Rule: Q[1, 3, 90]

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)
296.28962746979807631 - 4.4193608473315535742e-4091j 6.46e-2008, 6.46e-2008j
309.59691299254410341 + 3.6513248099581848316e-4095j 2.36e-2009, 2.36e-2009j
284.33327460308506654 - 2.1146078462966312962e-4086j 1.16e-2006, 1.16e-2006j
344.0790732292229658 - 9.4554574577425979641e-4102j 2.77e-2013, 2.77e-2013j
227.98105885155882224 + 7.2168948972487532296e-4085j 2.02e-2001, 2.02e-2001j
59.332893078535763544 - 5.8058336811653728258e-4095j 1.78e-2000, 1.78e-2000j
73.992339785446426835 - 5.4205499968020608789e-4093j 1.06e-1998, 1.06e-1998j
244.65185124859689989 - 1.7354417531485421983e-4090j 7.84e-2003, 7.84e-2003j
83.773559710706951495 - 3.2811522667264532406e-4099j 7.36e-1998, 7.36e-1998j
22.821850715404417844 + 3.676077946504533081e-4113j 1.49e-2010, 1.49e-2010j
8.7602448688256253926 - 4.1522581654210901698e-4123j 6.37e-2020, 6.37e-2020j
33.533193468099898198 - 5.864816093351782327e-4109j 2.28e-2006, 2.28e-2006j
87.209153930584050542 + 4.4680417267153653133e-4098j 1.2e-1997, 1.2e-1997j
162.0837514082937071 - 6.3747437450740870361e-4103j 2.5e-1997, 2.5e-1997j
35.539446286853997225 - 4.6989822945525288017e-4134j 9.89e-2006, 9.89e-2006j
136.33712827261790273 + 8.0198165588965033843e-4124j 1.41e-1996, 1.41e-1996j
263.19392469910771466 + 4.0097973651443618923e-4140j 1.64e-2004, 1.64e-2004j
41.952171990067425904 - 1.1075767174631594087e-4160j 6.2e-2004, 6.2e-2004j
9.7529476345166832379 - 7.2828570883239097654e-4176j 5.27e-2019, 5.27e-2019j
51.455137521609573632 - 1.3651166529057843871e-4158j 6.94e-2002, 6.94e-2002j
90.735857266942502689 - 2.2211341428174086958e-4152j 2.07e-1997, 2.07e-1997j
141.19497755144058654 + 2.6209378180982638539e-4203j 1.11e-1996, 1.11e-1996j
146.19195952311435469 + 1.4813626859548825467e-4293j 8.23e-1997, 8.23e-1997j
167.70690400117790978 + 9.8776814998647949352e-4399j 1.46e-1997, 1.46e-1997j
4.6295048762720645016 + 1.4632091785333012823e-4518j 6.06e-2025, 6.06e-2025j
131.61269132782398307 - 5.3771397973651101408e-4499j 1.53e-1996, 1.53e-1996j
198.7275595301178007 - 1.4125276966292984755e-4566j 2.87e-1999, 2.87e-1999j
324.93760090698083028 + 1.305032642734958832e-4592j 4.56e-2011, 4.56e-2011j
94.355984299984258207 + 4.2069938432693495341e-4610j 3.23e-1997, 3.23e-1997j
77.16713589062059156 + 1.4564084217669505234e-4687j 2.06e-1998, 2.06e-1998j
15.563324371833668715 + 1.9916788086782923213e-4760j 1.57e-2014, 1.57e-2014j
6.9417728267025031348 + 6.3377815398392398489e-4767j 6.5e-2022, 6.5e-2022j
109.82272958927259573 - 8.5266357669884624775e-4816j 1.11e-1996, 1.11e-1996j
179.49773027748023316 - 1.0837464673369419531e-4931j 3.87e-1998, 3.87e-1998j
192.09280596538465927 + 5.6653357005280897731e-4993j 7.6e-1999, 7.6e-1999j
54.007679696067273919 + 4.655132339164981333e-5033j 2.11e-2001, 2.11e-2001j
253.65382242717744642 + 1.7128186238048534142e-5028j 1.19e-2003, 1.19e-2003j
2.8329487074983686874 - 8.47840967938953122e-5095j 7.14e-2028, 7.14e-2028j
