Rule: Q[2, 86]

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)
324.33596392584129022 - 5.5673336235025601453e-4107j 9.97e-2015, 9.97e-2015j
245.19917206337213448 - 1.7282911664518698815e-4122j 3.07e-2006, 3.07e-2006j
305.57597637424051695 + 1.1062705970053427247e-4145j 1.4e-2012, 1.4e-2012j
265.84437673196806792 + 1.5657421366379962384e-4193j 2.79e-2008, 2.79e-2008j
290.55422852088190752 + 4.8734125875106553129e-4288j 6.79e-2011, 6.79e-2011j
147.00253435401315784 - 4.2396495559752702734e-4407j 1.47e-1999, 1.47e-1999j
7.1601922217124754886 - 8.7291163019316881431e-4491j 1.72e-2022, 1.72e-2022j
96.843555044104815826 - 2.1477180982863387802e-4530j 2.01e-1999, 2.01e-1999j
158.03716065100796877 - 3.0778998204526722938e-4617j 5.63e-2000, 5.63e-2000j
277.53397385657722308 - 3.7281229756903284892e-4653j 1.6e-2009, 1.6e-2009j
44.322066548994465421 + 1.3758529694499073219e-4665j 4.88e-2005, 4.88e-2005j
31.278454581607618443 - 2.7698727810412552471e-4670j 1.58e-2008, 1.58e-2008j
23.955852436969711024 - 4.9956343030368052425e-4673j 2.66e-2011, 2.66e-2011j
57.217841977057225171 - 2.2861908415226416294e-4660j 1.07e-2002, 1.07e-2002j
49.249943002198113384 + 7.9403170605121457242e-4671j 5.22e-2004, 5.22e-2004j
33.277114399766964791 + 1.4690855275428106961e-4681j 6.98e-2008, 6.98e-2008j
16.261344463022159686 + 3.986764987770596948e-4689j 3.58e-2015, 3.58e-2015j
25.687237885376198345 + 3.6618523183274518601e-4684j 1.44e-2010, 1.44e-2010j
68.97784502776340213 - 6.6933511582736445953e-4673j 3.26e-2001, 3.26e-2001j
35.344626761304634219 - 4.6203138813655671681e-4708j 2.78e-2007, 2.78e-2007j
54.483271914380033903 + 1.0048527789886440021e-4699j 4.33e-2003, 4.33e-2003j
152.43139846930383683 - 8.3360578287273232872e-4734j 9.18e-2000, 9.18e-2000j
65.911251173824613851 + 1.3722102392238001482e-4762j 1.53e-2001, 1.53e-2001j
163.83030764778951936 - 2.860106001297326606e-4777j 2.95e-2000, 2.95e-2000j
5.4836316107488973957 - 4.6196963999391634612e-4823j 1.65e-2024, 1.65e-2024j
218.79937592137336749 - 1.1507042571457108293e-4797j 6.31e-2004, 6.31e-2004j
78.710335041526960354 + 2.8130323950317005212e-4808j 2.48e-2000, 2.48e-2000j
51.827772587542514368 - 1.809335680686535255e-4818j 1.47e-2003, 1.47e-2003j
141.74123016653746626 + 2.3612559675441088333e-4813j 1.97e-1999, 1.97e-1999j
12.394274420383716653 + 1.3675314146205240557e-4846j 9.23e-2018, 9.23e-2018j
8.0874451633532083134 + 1.6050392382298684683e-4850j 1.52e-2021, 1.52e-2021j
72.131871881653264425 - 8.8826169652891886648e-4829j 6.58e-2001, 6.58e-2001j
1.4937807619677246585 + 2.4916736629165875665e-4860j 6.12e-2032, 6.12e-2032j
62.93021366976969787 - 2.1580134739152202477e-4830j 6.36e-2002, 6.36e-2002j
4.7342553960251866358 + 3.2434982688365208468e-4854j 1.56e-2025, 1.56e-2025j
