Rule: Q[1, 7, 84]

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)
309.78186319252355399 + 2.5817173428939165387e-5194j 4.58e-2012, 4.58e-2012j
269.87806391130047999 - 8.7997311919961571826e-5214j 9.98e-2008, 9.98e-2008j
328.61737152902455788 - 5.8311432934439580425e-5239j 3.03e-2014, 3.03e-2014j
281.62020154994156046 + 1.9905153773858814273e-5280j 5.62e-2009, 5.62e-2009j
186.06167230750677067 - 2.8077326400057450304e-5352j 1.5e-2000, 1.5e-2000j
68.642218939514972057 + 3.3484432832080286238e-5469j 4.11e-2000, 4.11e-2000j
259.12052053179176943 - 4.2151210861957248562e-5701j 1.08e-2006, 1.08e-2006j
161.48578006597191229 + 2.9738955576638041731e-5929j 3.11e-1999, 3.11e-1999j
207.04458992984926372 + 3.4999365278554727332e-6089j 5.14e-2002, 5.14e-2002j
230.96353686604789949 + 5.4238801291603941053e-6211j 5.28e-2004, 5.28e-2004j
214.64478857474280772 - 2.0268891205741154563e-6304j 1.18e-2002, 1.18e-2002j
33.939999701395971425 - 6.9884368127439334153e-6366j 2.87e-2006, 2.87e-2006j
18.75251539166561618 + 1.0924656189387712848e-6394j 2.87e-2012, 2.87e-2012j
173.3464104144729568 - 1.3233746391840563492e-6405j 8.36e-2000, 8.36e-2000j
15.993949649305804235 + 4.4553649710925365104e-6488j 9.08e-2014, 9.08e-2014j
21.740836675711700467 + 1.5109202169448991892e-6479j 8.15e-2011, 8.15e-2011j
239.78327355597858218 - 2.7965632999089996689e-6514j 8.38e-2005, 8.38e-2005j
20.218655428150441075 - 1.9549069755296964093e-6579j 1.59e-2011, 1.59e-2011j
11.362170796131734124 - 7.7562049191594519923e-6588j 1.5e-2016, 1.5e-2016j
145.08007000387772861 - 2.1878084080976404354e-6584j 1.55e-1998, 1.55e-1998j
10.584516449723009839 - 1.6377237602577625747e-6639j 3.93e-2017, 3.93e-2017j
44.572414879257991941 - 4.4161392284173316827e-6626j 1.16e-2003, 1.16e-2003j
40.097807035601133896 + 8.4972404514546972407e-6627j 1.25e-2004, 1.25e-2004j
294.69708543833557433 + 1.3472658363697789374e-6620j 2.12e-2010, 2.12e-2010j
62.717271083807371635 - 4.7383053525170066986e-6640j 8.78e-2001, 8.78e-2001j
199.76627220806461133 + 7.3649085074286635352e-6659j 1.58e-2001, 1.58e-2001j
85.009126616222650146 + 9.2610990969396809528e-6671j 6.88e-1999, 6.88e-1999j
134.95607035895995254 + 8.9286684081554847497e-6670j 2.61e-1998, 2.61e-1998j
139.94206710755255579 + 2.2133368495843636362e-6681j 2.18e-1998, 2.18e-1998j
107.891273341514122 + 4.2982710779900526739e-6693j 3.67e-1998, 3.67e-1998j
32.023957906014735907 + 4.9860519764291497435e-6714j 7.51e-2007, 7.51e-2007j
49.356808724797044596 + 5.0151054804545373207e-6710j 1e-2002, 1e-2002j
9.7803534697092969099 - 3.5365719160224437066e-6725j 5.09e-2018, 5.09e-2018j
46.925435925679186168 + 2.7266869866745422346e-6710j 3.42e-2003, 3.42e-2003j
14.706104047913607885 + 1.2515588697776554494e-6721j 1.77e-2014, 1.77e-2014j
92.219577425413363057 - 3.2626602044371816264e-6704j 1.46e-1998, 1.46e-1998j
116.40505880183257946 + 2.9765300027863512472e-6722j 4.53e-1998, 4.53e-1998j
