Rule: Q[4, 95]

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)
363.75991430907298986 + 1.2847164792066215451e-4072j 6.43e-2012, 6.43e-2012j
302.80761271926730986 + 2.1087814016926286153e-4056j 4.38e-2005, 4.38e-2005j
281.19388701070648068 + 3.9239603344398456839e-4059j 6.59e-2003, 6.59e-2003j
328.60354336597576471 - 4.6042455507856743022e-4070j 7.05e-2008, 7.05e-2008j
344.25110206546458149 - 3.3816369602030808636e-4074j 1.25e-2009, 1.25e-2009j
189.09427817286737177 - 1.3091090352759086556e-4077j 8.74e-1996, 8.74e-1996j
262.21090942781864972 + 1.1486195878747862185e-4113j 3.78e-2001, 3.78e-2001j
177.29885622817272768 + 4.2277124748472133e-4170j 3.43e-1995, 3.43e-1995j
195.27140215457887309 - 5.7724718660970920339e-4243j 4.01e-1996, 4.01e-1996j
271.43002442199039391 + 2.708020434086161717e-4323j 5.36e-2002, 5.36e-2002j
41.944536143544137228 + 1.6886571248713190806e-4380j 1.99e-2002, 1.99e-2002j
183.10703457125285139 + 5.2968553739791134952e-4435j 1.82e-1995, 1.82e-1995j
30.047954498502785981 + 3.4568274190318628672e-4507j 3.39e-2006, 3.39e-2006j
58.722707343361102847 - 9.04038478989626407e-4505j 7.89e-1999, 7.89e-1999j
131.76970518512018863 + 1.4179151275876997388e-4576j 4.42e-1994, 4.42e-1994j
53.594680732456719395 - 3.8909225295678701898e-4629j 9.24e-2000, 9.24e-2000j
31.879061399985772598 + 7.2724386992361119538e-4641j 1.61e-2005, 1.61e-2005j
61.391041810592150994 - 1.3059579425833980786e-4628j 2.01e-1998, 2.01e-1998j
150.63919100790127739 + 3.7635534177227844321e-4666j 2.49e-1994, 2.49e-1994j
21.768436944375766258 - 4.9940147030448262242e-4725j 7.62e-2010, 7.62e-2010j
26.562628664829997315 + 1.3064987762464488724e-4722j 1.3e-2007, 1.3e-2007j
33.769941613794532678 - 6.1693628249203330107e-4720j 7.3e-2005, 7.3e-2005j
136.3037499281299745 + 1.16739150937987702e-4707j 4.2e-1994, 4.2e-1994j
99.347891727883534806 + 1.0300323318483570292e-4730j 9.22e-1995, 9.22e-1995j
23.30936808841722641 - 7.2104433484176975092e-4760j 4.67e-2009, 4.67e-2009j
64.130426988805593122 + 4.9228492221409528309e-4749j 5.76e-1998, 5.76e-1998j
35.721238923212825756 + 3.4783143144189218836e-4755j 3.23e-2004, 3.23e-2004j
291.604842564388957 - 2.9031700911355510588e-4744j 5.99e-2004, 5.99e-2004j
66.94206357561062859 - 4.8947085934856243652e-4753j 1.35e-1997, 1.35e-1997j
56.124282203753660544 - 4.6668339312897237578e-4765j 2.73e-1999, 2.73e-1999j
114.746747624077793 + 4.2638371943583542528e-4761j 2.95e-1994, 2.95e-1994j
17.482636332695491527 - 2.8762736237445598977e-4810j 2.88e-2012, 2.88e-2012j
1.7457611011583465757 + 4.9706911459604495447e-4828j 2.97e-2030, 2.97e-2030j
10.389736106824211401 - 1.6422046219747917597e-4815j 1.5e-2017, 1.5e-2017j
14.901858532952281524 - 7.6422786635584242552e-4812j 6.58e-2014, 6.58e-2014j
39.807813328536743583 + 9.7436443723567274429e-4801j 5.38e-2003, 5.38e-2003j
44.144570950728083299 + 1.6585599503082291749e-4799j 7.15e-2002, 7.15e-2002j
127.35067919524705655 + 4.9819257020944792988e-4791j 4.23e-1994, 4.23e-1994j
5.2126249633141045037 + 1.4300449570745198685e-4833j 2.57e-2023, 2.57e-2023j
8.4532141550855388497 + 6.6111267969081975069e-4830j 2.01e-2019, 2.01e-2019j
