Rule: Q[4, 93]

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)
336.30799021669128265 - 4.1869659760276980106e-4529j 3.18e-2010, 3.18e-2010j
295.19678746388038601 - 1.9682576692016403911e-4523j 1.02e-2005, 1.02e-2005j
273.77084804486888003 + 4.0307466365588436748e-4517j 1.35e-2003, 1.35e-2003j
254.96237279037603138 + 6.0222515257023138361e-4513j 7.64e-2002, 7.64e-2002j
264.09554997850197865 + 4.8144056783055932715e-4516j 1.16e-2002, 1.16e-2002j
139.84503052005207051 + 1.7744555768484079852e-4519j 3.55e-1995, 3.55e-1995j
97.878825342883407582 + 5.9605926026840700264e-4529j 8.67e-1996, 8.67e-1996j
101.60804515776471573 - 1.2484490461937691193e-4552j 1.33e-1995, 1.33e-1995j
320.78195871355482432 + 1.599367716626501505e-4571j 1.75e-2008, 1.75e-2008j
307.30797498565915944 - 3.7849206567580230329e-4578j 5.07e-2007, 5.07e-2007j
21.996944819632318487 + 1.6578453022505520689e-4626j 3.44e-2010, 3.44e-2010j
38.316738410056415902 - 1.1768485863491448847e-4611j 5.03e-2004, 5.03e-2004j
165.41156656421477598 + 1.6395372410654642065e-4623j 7.42e-1996, 7.42e-1996j
160.00607615778340294 - 7.4747978475080971452e-4695j 1.26e-1995, 1.26e-1995j
52.040203592639910777 - 1.1536298361651638722e-4732j 8.65e-2001, 8.65e-2001j
65.372855342172551499 + 2.2446281834069069624e-4726j 1.25e-1998, 1.25e-1998j
17.62435976596016818 + 1.761274141133611875e-4778j 1.41e-2012, 1.41e-2012j
90.697877304659639584 - 2.6738988547189238455e-4760j 3.52e-1996, 3.52e-1996j
54.56392776058528636 - 1.649105824046694642e-4804j 2.49e-2000, 2.49e-2000j
230.14434542873505671 + 1.0949421086106734242e-4849j 9.73e-2000, 9.73e-2000j
16.281062221569843762 - 4.8783440119604909231e-4913j 2.23e-2013, 2.23e-2013j
20.481867215743094182 + 7.4068104591175583528e-4910j 5.71e-2011, 5.71e-2011j
49.585658567860001598 - 2.9798638306877559873e-4894j 2.62e-2001, 2.62e-2001j
36.257577772222229715 - 9.8285369931160238767e-4916j 1.21e-2004, 1.21e-2004j
68.259683263375490464 + 7.0571604804561579069e-4914j 3.12e-1998, 3.12e-1998j
182.62617742062554323 + 1.2179051666610616823e-4964j 1.22e-1996, 1.22e-1996j
284.08998515452665183 + 9.6397802237772870758e-4989j 1.4e-2004, 1.4e-2004j
83.872012827541432162 + 5.287641874708841636e-5001j 1.07e-1996, 1.07e-1996j
42.627182221961877532 - 2.2599502452991541539e-5050j 6.78e-2003, 6.78e-2003j
8.4406787167172294824 - 7.2207631441325394777e-5071j 1.3e-2019, 1.3e-2019j
7.5413542128733066664 + 5.2561432602388027518e-5073j 1.49e-2020, 1.49e-2020j
109.35647167074603691 - 3.8213383618462074031e-5045j 2.6e-1995, 2.6e-1995j
62.561147748326824502 - 4.1931267240292877422e-5082j 4.87e-1999, 4.87e-1999j
40.439675663505556167 + 2.8533151508251982316e-5111j 1.88e-2003, 1.88e-2003j
176.71254261281191264 - 4.6283014457138338461e-5119j 2.61e-1996, 2.61e-1996j
71.223018961116277379 + 2.369443908541020659e-5157j 6.67e-1998, 6.67e-1998j
238.03849989580657313 + 5.5556720862800891661e-5199j 2.39e-2000, 2.39e-2000j
6.6975949064755287907 + 3.7527619966431258558e-5306j 1.96e-2021, 1.96e-2021j
222.5766731679152614 - 3.357868567071854196e-5279j 3.9e-1999, 3.9e-1999j