37.973575680081861438 - 1.3993143783656525582e-6755j 3.83e-2005, 3.83e-2005j
26.63472565257549137 + 1.022267042382866539e-6758j 9.5e-2009, 9.5e-2009j
99.838881152569577015 - 2.3324657783796126095e-6747j 2.54e-1998, 2.54e-1998j
120.84514609201789889 + 1.4683607637399230325e-6773j 4.18e-1998, 4.18e-1998j
192.78021297312565983 - 2.4608155562821936371e-6793j 5.09e-2001, 5.09e-2001j
249.13578567175449118 + 9.0236063319473726975e-6811j 1.06e-2005, 1.06e-2005j
1.2986807624498493211 - 2.2474254263300095709e-6860j 5.73e-2032, 5.73e-2032j
71.734424888886786741 - 4.4805425089375183401e-6826j 7.6e-2000, 7.6e-2000j
150.37761082785866443 + 1.413685923731252934e-6833j 9.52e-1999, 9.52e-1999j
2.5000206754193299535 + 1.554758532043216276e-6885j 1.49e-2028, 1.49e-2028j
78.186704771318921612 - 2.3882769293033443791e-6854j 2.36e-1999, 2.36e-1999j
3.5247586073812725287 + 3.691842551558623782e-6906j 2.04e-2026, 2.04e-2026j
167.31627073401228223 - 3.2782948542810630959e-6877j 1.64e-1999, 1.64e-1999j
35.921979094684760873 + 1.0435354001062749766e-6903j 1.1e-2005, 1.1e-2005j
2.0543457690713855228 + 8.4695628687659689918e-6929j 1.05e-2029, 1.05e-2029j
74.915310099811878055 - 9.3348683210967994622e-6896j 1.45e-1999, 1.45e-1999j
54.457657812750944779 + 3.3043354890941056114e-6909j 6.82e-2002, 6.82e-2002j
2.9884138653146795273 + 1.7888564240813744899e-6935j 1.91e-2027, 1.91e-2027j
30.169938940393323256 - 1.2406670704135344328e-6915j 1.83e-2007, 1.83e-2007j
222.60289334462628916 + 2.6636562218606295568e-6905j 2.63e-2003, 2.63e-2003j
51.867290264199593785 + 1.8773061560672586205e-6920j 2.54e-2002, 2.54e-2002j
7.9509208918881512072 + 2.255090408582339105e-6938j 3.98e-2020, 3.98e-2020j
0.75133489644780921912 + 2.3055472115010141179e-6952j 3.32e-2034, 3.32e-2034j
103.80927667207123745 + 3.5821751353915274957e-6915j 3.12e-1998, 3.12e-1998j
65.637012169680242164 - 1.4522424188524486864e-6931j 1.83e-2000, 1.83e-2000j
57.128771276771633346 - 2.8204102103103690754e-6936j 1.66e-2001, 1.66e-2001j
4.1162849964681959556 - 3.6231646739171335813e-6964j 2.31e-2025, 2.31e-2025j
8.8664852405340366634 - 2.7743985888276195102e-6958j 4.65e-2019, 4.65e-2019j
12.35199612685986194 - 1.0904692423164716199e-6954j 6.11e-2016, 6.11e-2016j
1.652070898194102094 + 2.9527183111950329955e-6970j 7.95e-2031, 7.95e-2031j
88.564620504967365388 + 8.4870475615453451718e-6936j 9.79e-1999, 9.79e-1999j
0.014735824930850318363 - 4.3627424350766723677e-7075j 1.2e-2041, 1.2e-2041j
1 + 1.144582031002310451e-7007j 4.91e-2033, 4.91e-2033j
0.53414908405267519679 - 1.1969531388456716209e-7009j 1.88e-2035, 1.88e-2035j
155.84306272041232663 + 2.1585910095900479663e-6971j 5.94e-1999, 5.94e-1999j
23.318012944480399754 + 2.997785629478928615e-7018j 4.42e-2010, 4.42e-2010j
28.374404569399562566 - 2.7386834319413141098e-7016j 4.44e-2008, 4.44e-2008j
24.949411810096524977 - 2.3231899922454438802e-7018j 2.06e-2009, 2.06e-2009j
