Rule: Q[3, 74]

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)
279.66604129982717147 - 9.775892362518799472e-4422j 7.86e-2018, 7.86e-2018j
1.3586791660022804183 - 1.0239092134836563721e-4441j 3.32e-2033, 3.32e-2033j
0.41577455678347908331 - 5.585775394237544649e-4445j 3.21e-2037, 3.21e-2037j
0.98298319861696953998 - 3.9152392854303846267e-4443j 1.72e-2034, 1.72e-2034j
1.7959357395233436295 - 3.3416543991654351913e-4440j 6.8e-2032, 6.8e-2032j
0.66880707242043273078 - 1.3443122722474690006e-4443j 7.35e-2036, 7.35e-2036j
0.090651362043131795161 + 1.2994094949404318144e-4448j 4.97e-2040, 4.97e-2040j
0.01718158231959721291 - 3.8832539007425025638e-4449j 1.17e-2041, 1.17e-2041j
0.22328943114171599477 - 5.6814698237729905543e-4446j 1.38e-2038, 1.38e-2038j
247.6088042391908647 - 3.5914436011616040955e-4413j 3.03e-2014, 3.03e-2014j
261.84466710288313447 - 1.4476745370462298718e-4418j 8.14e-2016, 8.14e-2016j
235.29672778872973581 - 8.3184862443586292376e-4413j 6.15e-2013, 6.15e-2013j
21.424245922798000986 - 2.0345527017552011048e-4425j 1.06e-2014, 1.06e-2014j
50.522728852755725053 - 1.156803238351703846e-4414j 1.73e-2007, 1.73e-2007j
100.05547777767349053 - 4.473323318219599269e-4446j 1.74e-2004, 1.74e-2004j
83.571912701214398145 + 9.5602237026572098814e-4528j 8.2e-2005, 8.2e-2005j
79.771074082016791013 - 6.0594634040614416055e-4621j 5.68e-2005, 5.68e-2005j
28.907413871571355865 + 6.704740929944994881e-4664j 4.11e-2012, 4.11e-2012j
40.058670980372873497 - 1.1093268575900771928e-4711j 2.42e-2009, 2.42e-2009j
146.40396686356659643 + 4.3816915895077788498e-4823j 9.96e-2006, 9.96e-2006j
129.27175842912077828 - 2.3348527967046874065e-4912j 5.72e-2005, 5.72e-2005j
35.35003833295127025 + 1.6815896788530036808e-4951j 2.44e-2010, 2.44e-2010j
19.744428795030907058 - 1.0904688814376388102e-4956j 2.21e-2015, 2.21e-2015j
18.139381946973378756 + 3.0857185429282022031e-4957j 4.09e-2016, 4.09e-2016j
69.068566500701975688 + 3.1008549598830190984e-4945j 1.43e-2005, 1.43e-2005j
42.541348711102197543 - 7.9920329138205138781e-4959j 7.78e-2009, 7.78e-2009j
25.011246227440838653 - 2.5207473015322721019e-4964j 2.31e-2013, 2.31e-2013j
5.5542910721234595204 - 4.1518596378687641566e-4976j 5e-2025, 5e-2025j
56.307026334044537358 - 1.1617476696754719742e-4954j 8.4e-2007, 8.4e-2007j
59.344568434099351771 + 2.7908227725578195824e-4978j 1.98e-2006, 1.98e-2006j
16.608482295184912341 + 1.9012544496866739209e-5029j 7.2e-2017, 7.2e-2017j
53.367170374310755674 - 3.6291668284438721236e-5045j 3.92e-2007, 3.92e-2007j
13.76744358853804326 + 3.4139416762778536369e-5103j 1.91e-2018, 1.91e-2018j
159.00708118768459653 - 1.8479903673525790956e-5167j 1.87e-2006, 1.87e-2006j
10.060338459114020071 + 7.5504141451592310941e-5244j 6.97e-2021, 6.97e-2021j
30.974002822620515135 - 1.3819073975260728704e-5237j 1.77e-2011, 1.77e-2011j
165.72418231075398999 + 7.3602405887192021976e-5292j 7.09e-2007, 7.09e-2007j
47.771579699237886972 - 1.9000240037139652896e-5370j 6.42e-2008, 6.42e-2008j
224.2660790879065845 + 1.3922194251819605753e-5483j 8.48e-2012, 8.48e-2012j
