Rule: Q[2, 4, 42]

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.

Warning: This rule has negative weights!

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)
161.78320328330557296 - 2.0496656047969276997e-1287j 8.86e-495, 8.86e-495j
108.7013160161133257 + 4.4694936772601959822e-1280j 1.34e-489, 1.34e-489j
135.44111701180808598 - 2.6860132830003306816e-1284j 5.64e-492, 5.64e-492j
147.06415359507894259 + 4.8320931656348097918e-1289j 3.53e-493, 3.53e-493j
76.933440550049229388 - 6.0040306648554243873e-1291j 8.07e-488, 8.07e-488j
125.4958477719035329 - 3.9354532880729845167e-1302j 4.94e-491, 4.94e-491j
30.054656955986684505 + 2.0255301529672114389e-1308j 2.59e-489, 2.59e-489j
8.1094477897617299182 - 8.8093416686952332513e-1339j 1.12e-495, 1.12e-495j
66.830074245272143873 - 3.6080587184657843049e-1330j 1.57e-487, 1.57e-487j
22.418068497200584694 + 4.5455897204997499675e-1349j 1.15e-490, 1.15e-490j
16.05853943054427416 + 1.9734831125084164714e-1357j 2.29e-492, 2.29e-492j
62.195129560263592945 - 9.9306298784433306891e-1353j 1.68e-487, 1.68e-487j
88.339753798357519694 - 3.632813871335185549e-1369j 2.65e-488, 2.65e-488j
3.4142135623730950488 + 6.1951945178926337239e-1415j 1.52e-499, 1.52e-499j
101.39084292977545746 - 2.030261989157073858e-1404j 4.67e-489, 4.67e-489j
82.456154512066209248 - 4.4031267586199929102e-1451j 5.62e-488, 5.62e-488j
9.4357136461012182542 + 2.9997374948967299194e-1489j 5.34e-495, 5.34e-495j
71.734681553817629621 - 7.3952004013464412558e-1494j 1.34e-487, 1.34e-487j
49.719220105326375841 + 1.4848722890041551701e-1540j 1.05e-487, 1.05e-487j
42.448928249232437453 + 3.1140548953005728914e-1601j 4.27e-488, 4.27e-488j
53.655694929705643254 + 1.6606793157724958027e-1653j 1.38e-487, 1.38e-487j
2.0790903892016382416 - 2.3687066985620928235e-1701j 1.54e-501, 1.54e-501j
57.809421105843262216 - 1.2389969975665150184e-1687j 1.57e-487, 1.57e-487j
94.631017601718014085 + 4.41677750502531898e-1696j 1.21e-488, 1.21e-488j
6.9239565457104964806 + 1.0211094884823864121e-1709j 2.4e-496, 2.4e-496j
18.042419232400390551 - 2.6308346260938067399e-1705j 9.02e-492, 9.02e-492j
14.207155093743340132 - 9.8785600446848265672e-1708j 5.65e-493, 5.65e-493j
32.904369338048589669 + 2.7509415034669137532e-1701j 6.36e-489, 6.36e-489j
0.47193845768537280597 - 9.1149616220397752866e-1726j 4.6e-504, 4.6e-504j
116.67827745964217466 - 3.8981055190731274237e-1709j 3.01e-490, 3.01e-490j
10.895795922494976825 - 2.3068545522316185312e-1720j 2.75e-494, 2.75e-494j
4.9885826185631556081 - 1.6932724538397888328e-1724j 8.29e-498, 8.29e-498j
27.360416715349626891 + 8.3331080546087318164e-1714j 9.39e-490, 9.39e-490j
5.8874090971161450302 + 2.5807502316483104885e-1740j 4.57e-497, 4.57e-497j
35.915429956660941101 - 1.3204182967470923352e-1731j 1.28e-488, 1.28e-488j
24.816429702400615233 - 2.1026584353476698766e-1746j 3.59e-490, 3.59e-490j
0.5857864376269049512 + 9.7665943181739848076e-1771j 1.89e-504, 1.89e-504j
0.15730983836210817337 - 1.9534641286917476181e-1774j 4.99e-508, 4.99e-508j
12.486507079040894342 + 1.1105670330275173915e-1759j 1.3e-493, 1.3e-493j
45.987304689614067973 + 2.3291571050293918447e-1753j 6.64e-488, 6.64e-488j
0.029583613195307343593 - 3.6882182374874092055e-1809j 4.72e-510, 4.72e-510j
2.7103311436011202222 + 1.9919534924192265475e-1777j 1.78e-500, 1.78e-500j
1.0406748406401594478 - 1.0287973989601782287e-1781j 9.28e-504, 9.28e-504j
0.45916707187927690119 + 1.8362202545881593239e-1781j 3.73e-504, 3.73e-504j
20.161251485168403787 + 2.1332029588548997384e-1768j 3.16e-491, 3.16e-491j
1.5233530710972028038 + 8.7383520529181443469e-1780j 1.15e-502, 1.15e-502j
39.094458497931252193 - 4.2089479488087607963e-1765j 2.48e-488, 2.48e-488j
4.1765568050087063468 - 9.991774713748947224e-1783j 1.27e-498, 1.27e-498j