46.74845864094907079 + 1.1245786794265734646e-4832j 1.64e-2004, 1.64e-2004j
100.7812959739492143 - 7.9609876470932140675e-4826j 2.66e-1999, 2.66e-1999j
255.13646938848626881 - 3.4486480409424972568e-4836j 3.36e-2007, 3.36e-2007j
227.11691132830352594 + 5.8728935349425101001e-4856j 1.23e-2004, 1.23e-2004j
126.88313401578539521 - 1.0443623743689813418e-4886j 4.11e-1999, 4.11e-1999j
235.89236105907074695 - 7.8926512221232298262e-4919j 1.96e-2005, 1.96e-2005j
85.664217772743325837 - 5.3549729248283275937e-4950j 6.57e-2000, 6.57e-2000j
2.844450164008516097 + 9.6311052568801282156e-5023j 1.05e-2028, 1.05e-2028j
14.910859536205816206 - 8.8218652999591468939e-5009j 5.16e-2016, 5.16e-2016j
13.621984488920532919 - 1.7072643398203719352e-5008j 7.84e-2017, 7.84e-2017j
189.14036108019173079 - 7.2412759231570755631e-4997j 1.09e-2001, 1.09e-2001j
117.68248526552426346 - 1.5091678623043185704e-5076j 4.43e-1999, 4.43e-1999j
108.99397918263204445 + 2.2350721877270218689e-5165j 4.14e-1999, 4.14e-1999j
22.289461542744102304 + 8.6970654213810420527e-5222j 5.12e-2012, 5.12e-2012j
41.969580861038499409 + 3.481260252931775253e-5214j 1.47e-2005, 1.47e-2005j
29.347789764576770329 - 4.1466974283047666089e-5260j 3.39e-2009, 3.39e-2009j
104.83020341065986641 + 6.3222115922571442595e-5361j 3.4e-1999, 3.4e-1999j
176.02778428299370225 - 3.1212353259972557742e-5465j 6.99e-2001, 6.99e-2001j
0.847108679755914081 - 3.0041959928396922398e-5545j 2.28e-2034, 2.28e-2034j
2.3354710535342507777 - 4.2172936274281559263e-5539j 8.89e-2030, 8.89e-2030j
169.82268862204101908 + 2.820450547696601475e-5507j 1.49e-2000, 1.49e-2000j
210.88337823882027915 + 1.1384269270833977877e-5517j 2.57e-2003, 2.57e-2003j
113.27662648731040513 - 4.6185403887265555555e-5527j 4.56e-1999, 4.56e-1999j
3.4142135623730950488 + 9.0433481180909565948e-5575j 1.09e-2027, 1.09e-2027j
1.149508030524417855 - 1.0509443918787869969e-5580j 4.06e-2033, 4.06e-2033j
131.6886930549778646 + 1.8881262831617469902e-5544j 3.36e-1999, 3.36e-1999j
1.8865548620838228416 - 3.6746135964640862886e-5596j 8.3e-2031, 8.3e-2031j
93.013549539282371795 - 2.6885110989566793025e-5563j 1.6e-1999, 1.6e-1999j
60.032965654342289191 + 1.8429342427092129373e-5581j 2.79e-2002, 2.79e-2002j
182.46105017319737011 + 3.1129293432400861135e-5588j 2.81e-2001, 2.81e-2001j
0.36884186730387954276 - 2.342488562047528898e-5676j 5.72e-2037, 5.72e-2037j
0.5857864376269049512 + 1.8267059844188678389e-5675j 1.13e-2035, 1.13e-2035j
10.120744641609373636 + 2.4126563128425715604e-5660j 1.36e-2019, 1.36e-2019j
89.288092490159129901 + 1.0679964212438302802e-5638j 1.03e-1999, 1.03e-1999j
4.0443282181657678738 + 2.4767937225925821453e-5706j 1.3e-2026, 1.3e-2026j
19.149092246376657799 - 4.3630647202013658577e-5693j 1.52e-2013, 1.52e-2013j
11.227319084879796392 - 2.3628140868206410425e-5698j 1.14e-2018, 1.14e-2018j