122.5435606137799058 + 4.9134510648519848697e-5062j 1.62e-1996, 1.62e-1996j
205.61051587319423161 + 1.4955898293972234928e-5097j 9.59e-2000, 9.59e-2000j
236.11336106850329594 + 3.8917882400898412499e-5128j 4.12e-2002, 4.12e-2002j
62.108089759575321446 - 6.615432392858891685e-5156j 4.26e-2000, 4.26e-2000j
44.223938596022368568 - 9.1982732496064134358e-5174j 2.06e-2003, 2.06e-2003j
37.610807786030253733 - 2.3732968180714989674e-5180j 4.02e-2005, 4.02e-2005j
46.564346584041166025 - 1.2129097727615733219e-5172j 7.51e-2003, 7.51e-2003j
220.2097314117668156 + 3.1255386902250952282e-5179j 8.46e-2001, 8.46e-2001j
273.37292124333209729 + 9.7352053127930192642e-5268j 1.63e-2005, 1.63e-2005j
29.712935295280265895 - 6.9136246799937864342e-5318j 1.12e-2007, 1.12e-2007j
127.01643531711641285 + 1.2919944065096215432e-5356j 1.58e-1996, 1.58e-1996j
26.144238805686894595 + 6.1763162686997471864e-5424j 4.44e-2009, 4.44e-2009j
24.452564819659688406 + 9.5022437127950359796e-5425j 8.49e-2010, 8.49e-2010j
173.50801211029116526 + 1.6748660971527540904e-5411j 7.99e-1998, 7.99e-1998j
31.591270340050668584 - 5.3545332193939279592e-5444j 5.31e-2007, 5.31e-2007j
13.068378216446405168 + 1.300678252891966354e-5453j 2.82e-2016, 2.82e-2016j
7.8232631436879996743 + 6.3594424195495944556e-5458j 6.99e-2021, 6.99e-2021j
10.801652745892237186 - 1.1316823377641184186e-5455j 4.49e-2018, 4.49e-2018j
101.88655278209944736 - 3.963619066376611994e-5433j 6.7e-1997, 6.7e-1997j
64.960146439591541348 + 1.9753545645160856975e-5458j 9.87e-2000, 9.87e-2000j
27.897482231064644981 + 4.4731270959689504043e-5468j 2.33e-2008, 2.33e-2008j
2.0041841849207288367 - 2.2907061563017947677e-5489j 1.25e-2029, 1.25e-2029j
56.633188478876053038 - 6.0340280108647132477e-5460j 6.08e-2001, 6.08e-2001j
67.890507727923290314 - 6.2671776463894569962e-5457j 2.23e-1999, 2.23e-1999j
105.80245318198099961 - 1.149645840190898782e-5466j 8.67e-1997, 8.67e-1997j
14.287125799142784265 + 1.4397256290528100896e-5544j 2.19e-2015, 2.19e-2015j
0.47798337596979241096 - 1.1903107956123271356e-5563j 4.71e-2036, 4.71e-2036j
16.897400170242106412 - 4.5049063367467666124e-5541j 1.05e-2013, 1.05e-2013j
39.748096360278726763 - 1.6387140260146409148e-5524j 1.69e-2004, 1.69e-2004j
21.251516192057001616 - 2.308735732530833937e-5549j 2.6e-2011, 2.6e-2011j
98.072003746887650279 - 4.7113965838462783259e-5533j 4.7e-1997, 4.7e-1997j
2.373957509959889009 + 2.0873903786130619508e-5674j 8.65e-2029, 8.65e-2029j
0.71585896289537958654 - 3.6016420317343539444e-5679j 1.13e-2034, 1.13e-2034j
3.369839231310923141 + 1.8763814609545547764e-5672j 6.2e-2027, 6.2e-2027j
151.33435107575842889 - 2.384926585413256123e-5640j 6.15e-1997, 6.15e-1997j
1 + 8.8443338254452580806e-5806j 2.71e-2033, 2.71e-2033j
212.7628860061411983 + 1.8654860970764278952e-5793j 3.15e-2000, 3.15e-2000j
0.056897625001077184683 + 2.7919695346255409857e-5969j 3.07e-2040, 3.07e-2040j
3.9705151743562254735 - 2.8024789991078768089e-5927j 5.77e-2026, 5.77e-2026j