Weights

Weight (ball center) Error (ball radius)
9.5477663326376056212e-70 - 6.4769026040326505915e-1340j 8.37e-74, 8.74e-443j
4.7164105622630584521e-47 - 1.1037020400997931228e-1326j 2.84e-66, 2.97e-435j
1.6079160463803937988e-58 - 8.2957022969719796309e-1334j 1.16e-70, 1.21e-439j
1.7285417468763215517e-63 + 1.5370538769371228739e-1336j 2.23e-72, 2.33e-441j
2.0749654023307520912e-33 + 1.0728281976797306273e-1320j 6.54e-62, 6.83e-431j
2.9324988855661994316e-54 + 2.1670529960895461499e-1331j 1.43e-69, 1.49e-438j
2.4551235749386067401e-13 + 5.7056396470687339489e-1310j 4.72e-47, 4.94e-416j
0.00037807659353450204567 - 9.5777670036060893049e-1304j 4.23e-25, 4.42e-394j
4.5105316443114220801e-29 + 1.7290049307042863842e-1318j 4.73e-60, 4.95e-429j
4.273110449512424225e-10 - 4.9112882556796222133e-1308j 4.75e-43, 4.97e-412j
2.0349293573237613436e-07 + 2.6337730029712854886e-1306j 5.61e-38, 5.86e-407j
4.394468667443028075e-27 - 1.8532868797053858668e-1317j 3.01e-59, 3.14e-428j
2.6202243879951731454e-38 + 4.1584291146482963757e-1323j 2.22e-65, 2.32e-434j
0.024226779753986914789 + 4.9159255813933445044e-1302j 1.87e-19, 1.95e-388j
6.4983691248661053941e-44 + 1.2796331527594160398e-1325j 6.61e-68, 6.91e-437j
8.8173745214784067797e-36 - 7.0696979898810074467e-1322j 3.32e-64, 3.47e-433j
0.00011127026310142729714 + 3.1154860561671160615e-1304j 1.55e-36, 1.62e-405j
3.5405835525007307745e-31 - 1.4434055682453314561e-1319j 3.14e-62, 3.28e-431j
9.7874284802301333281e-22 + 1.2416094906956409403e-1314j 1.33e-59, 1.39e-428j
1.2642821995852033012e-18 + 6.0442355639151542636e-1313j 2.3e-58, 2.41e-427j
2.0151768269146864875e-23 - 1.5615763667757692121e-1315j 1.63e-60, 1.71e-429j
0.074186944164109720416 + 1.1025100886780551897e-1301j 1.24e-27, 1.3e-396j
3.3405441616393990475e-25 + 1.7879436690226023428e-1316j 3.02e-61, 3.16e-430j
5.2013286658287866661e-41 - 2.2459170860319653055e-1324j 5.49e-69, 5.74e-438j
0.0010940554603494549873 + 2.8178305912608634906e-1303j 9.7e-42, 1.01e-410j
2.993784495825186569e-08 - 7.3130585271265525402e-1307j 2.51e-51, 2.63e-420j
1.2070953135599819813e-06 - 9.112719342394821503e-1306j 3.32e-49, 3.47e-418j
1.5017062831254877559e-14 - 1.1432035323625033168e-1310j 8e-58, 8.36e-427j
-3.1353570331421811564 + 1.6971839801955374303e-1299j 1.87e-36, 1.96e-405j
1.7764398649287161936e-50 - 4.2780261643894082177e-1329j 9.73e-75, 1.02e-443j
2.8279939399153380246e-05 - 9.8660011654326626111e-1305j 2.79e-48, 2.92e-417j
0.0057598324643225603156 + 1.6682299023532545384e-1302j 7.32e-44, 7.65e-413j
3.4319469611343743128e-12 - 2.6719344437640516741e-1309j 1.87e-56, 1.96e-425j
0.0026696046819802917617 - 7.5059460234780627293e-1303j 2.16e-45, 2.26e-414j
7.8096148241831049546e-16 + 2.1413305953322809756e-1311j 2.9e-59, 3.03e-428j
4.122280187850974794e-11 + 1.1783188310912798985e-1308j 4.41e-56, 4.61e-425j
0.46030264444978724558 - 2.0796646743981710925e-1300j 1.32e-43, 1.38e-412j
0.15497965897804344415 + 1.1699921593207701909e-1301j 3.76e-44, 3.93e-413j
6.2538364960446485305e-06 + 3.0439588972326299258e-1305j 1.45e-51, 1.52e-420j
3.8751142378107071571e-20 - 9.0339465935697443354e-1314j 5.8e-62, 6.06e-431j
0.073809801809771189975 - 2.4230211035050160334e-1302j 6.34e-45, 6.63e-414j
0.044491150589190703501 - 7.470618350337759923e-1302j 8.11e-48, 8.47e-417j
0.15834635436925540769 + 2.6553050128577663345e-1301j 2.1e-46, 2.19e-415j
3.0098590415113707399 - 1.5153436378892886488e-1299j 9.21e-44, 9.62e-413j
3.8369225907142282344e-09 + 1.9419694123825973565e-1307j 2.68e-55, 2.8e-424j
0.11304261148438319649 - 1.6250108751746892078e-1301j 7.58e-48, 7.91e-417j
3.4310911638936087452e-17 - 3.7353637173688931787e-1312j 1.81e-60, 1.89e-429j
0.012063227957855178383 - 3.0513927999469173248e-1302j 1.65e-49, 1.72e-418j

Download

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