Rule: Q[1, 5, 81]

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)
364.70488671967104226 - 3.7058332311273568931e-5259j 3.18e-2019, 3.18e-2019j
5.8057691850172600401 + 7.451321485125144104e-5263j 2.67e-2023, 2.67e-2023j
0.77396576205210044402 - 2.0699253321526929977e-5273j 2.9e-2034, 2.9e-2034j
3.1545902422201367634 + 1.1975219663969573462e-5267j 7.28e-2028, 7.28e-2028j
2.5922508199253002476 + 2.1827090235837616054e-5268j 4.84e-2029, 4.84e-2029j
3.7725969804218535432 - 7.8815217935890680745e-5267j 9.63e-2027, 9.63e-2027j
0.54552424341743693578 - 1.7244717540637540465e-5275j 1.27e-2035, 1.27e-2035j
1 + 8.1374857547143225686e-5273j 3.41e-2033, 3.41e-2033j
4.4400801361300083774 - 3.7973926456645737353e-5266j 1.54e-2025, 1.54e-2025j
0.18296039898248679851 + 9.2814191588449597149e-5279j 1.71e-2038, 1.71e-2038j
2.0888317533461807198 + 9.1967034419472132165e-5270j 3.54e-2030, 3.54e-2030j
0.073765441352378364894 + 4.7965673219203753294e-5280j 4.81e-2040, 4.81e-2040j
1.2795587377813284532 - 1.0903910662717807898e-5271j 2.58e-2032, 2.58e-2032j
0.013897592465495336133 + 1.400567511342109188e-5280j 8.03e-2042, 8.03e-2042j
1.648179548633091094 - 2.1695009043583035096e-5271j 2.88e-2031, 2.88e-2031j
5.1384848875831238418 - 4.8897796877936182232e-5264j 2.43e-2024, 2.43e-2024j
0.34176519325184011536 + 9.4247928693851589423e-5277j 5.09e-2037, 5.09e-2037j
307.31287767105730966 - 2.792486023179117284e-5248j 1.76e-2014, 1.76e-2014j
213.61719216964512015 - 6.1225908019304430227e-5239j 3.63e-2005, 3.63e-2005j
240.76063496413337399 - 2.5673193654198263832e-5254j 1.48e-2007, 1.48e-2007j
222.12216209340021935 + 9.606477812587296552e-5277j 7.47e-2006, 7.47e-2006j
289.40160492241457598 - 7.5993572935595038431e-5293j 1.59e-2012, 1.59e-2012j
251.1195132517658756 + 5.7123393046467272432e-5327j 1.58e-2008, 1.58e-2008j
95.376004193487653957 - 6.8777657118215423798e-5405j 1.2e-2000, 1.2e-2000j
19.13616205276710311 - 1.3762297324325692282e-5473j 6.97e-2014, 6.97e-2014j
183.53606035862039647 - 1.0260856057345564149e-5497j 7.09e-2003, 7.09e-2003j
25.805407590651580448 + 1.0205591441291464044e-5558j 5.95e-2011, 5.95e-2011j
13.524203796133260503 + 3.6282910447441628568e-5580j 4.7e-2017, 4.7e-2017j
49.993466849270057316 - 2.0528524338171444452e-5683j 1.02e-2004, 1.02e-2004j
73.650648639762012514 + 7.217621048374889326e-5903j 8.21e-2002, 8.21e-2002j
91.490029760198631267 + 6.6038308895326040058e-6019j 8.93e-2001, 8.93e-2001j
274.96674351104080728 - 5.2381634954502089761e-6126j 5.8e-2011, 5.8e-2011j
11.106852602481931262 + 1.822361414127862245e-6181j 1.06e-2018, 1.06e-2018j
112.09847531797186893 + 1.9568440268411643951e-6224j 2.38e-2000, 2.38e-2000j
116.5957295415205207 - 1.7877674322986759641e-6296j 2.18e-2000, 2.18e-2000j