126.09483238017376154 + 3.7983648563090612632e-5376j 4.35e-1995, 4.35e-1995j
113.3811961671940044 - 4.1308755188680706186e-5495j 3.09e-1995, 3.09e-1995j
28.644144936820355144 - 1.9752084318238085075e-5578j 2.92e-2007, 2.92e-2007j
32.327604359104835497 - 8.3044071319995616771e-5568j 7e-2006, 7e-2006j
4.0173395787583206367 + 3.2029386057795884506e-5615j 9.46e-2025, 9.46e-2025j
208.30464076788714435 - 1.8111207190211011899e-5627j 3.92e-1998, 3.92e-1998j
34.261439174049245177 - 2.4815276939452030072e-5700j 2.93e-2005, 2.93e-2005j
149.64638637603838882 - 4.2597771303740099042e-5746j 2.44e-1995, 2.44e-1995j
355.67130610786807499 + 4.6411225942102504727e-5823j 1.86e-2012, 1.86e-2012j
5.9108425753356069186 + 2.3381274417059603796e-5887j 2.12e-2022, 2.12e-2022j
26.893251344802581993 - 1.1910321512981034238e-5869j 5.85e-2008, 5.85e-2008j
30.45538974743111945 - 2.0673002134746930328e-5860j 1.42e-2006, 1.42e-2006j
3.607906896117170191 - 3.7398188325144178368e-5911j 1.84e-2025, 1.84e-2025j
117.51026845996490417 + 2.0661506685445983096e-5924j 3.89e-1995, 3.89e-1995j
77.385155250243299366 + 5.1092320641709831138e-6003j 3.33e-1997, 3.33e-1997j
25.202120991375079936 + 1.0004160953143739416e-6097j 1.14e-2008, 1.14e-2008j
144.67887391130817869 - 2.9437150059903711216e-6100j 3.32e-1995, 3.32e-1995j
80.587139772167144806 - 1.5234452522342563522e-6207j 6.25e-1997, 6.25e-1997j
188.72918629211687408 - 4.4293792379256550493e-6289j 5.96e-1997, 5.96e-1997j
5.1853947341130440922 + 3.6097486118275395664e-6368j 3.09e-2023, 3.09e-2023j
9.3950709123011331292 + 1.1068834336416522114e-6363j 1.13e-2018, 1.13e-2018j
10.404418657361846905 + 2.6208797383742109265e-6363j 9.41e-2018, 9.41e-2018j
94.242883020941013033 - 3.239447085215102896e-6340j 6.01e-1996, 6.01e-1996j
195.03371638688734482 - 4.676170357493589992e-6380j 2.77e-1997, 2.77e-1997j
14.994203110269341627 - 1.422305102240746409e-6431j 3.36e-2014, 3.36e-2014j
1.7457611011583465757 + 3.2616516457560489471e-6447j 1.98e-2030, 1.98e-2030j
1.0389366438050053153 - 3.8908155085000686247e-6450j 5.06e-2033, 5.06e-2033j
59.823245207469218966 - 3.3763479090014794312e-6416j 1.9e-1999, 1.9e-1999j
201.55358680404800848 - 1.7413043994006678754e-6411j 1.1e-1997, 1.1e-1997j
0.3225476896193923118 + 6.4946580470395964367e-6473j 4.66e-2037, 4.66e-2037j
1.3690892538838991254 - 7.4123391424122588306e-6467j 1.05e-2031, 1.05e-2031j
2.1686201479000441043 + 4.2902299764485095308e-6464j 3.61e-2029, 3.61e-2029j
19.024488023113109082 + 7.3879522603743642971e-6447j 9.44e-2012, 9.44e-2012j
4.5366202969211279833 - 4.3417478721638291899e-6460j 4.88e-2024, 4.88e-2024j
215.30520161631373858 + 2.1197626980227104128e-6429j 1.31e-1998, 1.31e-1998j
23.570195427312067421 - 1.5770969396777326387e-6454j 2.08e-2009, 2.08e-2009j
12.588381468946938365 - 1.5046040101482262159e-6461j 5.48e-2016, 5.48e-2016j
135.13957518778232411 - 3.1028080307521337528e-6439j 4.17e-1995, 4.17e-1995j
105.43303863543776201 - 1.3278125106228519815e-6444j 1.89e-1995, 1.89e-1995j
246.29596511213844605 - 1.050530380978147788e-6452j 4.68e-2001, 4.68e-2001j