4.7673099177671066141 + 2.2250644576161408032e-7032j 2.52e-2024, 2.52e-2024j
59.881606436859388499 + 4.5669671078480826451e-7006j 4.08e-2001, 4.08e-2001j
0.18807558052466950658 - 3.1863280943696402004e-7091j 2.45e-2038, 2.45e-2038j
125.41350671792776506 + 2.9274073001166835355e-7049j 3.92e-1998, 3.92e-1998j
42.296902474733708575 + 8.893764712336464024e-7084j 4.22e-2004, 4.22e-2004j
6.2483462326945142222 + 2.1264546117139685255e-7127j 2.95e-2022, 2.95e-2022j
7.0741499458083764219 - 3.1024458697625931571e-7126j 3.16e-2021, 3.16e-2021j
5.4784843217981563454 + 4.3940473925546990273e-7128j 2.54e-2023, 2.54e-2023j
179.58971248694880857 + 6.1314924323003457595e-7102j 3.88e-2000, 3.88e-2000j
112.08854137946488335 - 8.7302575117015573391e-7137j 4.07e-1998, 4.07e-1998j
17.343704060305738486 - 9.0268469742611852936e-7173j 5.4e-2013, 5.4e-2013j
0.077277668457187450472 - 1.0730710076988689082e-7260j 5.94e-2040, 5.94e-2040j
0.34311677002403123873 + 5.8986965920221940715e-7196j 7.86e-2037, 7.86e-2037j
130.11527465226994248 - 2.7202707705272257467e-7156j 3.44e-1998, 3.44e-1998j
81.550594367822889313 - 9.9945846729272324928e-7166j 4.28e-1999, 4.28e-1999j
95.976694620341308769 + 4.8052650483561146298e-7184j 2.02e-1998, 2.02e-1998j
13.48630087069814393 + 1.327641299314298278e-7214j 3.11e-2015, 3.11e-2015j

Weights

Weight (ball center) Error (ball radius)
4.7935841633562696451e-134 - 6.3337247039179896899e-5328j 4.05e-372, 2.62e-1878j
6.9647653629298724306e-117 + 1.9591808936876272687e-5320j 4.45e-367, 2.88e-1873j
4.2530026669787454934e-142 - 4.9902054516873803213e-5333j 3.84e-375, 2.48e-1881j
6.0953721010170204624e-122 - 7.0236493016201440859e-5323j 8.35e-369, 5.4e-1875j
1.0314825308538120729e-80 + 3.0630160343085467545e-5302j 1.74e-355, 1.13e-1861j
4.7112977154680594974e-30 + 1.7905385833770750335e-5275j 4.06e-320, 2.62e-1826j
3.020233384079436703e-112 - 3.7323535205434160674e-5318j 2.35e-366, 1.52e-1872j
4.2279617463650627153e-70 + 8.8440172773461782385e-5297j 2.72e-351, 1.76e-1857j
8.9720302306283710237e-90 - 7.2883580778993700138e-5307j 1.02e-359, 6.63e-1866j
4.2391137561874372458e-100 + 4.3477809536273194294e-5312j 6.96e-364, 4.5e-1870j
4.6936911036114024297e-93 + 1.5737254930883367659e-5308j 3.07e-361, 1.99e-1867j
3.5458010434313087595e-15 + 9.233741435280163335e-5267j 8.65e-303, 5.59e-1809j
1.0317130436796185338e-08 - 9.0779212615943576837e-5263j 5.64e-283, 3.65e-1789j
3.1943071473640345403e-75 + 2.0189746990134742522e-5299j 3.46e-355, 2.24e-1861j
1.4938375729595891804e-07 - 6.1355281137214128202e-5262j 2.51e-278, 1.62e-1784j
5.602216399029863471e-10 - 1.3510567028218028833e-5263j 1.53e-288, 9.87e-1795j
6.6245067118333759999e-104 - 5.3267939037687134084e-5314j 1.34e-365, 8.65e-1872j
2.4751569956698494256e-09 + 3.512019004295772923e-5263j 4.67e-286, 3.02e-1792j
1.0222766106372707767e-05 - 3.8086534167234351263e-5260j 6.38e-270, 4.13e-1776j
