Rule: Q[2, 5, 38]

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)
148.13471866958453225 + 1.6656168803457163671e-1301j 8.39e-496, 8.39e-496j
96.84684910662741867 - 5.867622720775474714e-1296j 7.52e-491, 7.52e-491j
113.01022242031376908 - 2.2387880786466507725e-1298j 3.13e-492, 3.13e-492j
122.61259405690427255 + 1.1600128798753510647e-1299j 4.29e-493, 4.29e-493j
133.85938601907734047 - 1.3627899064231595977e-1301j 2.98e-494, 2.98e-494j
13.090128715432888258 + 2.4531710176754976628e-1301j 1.51e-493, 1.51e-493j
83.36706678953584378 - 1.0958469991923766539e-1295j 5.7e-490, 5.7e-490j
37.507495288730359772 + 1.7197933162165005781e-1308j 1.05e-489, 1.05e-489j
77.362116123281384117 + 3.6089201045278015073e-1330j 1.14e-489, 1.14e-489j
18.426547563031984013 + 1.7757779527756497546e-1341j 3.2e-492, 3.2e-492j
40.960955029299548689 + 4.2295720705459749188e-1353j 1.81e-489, 1.81e-489j
3.4142135623730950488 - 6.5851455738614847889e-1379j 1.62e-499, 1.62e-499j
89.835234564437777537 + 1.163430536145395218e-1367j 2.2e-490, 2.2e-490j
25.568678025623184941 + 1.1427707473310196556e-1373j 6.16e-491, 6.16e-491j
31.178735314531446029 + 2.5924274120508124002e-1377j 3.07e-490, 3.07e-490j
11.699795418574124174 - 4.5797470972923276849e-1401j 3.98e-494, 3.98e-494j
6.196205771340291157 - 2.7516088780638671046e-1407j 1.65e-497, 1.65e-497j
104.51512823980165428 - 2.1009302671905122514e-1399j 1.83e-491, 1.83e-491j
8.8190918864090684438 + 4.8311594817208473673e-1431j 9.02e-496, 9.02e-496j
3.0113670301765209434 - 7.3851961944763219401e-1436j 3.99e-500, 3.99e-500j
4.0490489062447359409 - 3.2289729651005255408e-1432j 4.43e-499, 4.43e-499j
2.2716167028849493242 - 1.4179029211800463623e-1439j 1.43e-501, 1.43e-501j
0.11237331364323042761 + 9.0833530553626808998e-1442j 1.41e-508, 1.41e-508j
28.287064251073047932 + 1.3477983606494143927e-1445j 1.39e-490, 1.39e-490j
48.498296081623185584 - 4.1305762000848695496e-1480j 3.44e-489, 3.44e-489j
61.596339740592072302 + 5.6664320112670095542e-1526j 3.43e-489, 3.43e-489j
1.6054525833172712334 + 5.5580843316288540676e-1564j 5.43e-503, 5.43e-503j
14.608974312888737872 - 1.4265362494135820214e-1550j 3.83e-493, 3.83e-493j
16.402635230020449078 + 2.9239025232148312569e-1550j 1.07e-492, 1.07e-492j
71.760870936946891207 - 2.660673236979164897e-1573j 1.89e-489, 1.89e-489j
56.967923906431481876 + 1.7860704996766562046e-1614j 3.88e-489, 3.88e-489j
5.0546157316191983091 - 4.1326254985653838079e-1650j 2.44e-498, 2.44e-498j
0.5857864376269049512 - 9.8677304608192853066e-1657j 3.12e-505, 3.12e-505j
20.637391997130662648 + 4.0149737128076000735e-1640j 8.47e-492, 8.47e-492j
10.257801186785141083 - 9.0039248850698645711e-1653j 6.53e-495, 6.53e-495j
66.517631301903169851 + 1.4470856892246062534e-1661j 2.77e-489, 2.77e-489j
23.019313191028729717 + 1.6880161070849387126e-1686j 2.54e-491, 2.54e-491j
0.40758826003091409011 + 7.1057528493830421782e-1734j 2.09e-505, 2.09e-505j
44.620507024450506777 + 1.4738197212044843135e-1716j 2.59e-489, 2.59e-489j
34.249718949104166041 + 2.1506891744758150564e-1753j 6.16e-490, 6.16e-490j
0.015311120651975619629 - 7.7880245565226969887e-1805j 1.89e-510, 1.89e-510j
52.608528281902329199 - 5.6794695570403635786e-1777j 3.68e-489, 3.68e-489j
1.0487368785708240897 - 1.2339437670147529639e-1803j 3.09e-504, 3.09e-504j
0.36658876878467436123 + 1.4763227955440824703e-1804j 1.17e-505, 1.17e-505j
7.4553298819050324224 - 1.1178597997712854848e-1795j 1.15e-496, 1.15e-496j

