Rule: Q[1, 3, 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)
336.05720446198034034 + 1.3290815964070738925e-6024j 6.46e-2014, 6.46e-2014j
288.65825406826843845 + 5.3722215625082467785e-6009j 1.56e-2008, 1.56e-2008j
221.00477760460310227 - 1.2089356258338877723e-6012j 3.5e-2002, 3.5e-2002j
317.06662162679757187 - 7.8484655732201116681e-6044j 1.09e-2011, 1.09e-2011j
276.80734899752887555 + 7.8236938525111248905e-6033j 2.62e-2007, 2.62e-2007j
28.340488744021126219 + 1.8360492242761337378e-6041j 9.97e-2009, 9.97e-2009j
237.50287170819345961 + 4.0720024528146125895e-6030j 1.44e-2003, 1.44e-2003j
198.88199072623642907 - 6.0838952602576543515e-6054j 1.56e-2000, 1.56e-2000j
18.509462327900950559 + 8.4657365941057175401e-6091j 3.66e-2013, 3.66e-2013j
72.49320546507678599 - 4.4299031234944741107e-6076j 1.12e-1999, 1.12e-1999j
34.113423176880552244 - 4.6512783610447367294e-6085j 8.89e-2007, 8.89e-2007j
75.676977805173824025 - 2.5311363978497709184e-6075j 2.24e-1999, 2.24e-1999j
19.993418832751574908 + 2.239560417481480369e-6105j 2.14e-2012, 2.14e-2012j
229.05165533522243755 + 1.7419295940463527077e-6090j 7.82e-2003, 7.82e-2003j
9.7903991282961958647 - 9.5758084589660027062e-6143j 2.85e-2019, 2.85e-2019j
57.817825875953866973 + 5.3617117382886038412e-6119j 1.54e-2001, 1.54e-2001j
10.860215412260564831 - 1.6643881524975673388e-6142j 2.43e-2018, 2.43e-2018j
42.744949014240647878 - 3.4971477878590743953e-6128j 1.97e-2004, 1.97e-2004j
52.498448635169397793 + 2.3309277905591606784e-6124j 2.08e-2002, 2.08e-2002j
167.17380682316350934 - 5.4361627167240629775e-6121j 1.05e-1998, 1.05e-1998j
15.72261907921621656 - 1.4552856301789383481e-6157j 7.74e-2015, 7.74e-2015j
265.94676997357165794 + 3.5575994908941469287e-6138j 3.04e-2006, 3.04e-2006j
55.120226799826422709 + 1.1399143947905738779e-6146j 5.71e-2002, 5.71e-2002j
246.41535694804792867 + 5.5317660814376105983e-6142j 2.33e-2004, 2.33e-2004j
135.31777106168808968 + 2.2267871222113935829e-6162j 1.26e-1997, 1.26e-1997j
121.3646492167039069 + 2.2433114387532152347e-6189j 1.65e-1997, 1.65e-1997j
23.145031809657074916 - 1.5372863256696849823e-6241j 7.41e-2011, 7.41e-2011j
192.07941373911242412 + 1.0889616796054602649e-6228j 4.66e-2000, 4.66e-2000j
108.52356298822769749 - 9.6193368994165614749e-6297j 1.15e-1997, 1.15e-1997j
116.96671760673377167 + 9.0641323374671956604e-6377j 1.46e-1997, 1.46e-1997j
69.394625257083053996 - 2.3811321595543555124e-6449j 5.39e-2000, 5.39e-2000j
130.53519396365717666 - 6.1747153624422814684e-6508j 1.49e-1997, 1.49e-1997j
11.987967167632220156 + 2.1251523334372513683e-6573j 2.18e-2017, 2.18e-2017j
78.947847086314594945 - 1.3945306912358814404e-6554j 4.03e-1999, 4.03e-1999j
301.85205680990495214 + 2.768606168936683356e-6590j 5.35e-2010, 5.35e-2010j
8.7781822626085499829 - 1.5954917254690483831e-6657j 3.44e-2020, 3.44e-2020j
161.44974952025410455 + 1.478937138101129715e-6638j 1.99e-1998, 1.99e-1998j