17.63537587982276856 - 6.4074368131464430222e-6341j 1.2e-2014, 1.2e-2014j
20.702943009723597532 - 1.7298710036059452416e-6339j 3.84e-2013, 3.84e-2013j
52.650932528303100408 + 2.205051895271178829e-6326j 2.83e-2004, 2.83e-2004j
103.49327712999841776 - 9.8096127102354640725e-6354j 1.79e-2000, 1.79e-2000j
205.55433455315233822 - 4.7518380499297433071e-6396j 1.68e-2004, 1.68e-2004j
164.10005480562069588 - 2.4336398393091108236e-6422j 9.26e-2002, 9.26e-2002j
31.526205088514611046 + 1.0058069853736931748e-6445j 5.15e-2009, 5.15e-2009j
107.73264922622348588 - 2.3641873967103351379e-6436j 2.03e-2000, 2.03e-2000j
67.204118988551831266 - 1.8792829624599455209e-6446j 2.08e-2002, 2.08e-2002j
141.26393049692818846 + 1.3486883120713410039e-6444j 8.13e-2001, 8.13e-2001j
197.88006947872798892 + 1.7372645986302911964e-6446j 7e-2004, 7e-2004j
190.55205951252121761 - 3.1451223719708034776e-6448j 2.32e-2003, 2.32e-2003j
262.41313972076267048 - 1.8357987873172044046e-6466j 1.16e-2009, 1.16e-2009j
126.00680343963579355 - 8.0041310069680568027e-6456j 1.79e-2000, 1.79e-2000j
176.80386110024877131 + 8.3109859225692282844e-6478j 1.77e-2002, 1.77e-2002j
29.549239568130292819 - 4.9943143297768832696e-6501j 1.21e-2009, 1.21e-2009j
9.9960153251602673207 - 1.9968608109242457316e-6510j 1.6e-2019, 1.6e-2019j
24.036895404249636087 + 2.8184197345404419213e-6502j 1.11e-2011, 1.11e-2011j
231.13878618614262694 - 3.34639608847488571e-6491j 1.14e-2006, 1.14e-2006j
130.93315859812040834 + 3.6695008236023938624e-6496j 1.51e-2000, 1.51e-2000j
7.1121518020625852474 - 3.3790554823550309588e-6530j 6.89e-2022, 6.89e-2022j
44.919009095924465826 + 4.8094350185393009765e-6515j 1.19e-2005, 1.19e-2005j
47.416634762278390142 - 1.5713292456772769938e-6514j 3.66e-2005, 3.66e-2005j
12.283176196602546873 - 1.7154862476123269717e-6526j 7.29e-2018, 7.29e-2018j
87.714288880495121149 + 3.9134784934879291969e-6507j 6.04e-2001, 6.04e-2001j
27.642589837851714307 + 8.3185651262434025028e-6548j 2.74e-2010, 2.74e-2010j
37.888275942210005662 + 1.8908083702351434455e-6541j 2.93e-2007, 2.93e-2007j
84.045460316760202003 - 2.3220368210196636591e-6536j 4.01e-2001, 4.01e-2001j
14.829781217182764814 - 1.5992929654382316704e-6604j 3.25e-2016, 3.25e-2016j
158.09129474068730876 - 3.3495342357563558753e-6588j 1.77e-2001, 1.77e-2001j
99.375795234921221862 + 6.085672343180964632e-6640j 1.53e-2000, 1.53e-2000j
35.694740094089927687 - 1.0760882080756827082e-6676j 8.34e-2008, 8.34e-2008j
6.3983317013818745945 + 2.4626387979667467072e-6704j 1.51e-2022, 1.51e-2022j
61.122733620093376413 + 3.0313216080228498387e-6682j 4.75e-2003, 4.75e-2003j
146.6854155579584151 - 1.2129364864078130968e-6714j 5.31e-2001, 5.31e-2001j
64.11882708384905974 - 1.7754192606506319294e-6733j 1.02e-2002, 1.02e-2002j