113.95063025163116854 + 1.2267083554154342024e-5940j 1.38e-1996, 1.38e-1996j
19.741008936243439912 + 1.8775394672138213229e-6024j 4.34e-2012, 4.34e-2012j
0.010140400370423847955 + 2.3135452533881249213e-6066j 7.04e-2042, 7.04e-2042j
156.62906601443593362 - 1.4473465553103083038e-6020j 3.96e-1997, 3.96e-1997j
11.906679558015375502 + 6.825393080470511053e-6087j 3.72e-2017, 3.72e-2017j
18.28980347556303832 + 5.4892578727574584066e-6083j 7.44e-2013, 7.44e-2013j
185.68809654293546815 - 1.224587915002505798e-6065j 1.81e-1998, 1.81e-1998j
80.426901420446927095 - 1.161742274130815743e-6080j 4.23e-1998, 4.23e-1998j
1.6677130206506817142 - 6.9863831231458278046e-6114j 1.27e-2030, 1.27e-2030j
0.28869448725178243958 + 5.8533854330451392278e-6120j 2.18e-2037, 2.18e-2037j
5.3447907580721998129 - 1.9210341459484690266e-6106j 6.87e-2024, 6.87e-2024j
6.1156222177591665938 - 2.979360700553246296e-6106j 6.4e-2023, 6.4e-2023j
118.18965066130631897 - 1.4387572663678478004e-6077j 1.44e-1996, 1.44e-1996j
70.900700459522965508 + 1.6100598239223895812e-6089j 4.94e-1999, 4.94e-1999j
48.974395600776674685 + 5.6755743206261873825e-6092j 2.27e-2002, 2.27e-2002j
1.3236944953858776574 - 5.0743059618815126906e-6122j 6.36e-2032, 6.36e-2032j
0.14859348795341626575 - 1.0767184827624298306e-6128j 9.74e-2039, 9.74e-2039j

Weights

Weight (ball center) Error (ball radius)
2.6416281681772954709e-128 + 7.1173264978321001756e-4175j 3.72e-357, 4.76e-1863j
4.9542400157305630432e-134 - 8.645613956860966389e-4178j 3.6e-359, 4.6e-1865j
3.7417291422094446733e-123 - 2.9988994606906100994e-4172j 6.21e-356, 7.95e-1862j
8.3291600768864975205e-149 - 2.662909469347127583e-4185j 1.87e-364, 2.39e-1870j
7.7478868665106515794e-99 - 7.9859358275726672177e-4160j 4.81e-349, 6.15e-1855j
4.6704963728471278351e-26 + 1.4064869223810370788e-4120j 1.37e-299, 1.75e-1805j
2.2987145465979659115e-32 + 1.5842768494788916759e-4124j 4.4e-308, 5.64e-1814j
4.9150513475076629836e-106 - 1.649005042278284764e-4163j 7.95e-352, 1.02e-1857j
1.4057377018804422842e-36 - 2.8254273975400487248e-4127j 3.45e-313, 4.41e-1819j
1.9626047375273529049e-10 - 1.8337272319738707017e-4113j 8.49e-268, 1.09e-1773j
0.00015132506434710880903 + 4.8099301988018844068e-4110j 5.07e-234, 6.5e-1740j
5.3958237452930687601e-15 - 7.7953589397370039758e-4116j 1.27e-281, 1.63e-1787j
4.6475241189381120492e-38 + 4.4379081188110407571e-4128j 6e-315, 7.69e-1821j
2.2450656748721791864e-70 - 3.6839151991145944994e-4145j 1.64e-339, 2.1e-1845j
7.4948405209350345421e-16 + 2.8979019021418328172e-4116j 4.75e-285, 6.09e-1791j
2.950489736683376886e-59 + 2.2893070434309078499e-4139j 1.82e-333, 2.33e-1839j
4.8901743160453057063e-114 - 1.3418538232545615124e-4167j 1.94e-356, 2.49e-1862j
1.3496401940099443299e-18 - 1.3289021846333374273e-4117j 2.02e-292, 2.59e-1798j
5.9323534245674197844e-05 - 2.6062346087861721041e-4110j 1.31e-246, 1.68e-1752j
1.132678037359020042e-22 - 2.0251626966082188917e-4119j 2.17e-299, 2.78e-1805j