100.52519624303204294 - 1.3653554278041218007e-6716j 7.28e-1998, 7.28e-1998j
40.484373713298321107 - 3.883450325357781462e-6766j 5.51e-2005, 5.51e-2005j
21.538423663800987952 + 7.7773514305511706406e-6806j 1.33e-2011, 1.33e-2011j
213.31730977772795524 - 8.1281327397969615622e-6811j 1.38e-2001, 1.38e-2001j
45.075581945492106937 - 1.8922948745856389959e-6861j 6.66e-2004, 6.66e-2004j
3.9083082774205649373 + 2.8458619944105464014e-6893j 1.05e-2025, 1.05e-2025j
6.9253874564756024849 + 1.8354718223022949154e-6889j 4.4e-2022, 4.4e-2022j
49.951212480222891617 - 1.8589994619668064051e-6866j 6.85e-2003, 6.85e-2003j
185.5241768290003632 - 2.8612149860017475346e-6923j 1.08e-1999, 1.08e-1999j
155.90322034674984348 + 5.7119985835581403069e-6993j 3.23e-1998, 3.23e-1998j
255.86328482353802955 - 1.0544757853128777697e-7050j 3.15e-2005, 3.15e-2005j
1.3441734044819181049 + 8.7222712752748434921e-7145j 3.69e-2032, 3.69e-2032j
4.5736171568212884364 + 2.7605130441141737688e-7138j 7.23e-2025, 7.23e-2025j
125.8858855742890413 - 3.1698431275070341861e-7109j 1.67e-1997, 1.67e-1997j
38.292874496503135487 + 1.5870396901334626712e-7162j 1.39e-2005, 1.39e-2005j
96.684276876631497231 - 9.2040629114156244566e-7182j 5.03e-1998, 5.03e-1998j
6.0843820848441949239 - 1.6462663648767508289e-7271j 4.92e-2023, 4.92e-2023j
140.23929976885972088 + 1.0324689720661349405e-7245j 1.02e-1997, 1.02e-1997j
150.52479037123279027 + 1.1462798585220033549e-7289j 5.13e-1998, 5.13e-1998j
32.123745149474350566 + 7.9547264029562342855e-7324j 2.11e-2007, 2.11e-2007j
112.68770445186638585 - 1.2261534346308169878e-7312j 1.39e-1997, 1.39e-1997j
14.418764119200069061 + 4.1134295279408611138e-7347j 1.15e-2015, 1.15e-2015j
82.307837546375110803 - 3.3244178778130852776e-7329j 7.74e-1999, 7.74e-1999j
92.94479065103596216 - 4.0058760202525283848e-7351j 3.51e-1998, 3.51e-1998j
63.445965595109025498 - 9.869564445867015331e-7388j 1.01e-2000, 1.01e-2000j
2.192164213469460153 - 2.4924709213049751838e-7468j 1.86e-2029, 1.86e-2029j
5.3002580076216577014 - 2.5474582839544592349e-7462j 5.61e-2024, 5.61e-2024j
17.086028316205446555 - 9.451405174054520974e-7452j 5.29e-2014, 5.29e-2014j
1 - 2.4307183923837518837e-7471j 1.84e-2033, 1.84e-2033j
13.174019452239038364 + 2.4769653714846402412e-7454j 1.64e-2016, 1.64e-2016j
145.30601635992433147 + 2.0568207743802211455e-7434j 6.74e-1998, 6.74e-1998j
24.813828583397315827 - 1.4049322825428948596e-7489j 3.84e-2010, 3.84e-2010j
66.379442724520578053 - 3.1452127721049080626e-7476j 2.38e-2000, 2.38e-2000j
26.545430911787949764 - 1.599741638662346113e-7524j 2.01e-2009, 2.01e-2009j
2.6916764436308490992 - 6.3236534043247945242e-7558j 4.62e-2028, 4.62e-2028j
60.592596412853236109 - 3.7562933627522708948e-7531j 4.03e-2001, 4.03e-2001j
173.08598043537969285 + 1.2769175684574692034e-7619j 5.72e-1999, 5.72e-1999j
0.010372654600643481931 - 8.2077108745219102234e-7733j 5.57e-2042, 5.57e-2042j