92.203330252234670831 + 2.3309827629307522953e-4804j 3.4e-1995, 3.4e-1995j
1.3750274066308983896 - 6.322017363641914284e-4842j 1.35e-2031, 1.35e-2031j
315.0202815156895323 - 1.7842601152950195949e-4816j 2.14e-2006, 2.14e-2006j
103.05528623195654592 + 1.328802112112868194e-4802j 1.29e-1994, 1.29e-1994j
4.5366202969211279833 + 2.3186093548635886891e-4846j 2.77e-2024, 2.77e-2024j
118.84263014338422856 + 7.7850720745525358922e-4814j 3.5e-1994, 3.5e-1994j
222.15053977946132764 - 2.6690212486065842908e-4827j 7.49e-1998, 7.49e-1998j
85.404941766742939267 + 3.7666560181431236161e-4838j 1.17e-1995, 1.17e-1995j
2.541293607187861859 + 4.5176373642329558227e-4871j 7.61e-2028, 7.61e-2028j
72.787214167852351048 + 5.0699055859136206417e-4840j 7.15e-1997, 7.15e-1997j
110.75211348974266206 - 1.1698201327516696842e-4837j 2.34e-1994, 2.34e-1994j
253.46073002873943191 - 2.2433214886918734234e-4860j 2.39e-2000, 2.39e-2000j
229.49996889158941993 - 2.1981902103302149861e-4906j 2.09e-1998, 2.09e-1998j
3.9194594646869565397 + 7.8081283672562473098e-5004j 3.49e-2025, 3.49e-2025j
18.855527236324885174 + 1.0134118594203867554e-4989j 2e-2011, 2e-2011j
82.130718652578318738 - 1.4756525591172300101e-4972j 6.25e-1996, 6.25e-1996j
208.24584930212046699 + 7.9429244854735786381e-5068j 6.63e-1997, 6.63e-1997j
160.85728079832380939 + 2.3538559020490514894e-5157j 1.38e-1994, 1.38e-1994j
28.276006031328970672 - 3.1738179001911547481e-5241j 6.73e-2007, 6.73e-2007j
5.9433620301618339693 + 4.4258940930039824757e-5261j 2.3e-2022, 2.3e-2022j
166.18217416559164177 + 1.0640305531635306042e-5231j 9.2e-1995, 9.2e-1995j
123.04283915860120669 - 3.1164899440187517904e-5317j 4.14e-1994, 4.14e-1994j
0.51745972389347744988 + 1.2661947763821468555e-5454j 1.32e-2035, 1.32e-2035j
16.164881520749349709 - 3.5223252308647051709e-5419j 4.58e-2013, 4.58e-2013j
0.3225476896193923118 - 2.173764861858644766e-5455j 4.62e-2037, 4.62e-2037j
12.538493952290904412 - 1.7742594105604536414e-5419j 1.16e-2015, 1.16e-2015j
20.283978943456420057 + 6.1461717178134998654e-5416j 1.18e-2010, 1.18e-2010j
201.65062559766494239 - 5.2743105691505395998e-5413j 1.71e-1996, 1.71e-1996j
145.73381055354891613 - 2.5807009829268454453e-5485j 3.07e-1994, 3.07e-1994j
0.070612369773139596043 - 7.7126835513483973787e-5598j 6.18e-2040, 6.18e-2040j
3.372980634813155439 - 6.8037006823766598856e-5584j 3.93e-2026, 3.93e-2026j
2.9218319807566643015 - 1.0882434172990652061e-5584j 6.12e-2027, 6.12e-2027j
88.76186155101042712 - 5.2226312415374318258e-5551j 2.07e-1995, 2.07e-1995j
46.408730082106936663 - 2.9226286203906924348e-5590j 2.52e-2001, 2.52e-2001j
48.737865234487256106 + 1.3864855747955497948e-5609j 9.03e-2001, 9.03e-2001j
1.044588323169393218 + 1.7420678504816447084e-5724j 7.19e-2033, 7.19e-2033j
7.5639901270233977967 + 3.0669799662839319954e-5686j 2.26e-2020, 2.26e-2020j
106.85585499669247078 + 2.1716311824442318652e-5714j 1.78e-1994, 1.78e-1994j
155.67841113927978456 - 1.2711828799609315639e-5854j 1.88e-1994, 1.88e-1994j
140.95695566570776216 + 2.800066922090681761e-5941j 3.9e-1994, 3.9e-1994j
11.437449571414264248 + 1.9314621599409137345e-6004j 1.32e-2016, 1.32e-2016j