1.4026617815805527177e-39 - 6.6226041087432626682e-4129j 2.7e-318, 3.46e-1824j
2.3568484740920529226e-61 - 1.8301426830026230299e-4140j 4.08e-335, 5.23e-1841j
1.6387997239859290353e-63 + 1.3678524388457322341e-4141j 1.11e-336, 1.42e-1842j
8.3654243153356147706e-73 + 2.0285052967818133657e-4146j 1.72e-342, 2.2e-1848j
0.0067080653974281081723 - 8.5706045700913196579e-4109j 1.91e-235, 2.44e-1741j
3.233514937025130287e-57 - 2.6854605150081753544e-4138j 1.17e-333, 1.5e-1839j
3.3371921850225306218e-86 - 2.4555608108443808126e-4153j 4.71e-350, 6.03e-1856j
1.2757668369895031964e-140 + 3.8471222545745595606e-4181j 1.29e-369, 1.65e-1875j
3.8557100018744321562e-41 + 9.4483624639997746289e-4130j 5.98e-324, 7.65e-1830j
9.8670125107808422529e-34 - 7.3433731603477338097e-4126j 4.87e-318, 6.24e-1824j
2.2728248235955031052e-07 + 9.1055036756047063239e-4112j 1.23e-277, 1.58e-1783j
0.00082524781347265188256 + 1.5641017793561559226e-4109j 6.25e-256, 8e-1762j
8.2141984971506619113e-48 + 2.4955731049149945272e-4133j 5.33e-330, 6.83e-1836j
6.7545171300222800346e-78 + 4.7062751378027237638e-4149j 1.06e-346, 1.36e-1852j
2.4501755916280392402e-83 + 7.3440751339155320094e-4152j 2.05e-349, 2.62e-1855j
9.0753960405995823677e-24 + 7.9574028056115520444e-4120j 1.6e-312, 2.05e-1818j
6.3974229693855851189e-110 + 1.7006757520357016333e-4165j 1.41e-360, 1.81e-1866j
0.029497223109575551906 + 5.1043214375690430439e-4108j 3.01e-246, 3.85e-1752j
2.6589541848554748696e-53 - 3.0814126251916546213e-4136j 1.83e-335, 2.35e-1841j
3.5517571311587902897e-89 + 7.2605003269859014532e-4155j 8.69e-353, 1.11e-1858j
2.3864824885044463889e-102 + 1.2695590505076933116e-4161j 6.62e-358, 8.48e-1864j
2.9924689856024348291e-27 + 2.3608062471476183077e-4121j 4e-319, 5.12e-1825j
1.434275752666886973e-19 + 4.6268171981469651803e-4118j 3.32e-312, 4.25e-1818j
9.7480486966252011172e-17 - 1.0555612222333092065e-4116j 2.12e-309, 2.71e-1815j
1.4224446629456477917e-20 - 1.6045041417286538791e-4118j 1.91e-313, 2.45e-1819j
1.7585242479853637918e-95 + 4.1980712806296372007e-4158j 7.54e-357, 9.66e-1863j
1.9885811017694320687e-118 + 7.704012702419649059e-4170j 4.16e-366, 5.33e-1872j
2.3027730813541386643e-13 - 5.281164854647598575e-4115j 2.39e-308, 3.06e-1814j
3.1183530114712980902e-55 + 2.9624692599286825398e-4137j 3.31e-339, 4.23e-1845j
7.617701034488464371e-12 - 3.2625765085821942541e-4114j 6.06e-307, 7.76e-1813j
3.9882326476480420077e-11 + 7.8271000213261011446e-4114j 5.51e-306, 7.06e-1812j
2.6109784333092832306e-75 - 1.0234930659623176943e-4147j 2.98e-349, 3.81e-1855j
3.6401637116479896655e-14 + 2.0520021524160553802e-4115j 2e-309, 2.56e-1815j
2.5123499215199023214e-06 + 3.7063158381171062107e-4111j 2.8e-298, 3.59e-1804j
0.0003639660516429034768 - 8.7344220738765727567e-4110j 6.75e-290, 8.65e-1796j
2.1930114371023063567e-05 + 1.3871681779465682439e-4110j 5e-295, 6.4e-1801j
2.1794776625988214107e-44 + 1.6842379613291947444e-4131j 4.97e-336, 6.36e-1842j