3.369839231310923141 + 1.3929908383474073167e-7717j 3.17e-2026, 3.17e-2026j
30.199686583528804438 + 1.6763197312218346663e-7689j 4.71e-2008, 4.71e-2008j
179.19823368459245545 + 1.4231438627083419041e-7689j 2.73e-1999, 2.73e-1999j
36.169519366381978608 - 1.1670832195226102987e-7737j 3.62e-2006, 3.62e-2006j
89.30393796079711 + 4.1071208089934486588e-7729j 2.24e-1998, 2.24e-1998j
0.14650145104919154868 + 4.7805447538601491921e-7839j 6.69e-2039, 6.69e-2039j
0.47046969832733210457 - 5.4008399796668393215e-7833j 4.04e-2036, 4.04e-2036j
85.759102964870781245 - 9.8484897662115165139e-7807j 1.34e-1998, 1.34e-1998j
0.056897625001077184683 + 4.5136038398377927038e-7909j 2.22e-2040, 2.22e-2040j
104.47055026786374393 - 3.8348924135603670739e-7889j 1.01e-1997, 1.01e-1997j
0.28350420709714693599 + 1.3125713991676555476e-7982j 1.64e-2037, 1.64e-2037j
3.1726097502795508871 - 9.9802080973605257526e-7969j 1.29e-2026, 1.29e-2026j
47.477306534190936457 - 4.7380246886822866343e-7943j 2.2e-2003, 2.2e-2003j
0.7089680143963039206 + 4.2070233713611457287e-8003j 7.19e-2035, 7.19e-2035j
205.95298743615513345 - 1.2487932531962580803e-7985j 5.35e-2001, 5.35e-2001j
7.8232631436879996743 - 1.166570887996448971e-8035j 3.98e-2021, 3.98e-2021j
1.7417204509711153594 - 5.0751728933010669084e-8045j 8.14e-2031, 8.14e-2031j

Weights

Weight (ball center) Error (ball radius)
2.5182276594052404346e-145 + 6.2906384077716935434e-6124j 1.67e-372, 2.57e-1877j
5.3994538057578755616e-125 - 1.3697110926412132369e-6113j 8.3e-367, 1.27e-1871j
8.2090807355277965643e-96 + 1.0804823525301310378e-6098j 1.92e-357, 2.96e-1862j
3.3157139352005020123e-137 - 8.3988383975928514519e-6120j 9.39e-371, 1.44e-1875j
6.8806527077743608344e-120 + 5.4575896694781291673e-6111j 1.4e-365, 2.15e-1870j
8.987175790506096205e-13 - 9.1916070426246034781e-6054j 1.62e-284, 2.49e-1789j
6.1928379640594381423e-103 + 2.4515135273651033718e-6102j 1.34e-360, 2.06e-1865j
2.9347367724896479199e-86 - 8.5619655710745478739e-6094j 4.7e-355, 7.23e-1860j
1.3301191570538117864e-08 - 4.1260313746312479436e-6052j 1.68e-271, 2.58e-1776j
1.0319308968769709939e-31 + 2.8923416706638684225e-6065j 6.73e-321, 1.03e-1825j
3.0950729180695866035e-15 - 1.2456762088732971147e-6055j 2.18e-294, 3.35e-1799j
4.3924239493380580063e-33 - 5.209270456338399362e-6066j 1.64e-322, 2.52e-1827j
3.1420018921439178155e-09 + 2.0741373062679116256e-6052j 2.68e-276, 4.11e-1781j
2.7548237833434498947e-99 - 1.7998988642127417961e-6100j 5.93e-360, 9.12e-1865j
5.8279933592505431289e-05 + 4.5653020204520193414e-6050j 9.42e-255, 1.45e-1759j
2.1239582649469993374e-25 - 8.8196120035349215593e-6062j 5.84e-314, 8.97e-1819j
2.1103649838024704267e-05 - 2.3871238652933464779e-6050j 6.91e-259, 1.06e-1763j
6.2657022107357825111e-19 - 4.9698006792692893245e-6058j 4.46e-304, 6.86e-1809j
4.0978526132127793322e-23 - 1.7369895813310966129e-6060j 6.35e-311, 9.76e-1816j