39.689878724396647246 - 1.6462312659750299491e-5678j 4.33e-2006, 4.33e-2006j
122.21627327165680773 - 2.3249759353355495243e-5751j 4.47e-1999, 4.47e-1999j
136.63912450514889065 + 3.1150058767445399682e-5891j 2.73e-1999, 2.73e-1999j
0.081689990088083583306 - 3.13591722494343469e-6005j 5.48e-2040, 5.48e-2040j
9.074216682549748381 + 2.3713391698254417556e-5965j 1.52e-2020, 1.52e-2020j
27.484307419030368868 + 4.3198163591830986772e-5976j 7.36e-2010, 7.36e-2010j
203.32442361442417512 - 1.1532733975133588097e-6004j 1.06e-2002, 1.06e-2002j
196.08659608628097773 - 1.0163770220595336202e-6058j 3.47e-2002, 3.47e-2002j
0.015536760295954356444 + 4.9741119174026459445e-6120j 1.17e-2041, 1.17e-2041j
20.687413329014467995 - 1.2853874343999233721e-6091j 8.62e-2013, 8.62e-2013j
17.673917956195929502 + 1.0397639805534199639e-6093j 2.37e-2014, 2.37e-2014j
82.139159698492401137 + 6.4420692045548004196e-6078j 4.02e-2000, 4.02e-2000j
37.481896579141015829 - 3.840356648354473752e-6105j 1.07e-2006, 1.07e-2006j
6.2922844120746276179 + 3.4620048398688967464e-6122j 1.74e-2023, 1.74e-2023j
0.19995022191820164487 + 1.5503223532898358914e-6137j 1.66e-2038, 1.66e-2038j
75.375327154387647633 - 8.7761145815418028822e-6098j 1.33e-2000, 1.33e-2000j

Weights

Weight (ball center) Error (ball radius)
3.0646519513822128568e-140 + 2.6950423693649900488e-4247j 1.98e-370, 2.44e-1875j
3.1170944860165533535e-106 + 2.7072139547101984469e-4228j 1.74e-360, 2.15e-1865j
3.2023526223224090022e-132 + 7.1359259826569650709e-4243j 1.61e-368, 1.98e-1873j
3.9150366264522088242e-115 - 8.7630686419511019622e-4234j 6.53e-364, 8.06e-1869j
9.0324372916445476588e-126 - 1.764453080319509817e-4239j 4.27e-367, 5.26e-1872j
7.681492476338923577e-64 + 1.1384414043770703974e-4208j 8.49e-346, 1.05e-1850j
0.00069731720172376181856 - 2.3662117688475120931e-4178j 8.7e-242, 1.07e-1746j
3.3929846907461852512e-42 - 6.2168297437780722318e-4198j 2.1e-332, 2.6e-1837j
1.3213724308959570923e-68 + 5.1221852451587122741e-4211j 2.65e-348, 3.28e-1853j
3.6116793196405660924e-120 + 1.6419751806358309478e-4236j 8.24e-366, 1.02e-1870j
1.3471999334350951887e-19 + 1.3744400221694581102e-4186j 1.66e-307, 2.05e-1812j
5.11913920035634866e-14 + 9.5761331011914160842e-4184j 2.26e-296, 2.79e-1801j
6.7025753562404682608e-11 + 3.8717482259735538014e-4182j 4.22e-288, 5.21e-1793j
3.9246974976332725587e-25 - 2.1926073622929012951e-4189j 9.35e-317, 1.15e-1821j
1.0369549196835886982e-21 + 1.1694868863656503111e-4187j 1.34e-311, 1.65e-1816j
7.178889263614966567e-15 - 3.5016708258091201279e-4184j 4.12e-299, 5.08e-1804j
1.1970766069160648735e-07 - 1.9628258601859630215e-4180j 3.95e-279, 4.88e-1784j
1.2322528596414499371e-11 - 1.6106183229255042364e-4182j 1.21e-291, 1.49e-1796j