5.1274480184053274129e-63 - 4.1785538383334443991e-5293j 2.22e-351, 1.44e-1857j
1.8565647913190849552e-05 + 7.0648442688621042729e-5260j 2.83e-268, 1.83e-1774j
1.0158522039252625623e-19 - 1.6426208499882188311e-5269j 9.89e-315, 6.4e-1821j
8.326638277758547954e-18 - 2.3358873358866485756e-5268j 4.13e-311, 2.67e-1817j
1.4402510938752578863e-127 + 1.706780762117310815e-5325j 3.66e-375, 2.37e-1881j
1.6643630019646627904e-27 + 4.8653763201414906876e-5274j 7.72e-327, 5e-1833j
1.2461196404576457027e-86 + 2.8996364898258297128e-5305j 3.93e-360, 2.55e-1866j
4.2256457553509069161e-37 - 2.3309376583837667066e-5279j 1.13e-337, 7.29e-1844j
1.2039536809208610179e-58 - 7.9760707254311714268e-5291j 7.02e-351, 4.54e-1857j
8.4752472456397531744e-61 + 5.9864070264150484114e-5292j 1.67e-351, 1.08e-1857j
5.7585130602107214985e-47 - 1.1509662578959005644e-5284j 4.23e-346, 2.73e-1852j
2.3299261144434822789e-14 - 2.889071740135440553e-5266j 8.21e-311, 5.31e-1817j
9.0666796978146265723e-22 - 9.9599378432205618991e-5271j 1.97e-323, 1.27e-1829j
4.9823089752411928544e-05 - 8.9966392576167043981e-5260j 1e-282, 6.5e-1789j
9.9842544206181706154e-21 + 4.1179457915758327369e-5270j 1.15e-321, 7.43e-1828j
5.1520502431934025056e-07 + 1.6391003942228198593e-5261j 1.28e-292, 8.3e-1799j
3.299145536986617891e-40 - 4.8147254484881078388e-5281j 8.45e-343, 5.46e-1849j
1.2222402806342174308e-50 - 1.2953298087706607748e-5286j 1.67e-349, 1.08e-1855j
6.7283319130468899934e-17 + 8.3001147890022280571e-5268j 4.69e-318, 3.03e-1824j
4.6374178476253509664e-12 + 7.0475305830940662199e-5265j 1.68e-310, 1.09e-1816j
1.711352662615644654e-43 - 8.2345709436855128691e-5283j 1.27e-345, 8.19e-1852j
1.4830677068596615273e-52 + 1.2603019424794558352e-5287j 1.01e-350, 6.56e-1857j
1.2948344787416039865e-83 - 1.0043359845017083155e-5303j 8.28e-365, 5.35e-1871j
6.1122148251854922788e-108 + 5.1270298858301733709e-5316j 5.89e-375, 3.81e-1881j
0.089140071560923912692 + 5.5805033183174214495e-5258j 5.32e-260, 3.44e-1766j
2.2006259282132148093e-31 - 3.244255724896590902e-5276j 7.33e-339, 4.74e-1845j
2.6461694150091228803e-65 + 2.7025248492123910535e-5294j 9.45e-358, 6.11e-1864j
0.038301130349032617 - 3.0185293385539943562e-5258j 4.05e-277, 2.62e-1783j
3.6705406844743663837e-34 - 9.4526120502501684415e-5278j 1.11e-341, 7.2e-1848j
0.016581527732582088559 - 1.6134518421383382328e-5258j 1.94e-285, 1.25e-1791j
1.2834839147933557746e-72 - 4.4323660326263852392e-5298j 3.46e-361, 2.24e-1867j
5.056159279655309861e-16 - 2.8283419063329548384e-5267j 4.3e-324, 2.78e-1830j
0.054422746664411508206 + 3.8011119675589931517e-5258j 1.68e-279, 1.09e-1785j
9.4044767257021717926e-33 + 5.6510729030437467564e-5277j 1.5e-340, 9.71e-1847j
5.8802067472361843219e-24 - 5.2441253736469695945e-5272j 1.33e-334, 8.61e-1841j
0.025743946823754640663 + 2.278479553421176328e-5258j 4.48e-289, 2.9e-1795j
1.4402773068692771332e-13 + 8.6802640623180410759e-5266j 3.73e-323, 2.41e-1829j