1.4520474515721381025e-72 + 9.6265106501838125822e-6087j 1.44e-352, 2.21e-1857j
1.9804529158976237542e-07 - 1.6409555061255574392e-6051j 1.01e-273, 1.55e-1778j
3.3086129372468178078e-115 - 1.3294750044169504302e-6108j 2.94e-367, 4.52e-1872j
3.0646769319286855882e-24 + 3.9719692469424704891e-6061j 8.28e-314, 1.27e-1818j
8.8176436193632157247e-107 - 2.6537055954319584519e-6104j 3.58e-364, 5.5e-1869j
8.2808621657347055502e-59 + 1.3008789801279687872e-6079j 3.55e-347, 5.45e-1852j
8.734192269467464835e-53 - 1.813385054513638616e-6076j 5.4e-344, 8.3e-1849j
1.4536131596360243038e-10 + 5.6203859655923359215e-6053j 1.97e-292, 3.02e-1797j
2.5436966648089311153e-83 + 2.7675641649980824589e-6092j 5.01e-358, 7.7e-1863j
3.036990529853533396e-47 + 1.4713659057688243454e-6073j 3.04e-341, 4.67e-1846j
6.9066363283426864665e-51 + 1.7905587685390254844e-6075j 3.65e-343, 5.6e-1848j
2.2260479590361509587e-30 - 1.5454645496050578991e-6064j 3.79e-327, 5.82e-1832j
9.6110487400965851787e-57 - 1.5496563602925607741e-6078j 6.82e-347, 1.05e-1851j
7.1939082486641437137e-06 + 1.2387510409763595894e-6050j 5.76e-283, 8.85e-1788j
1.7134835334802716792e-34 + 9.0170792252576013595e-6067j 1.04e-331, 1.59e-1836j
1.1346709917731697955e-130 + 1.7664891469113674291e-6116j 1.32e-377, 2.03e-1882j
0.00015151915238573398197 - 8.6868611607340885517e-6050j 5.25e-279, 8.06e-1784j
4.3057927186758843235e-70 - 1.8228753827872270842e-6085j 8.83e-355, 1.36e-1859j
8.5645359438845915661e-44 + 9.7568354740550128637e-6072j 1.93e-340, 2.96e-1845j
5.8258758924536667402e-18 + 1.9582018560581430444e-6057j 2.01e-316, 3.08e-1821j
6.9736180927480397683e-10 - 1.0590843669965697127e-6052j 3.4e-301, 5.23e-1806j
1.7128258210520715803e-92 - 5.4235150241327556637e-6097j 1.43e-363, 2.2e-1868j
6.2796954263900591241e-20 + 1.2458358675156601032e-6058j 3.51e-319, 5.4e-1824j
0.012639781537792433181 - 7.6662542139208055364e-6048j 2.18e-272, 3.36e-1777j
0.00085422608728335269525 - 3.1591592170495242559e-6049j 1.46e-282, 2.24e-1787j
5.0839651353351914687e-22 + 7.3912336724410826746e-6060j 1.5e-321, 2.31e-1826j
1.7242943896156597951e-80 - 7.9116912351083048158e-6091j 9.4e-360, 1.44e-1864j
1.069950051608950786e-67 + 3.1619213547527040233e-6084j 1.09e-354, 1.68e-1859j
7.3930683569508912439e-111 + 2.2002389549167657959e-6106j 1.1e-371, 1.7e-1876j
0.096703343567397793955 - 9.4855158424039116631e-6048j 1.95e-263, 2.99e-1768j
0.0071962424516970950494 + 2.7639945466441908432e-6048j 3.42e-283, 5.25e-1788j
9.7665504398040797284e-55 + 1.7295415187019779611e-6077j 4.56e-348, 7e-1853j
5.0526776009893647444e-17 - 7.6836431845295700228e-6057j 8.27e-321, 1.27e-1825j
3.8829266870786804665e-42 - 7.3650035482829791787e-6071j 7.68e-343, 1.18e-1847j
0.0018512244497990228995 + 6.1528366313773871484e-6049j 2.08e-292, 3.2e-1797j
6.2116994668940037625e-61 - 1.0201549409500171569e-6080j 4.19e-352, 6.43e-1857j
2.2488796435997102084e-65 - 5.0480530645075613384e-6083j 1.86e-354, 2.86e-1859j