3.436063994833424386e-30 - 6.2788191294565892096e-4192j 1.38e-324, 1.7e-1829j
9.390855164657387493e-16 + 1.2384392961960034541e-4184j 9.51e-302, 1.17e-1806j
5.8713952030346691156e-24 + 8.5756766886238390441e-4189j 9.8e-316, 1.21e-1820j
3.4792276625840531333e-66 - 7.9581871442360852884e-4210j 2.39e-351, 2.95e-1856j
7.1716496434191256463e-29 + 2.8868772519175270894e-4191j 1.82e-323, 2.25e-1828j
4.1645263418783615392e-71 - 3.0227181730864616323e-4212j 1.97e-354, 2.43e-1859j
0.0032362554275611224254 - 6.0446126284252361959e-4178j 5.82e-259, 7.18e-1764j
7.6838456911505719056e-95 - 1.0830194061480349374e-4223j 1.15e-365, 1.42e-1870j
2.2164025279172366059e-34 + 4.9843791777733840596e-4194j 2.66e-331, 3.29e-1836j
8.1132474360589595409e-23 - 3.2273560981418368325e-4188j 1.04e-316, 1.28e-1821j
1.4352512821811634981e-61 - 1.5053045689570207458e-4207j 3.32e-350, 4.1e-1855j
4.959365629344487017e-06 + 1.4540745576659439769e-4179j 7.67e-285, 9.46e-1790j
0.00029415003152550747106 + 1.4270027782206574753e-4178j 2.02e-274, 2.49e-1779j
1.5081988077945497346e-31 + 1.3086972742101533101e-4192j 5.56e-328, 6.86e-1833j
0.082420646750987926381 + 5.9692094405056114085e-4177j 4.98e-239, 6.14e-1744j
1.3738329074531451304e-27 - 1.2731571899397332607e-4190j 2.35e-323, 2.9e-1828j
0.0063253948414555626709 + 9.3237356904882566875e-4178j 8.02e-266, 9.9e-1771j
1.2274290325885497091e-20 - 4.0831761007396871736e-4187j 2.48e-315, 3.06e-1820j
6.800006081019369548e-44 + 8.8566010695758525549e-4199j 5.69e-341, 7.02e-1846j
1.6152994557334679063e-110 + 3.8049199045109646098e-4231j 1.91e-372, 2.36e-1877j
1.9752743371959597515e-98 + 2.482035265473942022e-4225j 3.97e-369, 4.9e-1874j
3.7213115980273278545e-55 + 2.2448696303162237556e-4204j 7.93e-351, 9.78e-1856j
3.226994680980839734e-102 - 6.0290557161628498748e-4227j 2.65e-370, 3.27e-1875j
2.2369694386948730167e-37 + 1.5816437709752495439e-4195j 1.61e-338, 1.99e-1843j
0.031374954998690204176 - 2.9434044708529099781e-4177j 3.68e-271, 4.54e-1776j
4.413054375234337079e-07 + 3.9372307599335984944e-4180j 2.51e-301, 3.1e-1806j
1.5268779417273641129e-06 - 7.6741044874373624997e-4180j 1.19e-299, 1.47e-1804j
4.903076776672858038e-82 - 1.3951378080234655106e-4217j 1.05e-364, 1.29e-1869j
3.4782173115617026096e-51 + 2.0937553846169803017e-4202j 2.25e-349, 2.78e-1854j
1.9502385774879523748e-47 + 1.5271928759115351401e-4200j 3.39e-347, 4.18e-1852j
3.4126534759635876184e-10 - 9.0215389152682106746e-4182j 3.37e-313, 4.16e-1818j
1.3726652690131701298e-18 - 4.4630975477416801537e-4186j 1.2e-323, 1.48e-1828j
3.407774554299816267e-13 - 2.5340767585351654372e-4183j 1.26e-317, 1.56e-1822j
1.2195746805232615247e-45 - 1.1957017120856849615e-4199j 5.34e-346, 6.59e-1851j
2.2520375566835119778e-76 - 7.9615314922695297073e-4215j 1.09e-363, 1.34e-1868j
0.12097299821341433016 + 5.5298408961351720504e-4177j 2.92e-282, 3.61e-1787j