1.7750442101474093257e-28 - 2.7455008502999900222e-4122j 1.91e-325, 2.45e-1831j
1.366880085367374781e-12 + 1.3281354555101080824e-4114j 2.66e-310, 3.41e-1816j
0.045548722256388673674 + 1.3164275532398065212e-4107j 1.96e-279, 2.51e-1785j
6.7575841944799198765e-25 - 4.03461178820681882e-4120j 2.14e-322, 2.75e-1828j
9.7338762363982114024e-30 + 4.2260140864717545966e-4123j 8.11e-327, 1.04e-1832j
4.4576156023030192049e-46 - 2.0998217075824170778e-4132j 6.36e-338, 8.15e-1844j
7.7837207934618007144e-07 - 1.8570958482429239205e-4111j 7.14e-306, 9.15e-1812j
0.13255562690090878005 - 7.0948369384256373169e-4108j 3.97e-287, 5.09e-1793j
6.2531662468525395387e-08 - 4.3662782246896173212e-4112j 1.94e-308, 2.48e-1814j
1.1862819330716324467e-17 + 3.7745870653098138149e-4117j 1.54e-317, 1.97e-1823j
9.0823424443716362661e-10 + 4.1954585170264785105e-4113j 3.74e-311, 4.8e-1817j
9.6297564306064786385e-43 - 1.2899976521646505289e-4130j 3.88e-336, 4.97e-1842j
0.038449842994455031661 - 9.2276074931416803081e-4108j 5.6e-294, 7.17e-1800j
0.12786875800416066443 + 8.2096435461291868653e-4108j 7.42e-292, 9.5e-1798j
0.019611740923842251278 - 2.7477236422174147141e-4108j 2.69e-297, 3.44e-1803j
9.8577051469482017544e-66 - 9.5264603424899856798e-4143j 1.61e-349, 2.06e-1855j
0.11245291452838130809 - 9.5456610205350043588e-4108j 1.82e-293, 2.33e-1799j
2.8925548437973531035e-92 - 1.8782509031225915826e-4156j 3.11e-362, 3.98e-1868j
0.064528630256240719854 + 2.9321331071429241702e-4108j 5.63e-296, 7.2e-1802j
0.011890610666004823072 + 1.5193788494209233946e-4108j 5.84e-303, 7.48e-1809j
1.3593866239405281181e-49 - 2.8218387343098005833e-4134j 7.87e-342, 1.01e-1847j
3.9543639795444087708e-09 - 9.3754235122926478434e-4113j 6.32e-316, 8.1e-1822j
0.026264698214847894205 - 9.8853818007434139924e-4109j 5.67e-299, 7.26e-1805j
5.0945612777718125815e-68 + 6.1602031804410948153e-4144j 5.94e-351, 7.61e-1857j
7.6443478701367775868e-06 - 7.2430409515459793508e-4111j 3.74e-313, 4.79e-1819j
1.6205197603385697788e-08 + 2.046727579426216976e-4112j 6.8e-316, 8.71e-1822j
1.4311562066293398024e-80 - 1.9601909518706813823e-4150j 2.96e-357, 3.79e-1863j
3.8898560853265249159e-35 + 1.6618656917973780397e-4126j 7.51e-335, 9.62e-1841j
0.064674639968408241997 - 1.3519495079351695421e-4107j 2.04e-309, 2.62e-1815j
0.12339575780723154382 + 5.9633640039228530536e-4108j 2.61e-308, 3.35e-1814j
0.0035469055393672271503 + 4.874301334258034534e-4109j 3.77e-313, 4.83e-1819j
0.0017631749820704395543 - 2.7704137677021005543e-4109j 1.18e-313, 1.51e-1819j
2.0134100003280661847e-51 + 3.0295250644835214731e-4135j 2.55e-343, 3.26e-1849j
4.9272870879356715342e-31 - 7.8393408910498218156e-4124j 5.01e-333, 6.41e-1839j
1.3152472489234407342e-21 + 5.6105659266668039866e-4119j 6.21e-328, 7.95e-1834j
0.090157089634802762201 + 1.1405182368082174649e-4107j 7.59e-315, 9.76e-1821j
0.099652560040594642692 - 4.6279595358632480553e-4108j 6.01e-315, 7.6e-1821j

Download

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