8.9529512477548957267 - 5.5756321297236283576e-6799j 2.27e-2020, 2.27e-2020j
77.016414115799729966 - 4.6192458401286866772e-6779j 1.55e-2001, 1.55e-2001j
80.480459085705047923 + 3.2063146972690014165e-6880j 2.44e-2001, 2.44e-2001j
136.01617888926463286 + 1.6803776857629277605e-6981j 1.1e-2000, 1.1e-2000j
121.22985022116664056 - 9.9012998097170943381e-7043j 2.14e-2000, 2.14e-2000j
7.9843162107574581149 + 1.3918534991190431382e-7081j 3.79e-2021, 3.79e-2021j
55.390545128548039538 - 2.101898569771178899e-7061j 7.41e-2004, 7.41e-2004j
58.21391042599698358 + 1.9404535515037544333e-7069j 1.91e-2003, 1.91e-2003j
40.156065637088256576 - 9.9458982232869641727e-7083j 1.11e-2006, 1.11e-2006j
42.499243162379134736 - 1.2410384365941174969e-7080j 3.77e-2006, 3.77e-2006j
33.574386985879257873 - 1.4995488375327680394e-7089j 2.11e-2008, 2.11e-2008j
70.380662921939641995 - 9.0382814573503420029e-7111j 4.23e-2002, 4.23e-2002j
22.336306081122785411 + 2.7618205669380192523e-7146j 2.16e-2012, 2.16e-2012j
152.2907356209679864 + 2.0980722750457788053e-7171j 3.17e-2001, 3.17e-2001j
170.33186077318270411 + 4.5889146159464182212e-7219j 4.38e-2002, 4.38e-2002j
16.200062471866807423 + 2.1192039330491527677e-7259j 1.95e-2015, 1.95e-2015j

Weights

Weight (ball center) Error (ball radius)
4.4722106208065217144e-154 - 6.7460986007081461998e-5347j 1.38e-361, 7.06e-1871j
0.0018582094089013699239 + 7.500825349442456343e-5267j 3.69e-207, 1.89e-1716j
0.10497677168291650852 - 4.4335484466933282373e-5265j 1.8e-147, 9.24e-1657j
0.025201715129427780658 - 1.2151389692929086488e-5265j 5.08e-185, 2.6e-1694j
0.039923375751495882543 + 1.3919162310577790376e-5265j 2.97e-178, 1.52e-1687j
0.01481355059821945242 + 1.2129293944507004319e-5265j 7.24e-192, 3.71e-1701j
0.12848431227638826584 + 2.8923148515735288361e-5265j 1.18e-147, 6.05e-1657j
0.087448768962572413433 + 4.917806991970346544e-5265j 1.74e-150, 8.93e-1660j
0.0081158220387920924674 - 1.547901895891766266e-5265j 3.86e-198, 1.98e-1707j
0.11174952565211671056 + 1.0561924361328254965e-5265j 3.76e-148, 1.93e-1657j
0.058559417867088946636 - 1.7694234945584265741e-5265j 2.25e-172, 1.15e-1681j
0.078306135086368289189 - 5.3552954197570256337e-5266j 1.49e-148, 7.66e-1658j
0.090811760797485235024 - 3.7515383858989764451e-5265j 3.73e-157, 1.91e-1666j
0.035241982028249909877 + 1.547709554018091938e-5266j 7.18e-149, 3.68e-1658j
0.078314845239910791271 + 2.4822892518689698339e-5265j 3.72e-165, 1.91e-1674j
0.0041020822425931049987 + 2.2756409312590198147e-5265j 7.77e-204, 3.98e-1713j
0.12988465619623007582 - 1.7739910204146864709e-5265j 2.27e-149, 1.17e-1658j
7.1963389878505190724e-133 + 1.0658253592796613202e-5336j 1.15e-357, 5.92e-1867j
1.3961764779262493153e-92 + 2.8232398097255944341e-5316j 4.85e-345, 2.49e-1854j