0.75828522126306480515 - 1.4628600213601226876e-6023j 2.79e-2034, 2.79e-2034j
95.731311927937090502 - 5.6776888957423718585e-5981j 5.75e-1995, 5.75e-1995j
37.73362747312910046 - 4.7610356430754339475e-6014j 1.37e-2003, 1.37e-2003j
171.66011135581200262 + 1.3164114026450427649e-6002j 5.68e-1995, 5.68e-1995j
75.823463183266972477 - 8.6326663813208096522e-6023j 1.61e-1996, 1.61e-1996j
9.3950709123011331292 - 5.0197723239538202184e-6045j 1.83e-2018, 1.83e-2018j
69.827215494963776851 + 3.4227716524719770622e-6023j 3.07e-1997, 3.07e-1997j
51.132869693511504094 + 7.0951937977846142702e-6027j 2.81e-2000, 2.81e-2000j
215.07301012670675181 + 2.3088931104963414399e-6019j 2.43e-1997, 2.43e-1997j
245.12130836208533552 - 7.4885783158713302309e-6027j 1.21e-1999, 1.21e-1999j
2.1451041073607839804 - 1.4439266081878364231e-6076j 5.89e-2029, 5.89e-2029j
13.693183578982118048 + 9.4792977400979148586e-6063j 8.92e-2015, 8.92e-2015j
78.937443416995445343 + 1.4681879897967281018e-6041j 3.21e-1996, 3.21e-1996j
237.1467377235410598 - 9.3851527674769937215e-6041j 5.31e-1999, 5.31e-1999j
0.013397743690669721619 - 1.4019184641762233177e-6102j 9.44e-2042, 9.44e-2042j
6.7273298557721838145 - 5.2771708601191630208e-6083j 2.26e-2021, 2.26e-2021j
0.17362181075218492551 + 2.7054561667286653641e-6100j 1.6e-2038, 1.6e-2038j
24.907261339552913027 - 8.2876489350581954441e-6070j 2.43e-2008, 2.43e-2008j

Weights

Weight (ball center) Error (ball radius)
2.4065494360374140045e-157 - 2.5274422577662472168e-4199j 1.94e-358, 5.03e-1860j
3.6235031753533262026e-131 - 5.0510308613352673613e-4186j 5.08e-351, 1.32e-1852j
7.6202426854442870438e-122 - 1.9784803578976831656e-4180j 2.72e-348, 7.04e-1850j
2.813633959395009092e-142 - 1.1701852068242095313e-4191j 9.4e-355, 2.44e-1856j
5.3268067414174264851e-149 + 4.4612938773624659434e-4195j 8.81e-357, 2.28e-1858j
4.5848113556916740619e-82 + 3.0435256468051401471e-4159j 3.54e-335, 9.17e-1837j
1.1918474319359941486e-113 - 1.0341087549552574955e-4176j 3.01e-347, 7.78e-1849j
5.7230666632370432366e-77 + 1.9622334742258410674e-4157j 2.23e-333, 5.78e-1835j
9.8263226366668915901e-85 + 4.3103975144232221718e-4161j 5.24e-337, 1.36e-1838j
1.2476994715045356983e-117 + 1.1173943528609691102e-4178j 5.23e-349, 1.35e-1850j
1.3177349971505388752e-18 - 1.9087237876807174179e-4128j 7.49e-284, 1.94e-1785j
1.7708581135144368848e-79 - 2.0576179437294843769e-4158j 2.03e-334, 5.27e-1836j
1.6067783363260715859e-13 - 9.9661281497514327503e-4126j 3.57e-272, 9.25e-1774j
8.2705644403527491009e-26 + 3.3173135041588394787e-4132j 5.95e-297, 1.54e-1798j
2.6547388491750655688e-57 - 4.1855172283337569635e-4148j 2.57e-326, 6.66e-1828j
1.322178623582077784e-23 + 4.6069731927536768711e-4131j 5.38e-294, 1.39e-1795j
2.6596221927557331352e-14 + 3.7677814495129193812e-4126j 4.79e-276, 1.24e-1777j
5.8906354416070622688e-27 - 8.4740577614922848195e-4133j 6.19e-299, 1.6e-1800j
1.8823793290641060216e-65 - 4.3380482346954959293e-4152j 3.99e-331, 1.03e-1832j
5.3188328646241273491e-10 + 8.653453366606903009e-4124j 1.44e-265, 3.73e-1767j
4.9024309620051598315e-12 - 6.4294541353055391565e-4125j 1.83e-271, 4.75e-1773j