172.75458893111175624 - 5.9679934100100509179e-5588j 2.33e-2007, 2.33e-2007j
45.111738639566249994 - 9.815971329382217516e-5651j 2.5e-2008, 2.5e-2008j
6.2899450829374791969 + 8.7031807645843959604e-5696j 3.68e-2024, 3.68e-2024j
118.85566578037286434 - 5.3390493588790392959e-5707j 1.16e-2004, 1.16e-2004j
4.1322768424515584171 + 9.1560811190341098902e-5780j 3.59e-2027, 3.59e-2027j
87.496054827249274714 - 1.3838480783311240327e-5755j 1.21e-2004, 1.21e-2004j
65.722628019690356857 - 2.2375967300356972651e-5804j 7.8e-2006, 7.8e-2006j
152.57491013598139514 - 4.7427155599668628104e-5863j 4.85e-2006, 4.85e-2006j
91.54800683635148679 - 1.7350591506566143479e-5907j 1.37e-2004, 1.37e-2004j
196.11498592266502053 - 8.2081159855227811009e-5932j 3.2e-2009, 3.2e-2009j
3.4671805047402270705 + 2.4913570963928128197e-5966j 2.45e-2028, 2.45e-2028j
62.482231381049285959 - 1.8439465212401122984e-5942j 4.18e-2006, 4.18e-2006j
214.18248754367664161 - 8.301991962430822579e-5964j 7.57e-2011, 7.57e-2011j
180.132802582445168 - 7.1843267684388728362e-6005j 6.44e-2008, 6.44e-2008j
204.84359037218558339 - 4.9958761993317886213e-6042j 5.62e-2010, 5.62e-2010j
8.9790977475229542798 + 3.1574755499492942185e-6105j 9.84e-2022, 9.84e-2022j
7.0872867663984547197 - 3.3716635792629221563e-6104j 2.65e-2023, 2.65e-2023j
95.732686641764777813 + 1.9015579823019544433e-6086j 1.53e-2004, 1.53e-2004j
123.97130608687825177 + 2.4878095376546346615e-6123j 8.17e-2005, 8.17e-2005j
12.457107510846389235 - 3.7289291110166193544e-6165j 3.02e-2019, 3.02e-2019j
11.220864475379353708 + 9.1527895524706672255e-6167j 4.24e-2020, 4.24e-2020j
109.13965184103284029 + 3.7565302711578389652e-6149j 1.61e-2004, 1.61e-2004j
76.089398073453386645 + 1.4153740583840840644e-6165j 4.54e-2005, 4.54e-2005j
113.9147686620305127 - 3.0552102420370095464e-6177j 1.41e-2004, 1.41e-2004j
187.90155739332875306 - 1.7496724820892655258e-6201j 1.47e-2008, 1.47e-2008j
2.2942803602790417198 - 4.8935367453313255173e-6268j 1.19e-2030, 1.19e-2030j
23.179572726698391954 + 1.7082713444619712671e-6252j 4.99e-2014, 4.99e-2014j
104.52229330580662006 + 9.1913651541153887788e-6241j 1.79e-2004, 1.79e-2004j
33.121126845026613234 + 1.763374010660219363e-6288j 6.34e-2011, 6.34e-2011j
134.768402930039518 - 1.3648598215809783211e-6296j 3.53e-2005, 3.53e-2005j
2.8523669754318921433 + 3.4870623029896176613e-6372j 1.65e-2029, 1.65e-2029j
72.523069811974696193 + 7.9106551763485841012e-6345j 2.4e-2005, 2.4e-2005j
26.920190937559783788 + 4.3307806876874564195e-6381j 1.02e-2012, 1.02e-2012j
140.47418939621141589 + 3.7344643365193705885e-6395j 2.01e-2005, 2.01e-2005j
7.9843194650782570882 - 2.3953141092013462206e-6441j 1.59e-2022, 1.59e-2022j
15.151256754175363794 + 3.433870590021790041e-6435j 1.22e-2017, 1.22e-2017j
37.662076344979788273 + 1.4757327227958143247e-6427j 7.87e-2010, 7.87e-2010j
4.8345667673328607899 - 4.3769327228736181141e-6445j 4.38e-2026, 4.38e-2026j

Weights

Weight (ball center) Error (ball radius)
7.3203979974897607656e-121 + 1.2732832753790291174e-4488j 4.41e-377, 1.19e-1883j