13.763419642259262839 + 4.1575278883190364632e-6488j 4.21e-2015, 4.21e-2015j
3.1316508447848832416 + 3.5986303794147540338e-6499j 1.29e-2026, 1.29e-2026j
0.070937626783773000117 + 6.5635712104588390229e-6513j 4.68e-2040, 4.68e-2040j
44.880090842135402672 + 1.2998879008286216317e-6474j 2.38e-2002, 2.38e-2002j
74.26432712461517101 + 2.0240945260187255443e-6470j 1.41e-1997, 1.41e-1997j
170.97753057110352696 + 1.1718475304448652949e-6466j 4.78e-1996, 4.78e-1996j
57.157900003027645506 - 3.4235693436427025486e-6484j 6.94e-2000, 6.94e-2000j
0.75481593008118501797 + 7.9126824193375263893e-6519j 2.69e-2034, 2.69e-2034j
2.6347379154806620765 + 3.0554917177645843063e-6512j 7.22e-2028, 7.22e-2028j
121.74697023572773365 + 3.9000592305103374226e-6478j 4.16e-1995, 4.16e-1995j
154.75334200684270952 + 2.6085007842094560988e-6487j 1.8e-1995, 1.8e-1995j
47.199276473332076703 + 6.2917909524578898147e-6508j 8.16e-2002, 8.16e-2002j
11.46879607296098276 - 9.1424578573678042003e-6524j 7.05e-2017, 7.05e-2017j
0.51613387525465185797 - 3.328671937945813778e-6542j 1.2e-2035, 1.2e-2035j
0.17406361781411183403 + 3.0405382244655856488e-6545j 1.63e-2038, 1.63e-2038j
130.55766227584085122 - 1.9114962398165324291e-6500j 4.37e-1995, 4.37e-1995j
0.013476217951551738708 + 3.8185437838010767134e-6643j 8.41e-2042, 8.41e-2042j
87.241609738300967166 + 3.756587996584173624e-6515j 2.01e-1996, 2.01e-1996j

Weights

Weight (ball center) Error (ball radius)
1.4886496778143494287e-145 - 1.0207719919733595675e-4624j 7.96e-368, 2.49e-1871j
7.2574950893332362568e-128 + 1.0901675102094403795e-4615j 1.39e-362, 4.33e-1866j
1.2643018177323455582e-118 + 5.8865128239961799907e-4611j 7.27e-360, 2.27e-1863j
1.6599582429899779295e-110 + 8.6924558865694168433e-4607j 8.16e-358, 2.55e-1861j
1.8941700015632649917e-114 - 8.1792923345525791752e-4609j 8.38e-359, 2.62e-1862j
8.8000409269283768658e-61 - 7.8956510488706725303e-4580j 5.46e-337, 1.71e-1840j
1.1425391447364638535e-42 - 4.244535252623152746e-4571j 8.78e-324, 2.75e-1827j
2.8138212986982311535e-44 - 1.5147537940074893562e-4572j 3.5e-325, 1.09e-1828j
6.9612751156253864685e-139 + 2.5683332186828101702e-4621j 6.21e-369, 1.94e-1872j
4.3869645340781369582e-133 - 2.3452012895401162617e-4618j 8.41e-367, 2.63e-1870j
4.3203488389569309813e-10 - 7.3670715211565251445e-4555j 5.18e-273, 1.62e-1776j
4.7817776203426832868e-17 + 1.1711298250150137526e-4558j 1.87e-293, 5.84e-1797j
7.976207623167938704e-72 - 1.542977822751427829e-4586j 5.31e-346, 1.66e-1849j
1.7250409299236074835e-69 + 2.9934038405830904008e-4585j 1.02e-344, 3.2e-1848j
6.2408655050540437869e-23 + 9.8369370792167277473e-4562j 1.35e-306, 4.22e-1810j
1.1577868580712970958e-28 - 1.1697836352555769097e-4564j 5.53e-315, 1.73e-1818j
3.0414422962630411233e-08 + 8.6888612473817123282e-4554j 3.36e-271, 1.05e-1774j
1.4273002428889409091e-39 - 6.2548443210375311824e-4570j 6.1e-326, 1.91e-1829j
5.1428135069684675278e-24 - 2.7211449797010961813e-4562j 1.23e-308, 3.85e-1812j
8.6596573774175996103e-100 - 2.9276513066912187227e-4601j 3.03e-360, 9.47e-1864j