2.7379512089269867956e-104 - 3.0210493452634811319e-5322j 1.35e-349, 6.9e-1859j
2.9885246014791736539e-96 - 3.7708001045579968289e-5318j 9.81e-347, 5.03e-1856j
3.247808464830828209e-125 - 7.5536510965746342118e-5333j 4.91e-357, 2.52e-1866j
9.3978188282866331436e-109 + 1.6238584079495774492e-5324j 1.92e-351, 9.82e-1861j
1.4944218011567148724e-41 - 8.4303347403740528536e-5290j 4.18e-322, 2.14e-1831j
7.4990838867487608817e-09 + 3.939902572356053866e-5271j 1.31e-268, 6.7e-1778j
1.3435293991785999281e-79 + 1.2759145611631188072e-5309j 1.15e-342, 5.9e-1852j
1.1188755849574029387e-11 + 4.9795754835730043478e-5273j 2.85e-279, 1.46e-1788j
1.7038931881114978945e-06 + 2.5608611903311787388e-5269j 5.42e-258, 2.78e-1767j
5.0804363400605132912e-22 - 3.6036826703420440378e-5279j 7.53e-302, 3.86e-1811j
3.425603512956318782e-32 - 8.7960244225279895468e-5285j 1.37e-314, 7e-1824j
7.0731979553745138651e-40 + 6.563485800328546795e-5289j 3.68e-321, 1.89e-1830j
5.1159976751334536524e-119 + 1.0183672215938734869e-5329j 8.6e-357, 4.41e-1866j
1.7167296050215454502e-05 + 2.1437965800906695696e-5268j 4.15e-257, 2.13e-1766j
9.1774193166322100764e-49 - 1.3006787754104934758e-5293j 6.63e-329, 3.4e-1838j
1.0532562235673149937e-50 + 1.2436427698491808998e-5294j 2.12e-330, 1.09e-1839j
3.2193664364499320086e-08 - 1.1288315801072045214e-5270j 1.53e-273, 7.84e-1783j
1.6328177490013373749e-09 - 1.3569919335636182792e-5271j 1.88e-278, 9.64e-1788j
3.6734781352885949395e-23 + 8.2123144562168037853e-5280j 1.93e-307, 9.87e-1817j
4.724739686968557928e-45 - 1.178057886521404201e-5291j 9.25e-327, 4.75e-1836j
4.2106381051937756555e-89 - 1.7004396430137008083e-5314j 4.93e-349, 2.53e-1858j
3.3024414264610415846e-71 - 2.6844601264386221445e-5305j 1.86e-343, 9.56e-1853j
4.0931865578777166019e-14 - 1.4910371753032795009e-5274j 1.35e-296, 6.91e-1806j
7.0138380356363773532e-47 + 1.2763167255992449044e-5292j 1.33e-328, 6.84e-1838j
2.0381898945342794121e-29 - 2.8440230373482004997e-5283j 1.33e-317, 6.81e-1827j
2.3813800714824722756e-61 - 3.4327338198455218929e-5300j 2.83e-339, 1.45e-1848j
8.6405222140510478019e-86 + 8.4580897891196319313e-5313j 7.29e-349, 3.74e-1858j
1.2578264261154504057e-82 - 3.5474617591912339082e-5311j 6.5e-348, 3.34e-1857j
1.2860835573982758549e-113 - 5.5265478221580694659e-5327j 2.24e-360, 1.15e-1869j
9.1564582565225149084e-55 + 9.2845975621670688889e-5297j 2.87e-337, 1.47e-1846j
1.0826886962297751028e-76 - 3.990516085737190779e-5308j 1.23e-346, 6.31e-1856j
2.8516874813666578958e-13 + 4.9247377387153063125e-5274j 2.03e-304, 1.04e-1813j
4.9115549893601910591e-05 - 6.548253298135741838e-5268j 1.39e-281, 7.11e-1791j
6.3105300908078734854e-11 - 1.5290878517522035784e-5272j 2.01e-299, 1.03e-1808j