0.10447164302467135232 - 8.5517479537707135948e-4427j 5.44e-204, 1.46e-1710j
0.14690864296685146674 + 5.6478549991455287682e-4427j 2.25e-199, 6.03e-1706j
0.1290580909021492517 + 8.0102091039190221393e-4427j 1.85e-200, 4.97e-1707j
0.077664211142922122899 + 8.7101828492941333953e-4427j 3.12e-213, 8.39e-1720j
0.14525265452109155409 - 7.0364345461924792996e-4427j 1.3e-199, 3.49e-1706j
0.094025332330090884674 + 2.1750244410469431572e-4427j 3.66e-200, 9.83e-1707j
0.043356509119756325277 - 6.492488701174155906e-4428j 1.99e-200, 5.34e-1707j
0.12993527998632190664 - 3.9543176816072114658e-4427j 1.96e-200, 5.26e-1707j
3.8276547359347398899e-107 + 1.2120653262221361966e-4481j 2e-373, 5.37e-1880j
2.9845602802413205165e-113 - 9.42805832141498778e-4485j 2.72e-375, 7.3e-1882j
7.5223938749702395722e-102 - 6.0380367270468405635e-4479j 3.3e-372, 8.88e-1879j
8.5202007613602406859e-10 - 5.8461767259655439749e-4431j 6.89e-300, 1.85e-1806j
3.19904630865347865e-22 + 1.9322587788741385989e-4436j 9.32e-327, 2.5e-1833j
1.5463060251760453897e-43 - 7.8371766411954809734e-4449j 3.79e-348, 1.02e-1854j
1.9586913671359107579e-36 - 5.0608565595224975083e-4445j 8.12e-343, 2.18e-1849j
8.4879627229635034806e-35 + 3.9566035030657351237e-4444j 1.7e-341, 4.57e-1848j
5.6553954293310517866e-13 - 1.3814399715738020151e-4432j 3.88e-313, 1.04e-1819j
9.7727892246675367612e-18 + 8.0456533304839633755e-4435j 1.65e-322, 4.44e-1829j
1.58170340038488355e-63 + 2.7499526446188096406e-4459j 6.54e-362, 1.76e-1868j
3.8913768441628873032e-56 - 1.8902026517803242252e-4455j 6.55e-358, 1.76e-1864j
1.0086627486237547169e-15 + 6.5230364706881084847e-4434j 4.16e-320, 1.12e-1826j
4.3707974659403240454e-09 + 1.3989761108044829267e-4430j 3.2e-305, 8.61e-1812j
2.0772054704980293316e-08 - 3.2658079367943839124e-4430j 1.66e-303, 4.47e-1810j
3.4303864480300680086e-30 - 1.4650172502387835089e-4441j 5.81e-340, 1.56e-1846j
8.4528646669048071267e-19 - 2.8950205158719320627e-4435j 5.07e-326, 1.36e-1832j
2.5682054600426908655e-11 - 9.4570882468652215216e-4432j 7.81e-313, 2.1e-1819j
0.0028019996563520790514 + 5.9746183214273971133e-4427j 5.45e-280, 1.46e-1786j
1.0509799402291632243e-24 - 3.2508216531484826627e-4438j 1.19e-334, 3.19e-1841j
5.2064738576365306305e-26 + 4.4773312667955369505e-4439j 1.78e-336, 4.79e-1843j
9.1490920931691217573e-08 + 7.4435331241356961763e-4430j 1.46e-306, 3.91e-1813j
1.9235261449111576726e-23 + 3.001251467894164095e-4437j 3.41e-333, 9.18e-1840j
1.4134546893960022229e-06 + 3.6220542329885201478e-4429j 4.52e-304, 1.22e-1810j
5.7768310506408282983e-69 + 4.2640972087042100974e-4462j 2.12e-369, 5.69e-1876j
4.7943712999362319386e-05 - 3.4270162432353590925e-4428j 2.28e-300, 6.12e-1807j
7.4431173645393444381e-14 + 5.093350873635314744e-4433j 6.92e-322, 1.86e-1828j
7.3074948462937125154e-72 - 1.3683702961218432175e-4463j 3.99e-371, 1.07e-1877j
4.8446450501084261071e-21 - 5.5741535163143833483e-4436j 5.26e-333, 1.41e-1839j
4.2102566514208966142e-97 + 1.5956774608714177096e-4476j 7.63e-382, 2.05e-1888j