1.1172627904910859966e-07 - 1.8924606813670501158e-4553j 1.52e-270, 4.76e-1774j
1.8919131306241467501e-09 + 1.7157400554621637273e-4554j 1.37e-277, 4.28e-1781j
7.0646560356396114924e-22 - 3.4492838285511313645e-4561j 5.94e-306, 1.86e-1809j
3.6349687337552371314e-16 - 3.4453829597142446578e-4558j 8.81e-297, 2.75e-1800j
6.6267254132656542838e-30 + 2.7723487042854600952e-4565j 3.43e-317, 1.07e-1820j
2.9179290022507783458e-79 + 1.5562261579987017953e-4590j 3.4e-353, 1.06e-1856j
4.4671895288689827003e-123 - 3.0795439041163230987e-4613j 4.51e-368, 1.41e-1871j
1.2499424378308118815e-36 - 1.3739819635108765668e-4568j 2.49e-325, 7.77e-1829j
6.8173523584989354746e-19 + 1.2425431269409016017e-4559j 6.8e-304, 2.13e-1807j
0.00020012086799286814407 + 2.720630163471474132e-4551j 2.62e-261, 8.19e-1765j
0.00046257887910529379096 - 5.3409276921440128808e-4551j 2.38e-258, 7.43e-1762j
1.2772341627880486574e-47 + 1.1695799889042535701e-4574j 3.52e-335, 1.1e-1838j
1.8760215526245741274e-27 + 4.7861290210730781034e-4564j 1.28e-315, 4.02e-1819j
5.8984339391305880063e-18 - 3.8698017118847230843e-4559j 5.66e-303, 1.77e-1806j
1.0467368382885218329e-76 - 3.5692183441630206543e-4589j 1.76e-352, 5.52e-1856j
3.5128277575102330159e-31 - 6.3746650894873232315e-4566j 1.63e-320, 5.1e-1824j
3.3729837734412503742e-103 + 5.0660406605904252603e-4603j 9.42e-364, 2.95e-1867j
0.0010063840640933470177 + 1.0590361263901359898e-4550j 3.27e-265, 1.02e-1768j
1.6080118998598854836e-96 + 1.4432147995168096951e-4599j 1e-361, 3.13e-1865j
7.6142151728499996119e-55 + 1.103749757597033736e-4577j 9.94e-343, 3.11e-1846j
2.3412395555395596415e-49 - 2.6082923559792028772e-4575j 1.88e-338, 5.87e-1842j
6.4663945571819240616e-13 - 1.9617993079935653978e-4556j 6.36e-303, 1.99e-1806j
1.7366763203987653925e-14 - 2.7440029967954325958e-4557j 2.87e-305, 8.99e-1809j
0.0078195885399667563268 + 2.099855742690374972e-4549j 3.03e-263, 9.48e-1767j
2.3526642549557686451e-90 + 2.3131411218793930395e-4596j 5.04e-361, 1.58e-1864j
2.5928645678428287041e-15 + 9.8575323736369899825e-4558j 1.64e-306, 5.12e-1810j
5.1464231417692704833e-65 + 1.1448229075835844462e-4582j 3.53e-349, 1.1e-1852j
7.781302513108195382e-154 + 6.1884895901404418265e-4629j 1.37e-386, 4.28e-1890j
0.0020520922802951366917 - 2.1550806803845967523e-4550j 5.2e-276, 1.63e-1779j
3.5988946316177530581e-12 + 5.0433284916742617376e-4556j 5.72e-304, 1.79e-1807j
1.0929322866506215595e-13 + 7.4349822808522183055e-4557j 1.33e-305, 4.16e-1809j
0.011724709339380860052 - 2.5516114918981114895e-4549j 3.9e-270, 1.22e-1773j
3.866839239856264821e-51 + 4.5228281746487615099e-4576j 2.22e-341, 6.93e-1845j
7.7964317118345531653e-34 - 3.0947258276743051559e-4567j 1.16e-329, 3.64e-1833j
1.8851324815645756411e-11 - 1.2638257742346876014e-4555j 6.41e-305, 2e-1808j
7.1934645821359242475e-63 - 2.8365402298377547195e-4581j 1.33e-348, 4.16e-1852j
3.2539769948576732274e-35 + 6.5725406114255138479e-4568j 7.23e-331, 2.26e-1834j
6.7369090813042280259e-82 - 6.266451877750650102e-4592j 8.42e-359, 2.63e-1862j
0.0038710754873225754986 + 4.6163239655324952429e-4550j 1.68e-285, 5.24e-1789j