3.8568598036343094001e-100 + 3.9160142998318526403e-5320j 2.08e-355, 1.07e-1864j
6.850435564207721695e-57 - 7.2035551754274070042e-5298j 8.59e-339, 4.4e-1848j
0.00065768302457925421832 + 3.5542286873546626527e-5266j 3.3e-278, 1.69e-1787j
7.6311239378107518568e-20 - 6.239564890079489462e-5278j 3.14e-316, 1.61e-1825j
6.4794371301252607301e-21 + 1.5257882879575532105e-5278j 4.73e-317, 2.42e-1826j
5.5952115827835164821e-06 - 7.3236372650019433894e-5269j 3.07e-290, 1.57e-1799j
2.9985807347623913136e-38 - 4.8472968590901774652e-5288j 1.38e-330, 7.06e-1840j
1.8502495644605116748e-12 - 1.5851682158311049621e-5273j 3.5e-306, 1.79e-1815j
7.8294092327494355907e-17 + 3.4999149751114246905e-5276j 3.73e-314, 1.91e-1823j
1.1423498483602135466e-36 + 3.4017536108424391153e-5287j 2.55e-330, 1.31e-1839j
4.8520700123946286892e-07 - 9.0497701095176690566e-5270j 1.72e-297, 8.82e-1807j
1.2967263985638883189e-68 + 5.8813158491127561997e-5304j 3.15e-347, 1.62e-1856j
2.8180505493444803596e-43 + 1.0252132841978480766e-5290j 3.4e-333, 1.74e-1842j
6.7885244294997519413e-16 - 1.2584670654885042158e-5275j 1.51e-314, 7.74e-1824j
0.0010290753298526535017 - 1.7238208009069131692e-5265j 9.82e-290, 5.03e-1799j
8.4114726519582950572e-27 - 7.7601709102709589655e-5282j 6.94e-326, 3.56e-1835j
1.0879590632852303921e-63 + 2.0903958230680219011e-5301j 9.72e-346, 4.98e-1855j
4.3298454443093280563e-28 + 1.5165334517690418335e-5282j 8.93e-327, 4.58e-1836j
0.00013034026469090081244 + 2.152236408239557811e-5267j 6.64e-299, 3.4e-1808j
1.2176436070560456627e-33 + 1.4469128807813339169e-5285j 2.28e-330, 1.17e-1839j
3.9227448655834972144e-35 - 2.2722677730866759937e-5286j 4.69e-331, 2.41e-1840j
4.3843744789115065249e-59 + 5.1771754054627779647e-5299j 1.8e-344, 9.25e-1854j
1.0545277789570998363e-52 - 1.1125811383833174987e-5295j 7.24e-341, 3.71e-1850j
0.00031573229614591378564 - 7.9974418198716090547e-5267j 2.36e-304, 1.21e-1813j
2.4458295927158257487e-24 - 1.8038508480869277585e-5280j 4.62e-327, 2.37e-1836j
1.4971524332796147754e-25 + 3.8149833469637532378e-5281j 8.47e-328, 4.34e-1837j
8.3785273845500521468e-18 - 9.4403387468594411189e-5277j 4.64e-324, 2.38e-1833j
8.310384144688227271e-19 + 2.4670063696177120338e-5277j 1.07e-324, 5.48e-1834j
5.4669906263601794644e-15 + 4.3935806973835216403e-5275j 2.13e-322, 1.09e-1831j
8.7561192098258833478e-31 + 5.1120240757719545205e-5284j 5.78e-332, 2.96e-1841j
3.3217411538949903833e-10 + 4.5982038918465379813e-5272j 6.81e-320, 3.49e-1829j
4.1392219713130486715e-66 - 1.1632253793462314545e-5302j 7.1e-352, 3.64e-1861j
6.7376173783195717227e-74 + 1.0980111385506307803e-5306j 6.73e-356, 3.45e-1865j
1.2923404174065369833e-07 + 3.2036605514733504223e-5270j 1.24e-319, 6.35e-1829j

Download

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