6.7739909084440309109e-75 + 3.7617677464897708128e-4465j 5.16e-373, 1.39e-1879j
6.6936345023225448434e-20 + 1.123945475057534645e-4435j 6.68e-333, 1.8e-1839j
0.0014032887375619740251 - 4.458717858103742255e-4427j 6.99e-301, 1.88e-1807j
1.2103813139539842218e-51 - 4.1941159473529252815e-4453j 2.14e-362, 5.76e-1869j
0.011017624968429157556 + 7.3880355765188835884e-4427j 2.69e-296, 7.23e-1803j
3.9959599147019958176e-38 + 6.1528712454771645263e-4446j 8.3e-353, 2.23e-1859j
9.4313779144138261941e-29 + 9.8919128506368804951e-4441j 1.02e-344, 2.74e-1851j
3.4415724001584553385e-66 - 1.1546935961949410303e-4460j 1.96e-369, 5.27e-1876j
7.1752184515894511023e-40 - 7.0814738846817394991e-4447j 1.08e-354, 2.89e-1861j
5.6962514147884619889e-85 - 2.5415994591640483835e-4470j 1.46e-379, 3.91e-1886j
0.020016485205103186035 - 7.8319599187548920579e-4427j 1.68e-304, 4.5e-1811j
2.3329682497032280053e-27 - 6.6073069445891811556e-4440j 4.07e-345, 1.1e-1851j
9.2854785377018275375e-93 - 2.6371194914630787793e-4474j 9.22e-383, 2.48e-1889j
4.4479284632708720867e-78 - 8.7070769167462927097e-4467j 6.41e-377, 1.72e-1883j
9.8296410496815314951e-89 + 3.0121308050246789977e-4472j 2.46e-381, 6.62e-1888j
0.00013100758303128264973 + 7.0794729392421897519e-4428j 3.79e-324, 1.02e-1830j
0.00070615242036853929216 + 2.7233498985027361583e-4427j 2.89e-321, 7.77e-1828j
1.128488260363548134e-41 + 7.6859288307541548705e-4448j 1.48e-359, 3.97e-1866j
7.5244065001139765674e-54 + 2.943936070974892657e-4454j 3.38e-367, 9.08e-1874j
4.953710987554912634e-06 - 7.7675554466317828595e-4429j 1.71e-330, 4.59e-1837j
1.605380737524065508e-05 + 1.6411447457744823778e-4428j 2.11e-329, 5.66e-1836j
1.8744957016544479438e-47 - 6.653784179476397811e-4451j 1.54e-364, 4.13e-1871j
3.2651983783827837616e-33 - 2.9534212813069521956e-4443j 5.07e-356, 1.36e-1862j
1.6359747056038291809e-49 + 5.4951558106008946499e-4452j 1.11e-365, 2.99e-1872j
1.9835491935616688425e-81 + 1.6609494338281898252e-4468j 3.61e-381, 9.69e-1888j
0.053294920657917755834 - 8.5741740709057358556e-4427j 4.88e-327, 1.31e-1833j
1.5378192230927863186e-10 + 2.3822807498193716696e-4431j 6.89e-343, 1.85e-1849j
1.8352325595781199288e-45 + 7.479223600010279667e-4450j 1.08e-363, 2.91e-1870j
9.0299506725203548063e-15 - 1.8385570214028472096e-4433j 2.37e-347, 6.36e-1854j
1.6555025708758893385e-58 + 1.1035238418020402773e-4456j 2.55e-371, 6.86e-1878j
0.033883365642925702282 + 8.2483204831951615444e-4427j 4.3e-335, 1.16e-1841j
1.119230937703915455e-31 + 2.1160691636046640256e-4442j 2.2e-357, 5.92e-1864j
3.9653209236708241724e-12 + 3.6596963405024834401e-4432j 4.46e-347, 1.2e-1853j
5.7199743685469085332e-61 - 5.818712041664615115e-4458j 1.31e-372, 3.52e-1879j
0.00032301801686901955082 - 1.4328198772054492162e-4427j 1.05e-341, 2.82e-1848j
3.7353678050631822489e-07 - 1.6588935059538247548e-4429j 2.51e-344, 6.73e-1851j
1.0360661008338448531e-16 - 2.2897378978503315246e-4434j 5.33e-350, 1.43e-1856j
0.0056789172248817789532 - 6.8646533542551961015e-4427j 3.53e-341, 9.46e-1848j

Download

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