8.1625566183457715848e-05 - 1.3861221421374535605e-4551j 4.92e-295, 1.54e-1798j
3.1414493130178977709e-05 + 7.0185021008258491127e-4552j 3.94e-297, 1.23e-1800j
4.2261219470502993868e-41 + 1.6419940546435104232e-4570j 4.53e-336, 1.42e-1839j
1.272839698507454169e-84 + 2.3087961856268551758e-4593j 1.24e-360, 3.89e-1864j
3.8729726946421784347e-07 + 4.0382514983109995626e-4553j 1.02e-305, 3.19e-1809j
0.069795216407099483897 - 1.5846866207371635424e-4549j 4.72e-282, 1.48e-1785j
0.10863670590795292393 - 1.3912755265931983277e-4549j 1.38e-277, 4.31e-1781j
2.8228450641840557467e-26 - 1.8983767827845354469e-4563j 5.88e-327, 1.84e-1830j
1.9412226970195745466e-87 - 7.7120513691341603465e-4595j 3.58e-362, 1.12e-1865j
0.12390089950867043796 + 7.7008176598101659711e-4550j 7.07e-281, 2.21e-1784j
0.089874864583086270334 + 1.5040604933765541503e-4549j 2.12e-283, 6.62e-1787j
0.050921087103575951655 + 1.6690670001327758394e-4549j 1.05e-287, 3.27e-1791j
7.810974546543939906e-09 - 3.9044830421780131205e-4554j 3.99e-310, 1.25e-1813j
0.0063978400679438597244 - 1.0591558019512632743e-4549j 1.56e-294, 4.87e-1798j
2.2251528616441844949e-93 - 6.1652178453298840648e-4598j 5.1e-365, 1.6e-1868j
9.2980698117331121438e-11 + 3.0888497336177671873e-4555j 3.91e-313, 1.22e-1816j
3.9138099461339967408e-06 + 1.7378904512136786606e-4552j 7.46e-308, 2.33e-1811j
9.4714941273522888016e-59 + 3.5260461098541501477e-4579j 7.56e-350, 2.36e-1853j
6.2971661148123944567e-46 + 1.7455921214430138273e-4575j 3.56e-342, 1.11e-1845j
9.1633771634490272642e-107 - 7.3378350332247969277e-4605j 6.88e-372, 2.15e-1875j
1.2671773568395128017e-06 - 8.4524290633690684852e-4553j 7.17e-312, 2.24e-1815j
0.021877266400909880292 + 2.1571375370866845142e-4549j 2.09e-302, 6.53e-1806j
0.074835409912349260231 + 2.697108788471694844e-4550j 1.88e-299, 5.89e-1803j
7.3770204159569959476e-20 - 3.8752666551911008904e-4560j 4.05e-326, 1.27e-1829j
1.7221717482286699564e-32 + 1.4236959007942109784e-4566j 1.33e-334, 4.15e-1838j
3.1432002231369067014e-74 + 7.636780417733598003e-4588j 2.14e-357, 6.7e-1861j
3.9491811777980589992e-25 + 7.2994250457944939764e-4563j 1.17e-330, 3.64e-1834j
0.12284390857891337617 + 1.2291495858937116269e-4549j 9.13e-308, 2.85e-1811j
0.034806379685741785531 - 1.8218324398224025432e-4549j 2.87e-309, 8.97e-1813j
5.7357353067298155656e-53 - 7.1629058484784251686e-4577j 2.14e-347, 6.7e-1851j
3.2040662326746356608e-67 - 5.7299345721909248133e-4584j 1.11e-354, 3.46e-1858j
7.4673707789178466236e-21 + 1.1735279555513762411e-4560j 9.31e-330, 2.91e-1833j
1.1412112343318355932e-05 - 3.5164499992629071882e-4552j 1.28e-319, 4.01e-1823j
0.12897758395247408639 - 1.0173496058757014061e-4549j 7.06e-316, 2.21e-1819j
0.10575258042616214074 - 5.1128112364257265125e-4550j 2.06e-316, 6.45e-1820j
9.0120880957582177206e-57 - 1.7707943739598731846e-4578j 1.19e-349, 3.73e-1853j
0.034113535158902512182 - 7.8503238150323818118e-4551j 9.33e-319, 2.72e-1822j
4.4109835181344776482e-38 + 2.8726219922370209709e-4569j 7.28e-340, 2.28e-1843j

Download

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