4.1440340637750526387e-15 - 1.3857012185662748608e-4126j 7.5e-279, 1.94e-1780j
2.924968732515929289e-59 + 4.5443311760309000121e-4149j 3.62e-328, 9.37e-1830j
2.6147517979535733009e-43 - 3.992453440962733575e-4141j 6.85e-319, 1.77e-1820j
1.1819089258873627487e-10 - 3.7325568994741949933e-4124j 1.74e-269, 4.51e-1771j
3.9067916775911188734e-28 + 2.093282711085392121e-4133j 2.4e-302, 6.22e-1804j
6.0744517537678858235e-16 + 4.9556919067848116877e-4127j 7e-283, 1.81e-1784j
2.4556469772612717016e-126 + 7.2456052434864711943e-4184j 1.29e-357, 3.35e-1859j
2.4098961517509469184e-29 - 4.9974528693371969347e-4134j 1.48e-304, 3.82e-1806j
1.0824910671011331759e-24 - 1.2564678145323834317e-4131j 7.04e-298, 1.82e-1799j
5.9294413618144999795e-50 - 1.8622646002456073457e-4144j 8.52e-325, 2.21e-1826j
3.4370965616741758014e-08 - 9.2922058306602101091e-4123j 8.41e-268, 2.18e-1769j
0.067741068367975051639 + 1.6316404886306600636e-4118j 4.67e-207, 1.21e-1708j
3.1396590049650296567e-05 - 5.7764006449130995158e-4121j 9.19e-256, 2.38e-1757j
4.1701204233016957265e-07 - 4.0156305447933287796e-4122j 2.16e-264, 5.6e-1766j
1.0839422308689146755e-17 + 5.8186327247105734646e-4128j 7.91e-289, 2.05e-1790j
1.5029430358971052833e-19 + 6.0784804313503436721e-4129j 2.64e-292, 6.84e-1794j
2.1481761461383952375e-55 + 3.6716020653584343728e-4147j 4.96e-329, 1.29e-1830j
0.0038335872222083193808 - 1.9842341008032718105e-4119j 1.09e-243, 2.82e-1745j
0.00019520127661853614445 - 1.9568327176236183307e-4120j 4.34e-255, 1.12e-1756j
3.153036351479967391e-40 - 1.4311935409482542031e-4139j 1.57e-319, 4.06e-1821j
0.088893590426616109747 - 1.3469420001799460258e-4118j 1.84e-214, 4.76e-1716j
1.9784251969307395145e-136 + 1.0714436084109327364e-4188j 2.4e-365, 6.22e-1867j
6.5781391103384042889e-45 + 6.2632940314832186029e-4142j 5.43e-323, 1.41e-1824j
0.0069359800470887520649 + 3.5808661108027121372e-4119j 2e-246, 5.17e-1748j
1.0117878043341558207e-51 + 2.4471135756691539621e-4145j 1.5e-327, 3.88e-1829j
2.3941831644603008981e-96 + 1.0735520667709007882e-4167j 5.15e-353, 1.33e-1854j
2.6892066730752819245e-37 - 4.3654811218022862076e-4138j 9.28e-319, 2.4e-1820j
0.030026109486750800395 + 2.3602098785061205189e-4118j 6.22e-241, 1.61e-1742j
7.3405619372253826865e-32 - 2.5651116709715979771e-4135j 9.59e-314, 2.48e-1815j
3.1406060452912496233e-48 + 1.3539346512102310078e-4143j 9.35e-326, 2.42e-1827j
7.1560189660218482464e-110 + 8.7660479997185034597e-4175j 2.3e-358, 5.95e-1860j
1.5999767856618491246e-99 - 2.1956585752069542548e-4169j 7.24e-355, 1.88e-1856j
0.01161148005057773696 - 6.6413528177853349312e-4119j 6.21e-258, 1.61e-1759j
9.0669729312677436043e-09 + 4.3155813782303732322e-4123j 4.85e-287, 1.26e-1788j
6.930273676404152825e-36 + 2.2738811198590557782e-4137j 1.41e-319, 3.65e-1821j
2.4355227807693073379e-90 + 2.0159165214853431187e-4164j 3.26e-351, 8.45e-1853j
7.2576066895909766823e-70 - 3.3429341573720085335e-4154j 2.84e-342, 7.35e-1844j
9.1427355886384038809e-13 + 2.5654577979966535509e-4125j 1.29e-297, 3.34e-1799j
0.0019870560631188732035 + 1.1150967841651371849e-4119j 7.77e-274, 2.01e-1775j