0.046315349208168347439 + 4.0235397497425644881e-4177j 6.13e-288, 7.57e-1793j
1.0764964446610720175e-73 + 1.6279345278263330943e-4213j 4.77e-362, 5.89e-1867j
2.0078926256841637011e-91 + 4.3474759227108716113e-4222j 8.5e-371, 1.05e-1875j
2.7696569750796583022e-49 - 1.8419665125656148538e-4201j 3.54e-350, 4.37e-1855j
0.019742593857819735097 + 2.0641188158351275973e-4177j 1.95e-299, 2.4e-1804j
0.1022174336942879452 - 6.1166845565311795431e-4177j 6.54e-289, 8.07e-1794j
3.1366973940782336065e-57 - 2.1072548066797155952e-4205j 5.89e-355, 7.27e-1860j
0.063642249585607496397 - 5.1484865967163260235e-4177j 3.16e-295, 3.9e-1800j
1.5202005540602449193e-40 + 4.1420948852681984075e-4197j 3.07e-346, 3.79e-1851j
2.4196902668751774695e-26 + 5.3902561651202236749e-4190j 6.11e-337, 7.54e-1842j
3.7550722618180489703e-79 + 3.5167364686748726454e-4216j 2.01e-366, 2.48e-1871j
0.13377841613235307938 + 3.2669845031135914224e-4177j 1.02e-297, 1.26e-1802j
0.13349187234026000769 - 4.4760921394045340841e-4177j 1.41e-297, 1.75e-1802j
4.3314176693223321597e-05 + 4.8051996216295004655e-4179j 8.52e-319, 1.05e-1823j
6.1352972534075806447e-39 - 2.6234063493319202438e-4196j 1.13e-345, 1.4e-1850j
0.011565900021151825266 - 1.4047306412427316502e-4177j 2.61e-310, 3.22e-1815j
7.2722431216392314942e-09 - 4.4679614629212709239e-4181j 5.78e-326, 7.14e-1831j
1.512464982841219314e-05 - 2.6796248349042006011e-4179j 3.33e-320, 4.11e-1825j
1.2997612805193475457e-17 + 1.3988660098989619065e-4185j 5.14e-333, 6.34e-1838j
3.8445971269180846165e-53 - 2.2381926816150068105e-4203j 1.66e-353, 2.05e-1858j
2.288363633373135445e-59 + 1.8462527982378340298e-4206j 7.55e-357, 9.32e-1862j
0.085127074303107509902 + 1.0816230234016666082e-4177j 7.67e-313, 9.47e-1818j
0.00011648505002500186404 - 8.3895810765855563994e-4179j 1.25e-322, 1.54e-1827j
2.1193559554623022778e-12 + 6.4916920509586407952e-4183j 2.72e-331, 3.36e-1836j
3.6825214972584243185e-88 - 1.5566187563613741582e-4220j 1.66e-372, 2.04e-1877j
4.9109991952243778136e-85 + 4.9430594759956728581e-4219j 5.91e-371, 7.3e-1876j
0.039238753496303163884 - 3.1087762838137462131e-4178j 1.78e-320, 2.19e-1825j
1.6273977737601732737e-09 + 2.0384014834269932549e-4181j 7.92e-332, 9.77e-1837j
3.0466158704039625216e-08 + 9.5041791035737609602e-4181j 6.64e-331, 8.19e-1836j
7.3885901637327288802e-36 - 9.0889565992947901627e-4195j 9.82e-348, 1.21e-1852j
1.1449102412469303455e-16 - 4.2342882660273604642e-4185j 1.07e-337, 1.32e-1842j
0.0015512483025314904165 + 3.8276646467728816237e-4178j 6e-330, 7.38e-1835j
0.11782538067090225898 - 2.0986437654839807893e-4177j 2.14e-328, 2.58e-1833j
6.052817241649645319e-33 - 2.611541693010966972e-4193j 2.7e-346, 3.33e-1851j

Download

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