408368446 - 4.4849424061570577325e-4168j 6.11e-310, 1.22e-1816j
0.0064023916994223526964 - 1.0277150037431992357e-4167j 2.14e-308, 4.27e-1815j
1.0382333473155643241e-42 + 1.3650081003562552179e-4188j 2.2e-348, 4.38e-1855j
1.5504368183530610774e-24 - 8.612996837405969449e-4179j 2.71e-337, 5.41e-1844j
4.040916980239428152e-79 - 2.4985388098859683114e-4207j 7.47e-368, 1.49e-1874j
9.1789790616775915269e-31 + 2.9694092828508824887e-4182j 2.91e-341, 5.79e-1848j
0.043946761468464520297 - 3.3308785418715408935e-4167j 1.06e-309, 2.11e-1816j
0.061650728848473208899 + 3.7291239459605721473e-4167j 1.28e-308, 2.54e-1815j
0.10450735474983833717 + 3.5678953463199807147e-4167j 5.59e-307, 1.11e-1813j
0.084417754776606258249 - 6.2915646295312948895e-4168j 1.13e-306, 2.25e-1813j
0.011423254918140136442 + 1.4881525161496897566e-4167j 2.07e-313, 4.13e-1820j
0.019059674178404475578 - 2.0695286570978135722e-4167j 1.6e-312, 3.18e-1819j
3.6390249231369092715e-20 - 4.6852802520607166784e-4176j 1.44e-335, 2.87e-1842j
0.13546816925103817076 + 2.4984994212309261091e-4167j 1.56e-311, 3.1e-1818j
2.0690378597929860266e-36 + 2.8170863233410610692e-4185j 1.34e-345, 2.66e-1852j
4.1599199517284853366e-64 - 1.1842334809022110586e-4199j 1.73e-362, 3.45e-1869j
4.315430087192303764e-08 - 1.7289576765864001319e-4170j 1.12e-327, 2.23e-1834j
0.12385672147684972762 - 3.0986615276007099645e-4167j 3.14e-316, 6.25e-1823j
0.11745866256215514293 + 1.2052853731880834562e-4167j 7.18e-316, 1.43e-1822j
1.2823942476676514258e-51 - 3.1914261795206580199e-4193j 3.85e-356, 7.66e-1863j
1.4900029657889234016e-53 + 3.1909646485268994014e-4194j 2.75e-357, 5.48e-1864j
2.0576369186762251604e-66 + 7.7886636284736239503e-4201j 3.46e-364, 6.89e-1871j
0.03880214846328720842 + 1.8218126849334315845e-4168j 4.74e-325, 9.44e-1832j
2.7604127124003805318e-22 - 1.872747204282850527e-4177j 1.89e-341, 3.77e-1848j
1.8303035423948909361e-05 + 3.7205978403414096379e-4169j 2.54e-331, 5.06e-1838j
2.0647652749720300478e-15 - 9.3604090852917819628e-4174j 7.71e-338, 1.54e-1844j
6.8716899080665493911e-88 + 8.5380542990496213133e-4212j 3.06e-375, 6.1e-1882j

Download

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