2.1896139481022197947e-14 + 5.5652030922026709424e-6055j 1.59e-321, 2.45e-1826j
4.8502022981734697846e-49 - 1.6688728787294687113e-6074j 2.41e-346, 3.71e-1851j
6.970395980485521805e-07 + 3.2470851438703033959e-6051j 1.62e-310, 2.49e-1815j
6.1137871086682955876e-36 - 1.4980869689463545357e-6067j 1.31e-340, 2.01e-1845j
1.5906827095785204306e-40 + 5.2973473759745652881e-6070j 2.24e-343, 3.44e-1848j
8.0749597476322203882e-28 - 3.9537573809040389754e-6063j 9.65e-336, 1.48e-1840j
0.053189015712792907839 - 1.1020623076846695382e-6047j 3.05e-295, 4.69e-1800j
0.0037705706358395378849 - 1.2475637379886287063e-6048j 4.98e-303, 7.65e-1808j
5.2928500579745190217e-08 + 8.2395310856920877929e-6052j 1.08e-315, 1.65e-1820j
0.11681287161677678966 + 9.4679571809209933285e-6048j 2.67e-293, 4.1e-1798j
2.3082913197826979208e-06 - 6.3713417826285239229e-6051j 1.14e-312, 1.75e-1817j
4.0317388152866175791e-63 + 7.4496519378665552045e-6082j 5.9e-355, 9.07e-1860j
2.8442260704465951483e-11 - 3.2670006459864234244e-6053j 4.14e-322, 6.36e-1827j
4.4169597638449182259e-29 + 7.9576155901054327888e-6064j 6.82e-337, 1.05e-1841j
5.2212209849508100375e-12 + 2.4635820669836392405e-6053j 1.06e-323, 1.62e-1828j
0.035170238219029348711 + 1.5573100785468918094e-6047j 2.01e-306, 3.09e-1811j
1.3622815370396008238e-26 + 1.8982369540561223222e-6062j 2.58e-335, 3.96e-1840j
4.0606443572741860296e-75 - 4.6319516248802710335e-6088j 6.65e-363, 1.02e-1867j
0.026646884833571195078 + 1.5305115273913082748e-6048j 1.41e-308, 2.17e-1813j
0.011321682286826135103 + 3.1541815064280488086e-6047j 1.39e-311, 2.14e-1816j
1.4496069081914692323e-13 - 3.2173879808279303126e-6054j 3.01e-327, 4.63e-1832j
9.3058109882523627511e-78 + 2.0184716510047815166e-6089j 2.48e-364, 3.81e-1869j
4.0910682651576598956e-16 + 3.0424876134640328156e-6056j 5.61e-330, 8.61e-1835j
5.9044564127226844418e-39 - 3.6362173807304156519e-6069j 1.62e-345, 2.49e-1850j
0.097392057933630266784 + 7.0066841378479519821e-6048j 2.17e-316, 3.34e-1821j
0.13276705117983283105 + 9.2225386499784219767e-6048j 5.97e-317, 9.18e-1822j
1.991002621112983761e-37 + 2.3856148711590559841e-6068j 1.1e-344, 1.68e-1849j
0.063447793221221859111 - 4.5446608459279724679e-6048j 4.19e-318, 6.44e-1823j
1.7018736836393312122e-45 - 1.2295487958430717102e-6072j 4.29e-349, 6.59e-1854j
0.12175258019644760679 - 8.5016701239250447018e-6048j 1.32e-319, 2.03e-1824j
0.013307905922548495801 - 3.5390024880482241688e-6047j 1.4e-321, 2.15e-1826j
5.8591597129715948479e-21 - 3.0678210360748185157e-6059j 5.45e-336, 8.37e-1841j
0.13024030349475322403 - 9.4586271031465903041e-6048j 5.53e-322, 8.49e-1827j
2.593453518309917993e-89 + 2.3179643926828614174e-6095j 9.15e-372, 1.41e-1876j
0.00037083423100286893918 + 1.6515447472435267096e-6049j 8.76e-326, 1.35e-1830j
0.074324022152333101177 + 9.8007311755444501945e-6048j 2.13e-323, 3.25e-1828j

Download

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