1.7218952764373077433e-96 - 2.8726867784326836366e-5310j 8.38e-373, 5.42e-1879j
7.6017143806779954577e-23 + 2.3256838519659645501e-5271j 2.15e-333, 1.39e-1839j
0.00031687060248325341659 - 1.3796688662661842922e-5259j 3.43e-308, 2.22e-1814j
0.10846975425009720103 + 5.871420568176256093e-5258j 1.25e-285, 8.11e-1792j
3.319215922558630277e-45 + 9.9928889913454849807e-5284j 3.84e-350, 2.48e-1856j
9.243291409261792136e-29 - 9.5100286515307409003e-5275j 5.93e-339, 3.83e-1845j
4.193220467958291818e-25 + 1.141797727023777974e-5272j 2.38e-336, 1.54e-1842j
0.010123850105226083088 + 1.0808576952909795394e-5258j 4.43e-304, 2.86e-1810j
0.00013062266979255548161 + 1.0560183861465375266e-5259j 2.99e-312, 1.94e-1818j
4.6589465683320944673e-06 + 1.3440890741196968308e-5260j 6.09e-316, 3.94e-1822j
0.072632766835918027085 - 4.6559887784379918628e-5258j 5.64e-297, 3.65e-1803j
1.2409500890850745035e-38 + 3.4274343318334695851e-5280j 9.14e-347, 5.91e-1853j
0.037224643299855525253 - 2.0016973678636174737e-5259j 1.05e-296, 6.8e-1803j
0.099787848157379632797 - 6.2323382400278286479e-5258j 1.21e-296, 7.82e-1803j
0.12030037232402029569 - 4.4361074735586939518e-5258j 1.98e-296, 1.28e-1802j
1.1553175293701421968e-67 - 1.6129882889580004477e-5295j 5.98e-362, 3.87e-1868j
1.1979110131071236585e-10 + 5.1398390675865564856e-5264j 4.04e-325, 2.61e-1831j
8.403371350818691453e-13 - 2.5134324109327425583e-5265j 1.97e-327, 1.27e-1833j
2.4226220675422988146e-11 - 1.9237779729584667014e-5264j 3.94e-326, 2.55e-1832j
0.0057925567030462424134 - 7.0094730732199277035e-5259j 3.19e-314, 2.06e-1820j
2.7541242192824181626e-26 - 2.3996600882395106825e-5273j 6.58e-339, 4.26e-1845j
0.11092605003010430749 - 1.5732451210914597522e-5258j 3.02e-307, 1.95e-1813j
1.5833540858399018924e-54 - 1.1539066243762282146e-5288j 6.76e-358, 4.37e-1864j
9.558117077732431355e-19 + 6.3146259219789733676e-5269j 2.2e-333, 1.42e-1839j
0.0015438399892327843486 - 2.9308335632504698177e-5259j 2.11e-319, 1.37e-1825j
0.00072176624004961490066 + 1.9606738253974748215e-5259j 5.09e-320, 3.29e-1826j
0.0030936227816271046771 + 4.5076816940299991604e-5259j 8.38e-319, 5.42e-1825j
6.4310968363082295147e-78 - 8.3053237784425703595e-5301j 2.02e-369, 1.31e-1875j
8.9040434395237957322e-49 + 1.2558077332569156752e-5285j 2.72e-355, 1.76e-1861j
4.0503016265236821164e-08 + 2.3486371588686550764e-5262j 7.2e-329, 4.65e-1835j
0.080606328977439349501 + 7.3499527381096843433e-5259j 1.46e-319, 9.42e-1826j
0.12405405233573245287 + 2.8093523657964259827e-5258j 2.25e-319, 1.46e-1825j
1.4797897953481238768e-56 + 9.916260632925966826e-5290j 2.49e-359, 1.61e-1865j
1.3058343669102900662e-35 + 1.516583166279258851e-5278j 1.83e-348, 1.18e-1854j
7.9191585252722306022e-42 + 6.4519503098393869699e-5282j 6.19e-352, 4.01e-1858j
1.6425229770103036498e-06 - 4.5614348915372479791e-5261j 4.15e-330, 2.68e-1836j

Download

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