3.6341893881746741321e-72 + 2.7850369813110278699e-4155j 2.14e-343, 5.53e-1845j
1.5556633898483363919e-53 - 3.0693611166233159533e-4146j 2.01e-332, 5.21e-1834j
0.12987597324350195493 + 7.4036660061997451439e-4119j 1.94e-256, 5.03e-1758j
1.2313447625298491219e-07 + 1.9540596143487591275e-4122j 1.62e-291, 4.2e-1793j
0.1245179195217697096 - 5.487212782040999523e-4119j 2.48e-258, 6.41e-1760j
4.0442510178252817013e-06 - 1.5870560115939714895e-4121j 4.43e-289, 1.15e-1790j
2.2597179564811704226e-09 - 1.9564433058888973198e-4123j 1.46e-294, 3.79e-1796j
1.7224209388857838493e-87 - 8.5151601072166917891e-4163j 6.81e-351, 1.76e-1852j
2.4744567052472645541e-63 + 4.6240521238101640651e-4151j 2.59e-339, 6.72e-1841j
0.074627756474864940806 - 1.9036565779178675385e-4119j 8.65e-265, 2.24e-1766j
0.01725549812927952901 + 1.2514610775286540005e-4118j 3.04e-275, 7.88e-1777j
0.021569085688373587367 - 2.0449717827543355269e-4118j 9.62e-274, 2.49e-1775j
9.6061355553898883487e-39 + 8.0622194233290486748e-4139j 1.44e-325, 3.73e-1827j
1.6069834498683465505e-20 - 1.878393508094756199e-4129j 2.93e-312, 7.6e-1814j
1.609454723700315454e-21 + 5.6301811504479562685e-4130j 1.89e-313, 4.9e-1815j
0.10861861399876874574 + 1.1273749838817735311e-4118j 1.49e-272, 3.86e-1774j
0.00044769564385987674764 + 3.5243815445951119128e-4120j 2.02e-290, 5.24e-1792j
1.5077339022807346684e-46 - 9.4128105201248240289e-4143j 2.03e-330, 5.26e-1832j
1.2530797266488647084e-67 + 3.8873631831384800984e-4153j 1.39e-342, 3.61e-1844j
2.8614404488899222972e-61 - 4.6976046477980842367e-4150j 4.86e-339, 1.26e-1840j
1.1585533256201217566e-05 + 3.0574501230678955814e-4121j 8.64e-300, 2.24e-1801j
0.12352842775962711505 - 9.3158874990511618987e-4119j 9.77e-283, 2.53e-1784j
9.491208781583508947e-42 + 2.4401357574697131674e-4140j 6.09e-329, 1.58e-1830j
8.3713909785661852751e-17 - 1.7227178776590793346e-4127j 1.15e-312, 2.97e-1814j
1.5624267797466537372e-74 - 2.2937863059493781126e-4156j 1.05e-346, 2.73e-1848j
3.6150461247696693184e-33 + 5.5080608671778726299e-4136j 1.11e-325, 2.86e-1827j
8.0491313580417136737e-05 + 1.0718029751891365239e-4120j 3.59e-303, 9.31e-1805j
1.3808849208947621954e-30 + 1.1523837326262707859e-4134j 7.57e-324, 1.96e-1825j
1.5085851985179519758e-22 - 1.6360675576258119215e-4130j 1.1e-318, 2.85e-1820j
2.7346590537964823991e-93 - 4.7895462541739210577e-4166j 2.27e-358, 5.88e-1860j
2.8597973146205597151e-106 - 6.3816798702345121738e-4173j 8.17e-366, 2.12e-1867j
0.047431411099323848674 - 2.0320832637918420673e-4118j 4.35e-305, 1.13e-1806j
1.3353807387162873319e-06 + 8.0697250118311544989e-4122j 4.77e-312, 1.23e-1813j
1.6469387518503330158e-34 - 1.1402128468448679138e-4136j 8.43e-329, 2.18e-1830j
7.9590123700389241299e-103 + 4.002683537305406158e-4171j 4.42e-364, 1.14e-1865j
0.033927725768422891621 + 5.5458166842361119239e-4120j 1.09e-309, 2.82e-1811j
0.00097058910407935031856 - 6.284259850932878526e-4120j 4.72e-311, 1.22e-1812j
0.10587579103348891171 + 3.6134150956122204675e-4119j 1.94e-309, 4.96e-1811j
2.4784455868595896855e-11 + 1.5693823670952189001e-4124j 3.1e-316, 8.03e-1818j

Download

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