Weights

Weight (ball center) Error (ball radius)
7.8446323160075872892e-64 - 8.1648928038604498846e-1342j 2.17e-80, 3.09e-450j
6.3724456850461937939e-42 + 4.5308944153483222135e-1330j 8.89e-73, 1.26e-442j
7.4809825943089400219e-49 + 7.9706354436373229017e-1334j 1.04e-75, 1.47e-445j
5.7921590593044283904e-53 - 4.9473079585080485095e-1336j 1.99e-77, 2.82e-447j
9.0910125374062316089e-58 + 1.3492771338967816002e-1338j 2.68e-79, 3.81e-449j
2.9077894717876017795e-06 - 5.3425220879002997937e-1307j 4.48e-43, 6.38e-413j
3.8752233975634945073e-36 + 6.8116406384958282371e-1327j 2.78e-72, 3.96e-442j
1.7229267070492138836e-16 + 1.9481222711207199827e-1315j 1.79e-61, 2.54e-431j
1.4624332464649310896e-33 - 1.8429360937425654632e-1325j 1.19e-71, 1.7e-441j
2.1092589675022084778e-08 - 1.8840886388357825701e-1309j 1.2e-51, 1.71e-421j
5.7766800761351692637e-18 - 2.2803589650592714511e-1316j 3.83e-63, 5.45e-433j
0.0089416473560304093379 - 1.8720854344492264653e-1304j 1.27e-29, 1.81e-399j
6.4968217435971610382e-39 - 2.0080937625065572438e-1328j 1.37e-73, 1.95e-443j
2.07095916660192892e-11 + 5.7308636980848737508e-1312j 2.34e-57, 3.33e-427j
8.580098791870820455e-14 + 1.163490806368127599e-1313j 5.82e-60, 8.29e-430j
1.1705051159340444467e-05 + 1.2274733747567466469e-1306j 5.98e-48, 8.51e-418j
0.0024487227211185023033 + 7.225421156393745574e-1306j 1.71e-41, 2.44e-411j
3.2754791311079663563e-45 - 7.3836335217905483957e-1332j 6.6e-77, 9.39e-447j
0.00020832992548090375875 + 1.8658874786712704016e-1306j 1.63e-45, 2.31e-415j
0.034510596139617335935 + 1.9881049345241558101e-1304j 2.02e-34, 2.88e-404j
0.015953893208538453696 + 6.8834307184389472089e-1305j 1.67e-37, 2.38e-407j
0.074000143628803023098 - 1.3026193538852613029e-1304j 1.05e-32, 1.5e-402j
0.1387024501001954495 - 2.2147334761612626705e-1304j 1.04e-32, 1.48e-402j
1.4550769927695884651e-12 - 8.3103925019209312112e-1313j 2.52e-59, 3.58e-429j
3.4561169406403031704e-21 - 2.436112105057244437e-1318j 8.44e-68, 1.2e-437j
8.4647206643383581289e-27 + 1.2415663716539679207e-1321j 1.52e-71, 2.17e-441j
0.12291293397865861533 + 1.4683659114593380742e-1304j 2.07e-36, 2.94e-406j
7.490813706901469764e-07 - 1.422301445384176229e-1307j 6.63e-54, 9.43e-424j
1.4438948934472497408e-07 + 1.4776960239417085957e-1308j 2.82e-55, 4.01e-425j
3.7007630396893968713e-31 + 4.1026996423685963588e-1324j 1.17e-73, 1.67e-443j
8.1549262443226161593e-25 - 1.7486950914686570198e-1320j 4.1e-71, 5.84e-441j
0.0068843001879132570385 - 1.8681078127885492026e-1305j 2.02e-49, 2.87e-419j
0.26885156749601512746 + 9.6113440150494895811e-1304j 1.62e-44, 2.3e-414j
2.5036792123174824256e-09 + 2.6481636772355406646e-1310j 8e-60, 1.14e-429j
5.1108376731558570732e-05 - 1.2767553616735786768e-1306j 2.01e-54, 2.86e-424j
6.5668808064844513342e-29 - 7.6986163094563878487e-1323j 3.96e-73, 5.64e-443j
2.4818594054385071207e-10 - 3.8829114605425943288e-1311j 2.37e-61, 3.37e-431j
-0.47582954498286171548 - 4.103838239674845581e-1303j 2.13e-50, 3.03e-420j
1.5757834520416206392e-19 + 2.464577261233495399e-1317j 1.08e-68, 1.53e-438j
4.223160841703484174e-15 - 1.5514498860357742901e-1314j 5.71e-66, 8.12e-436j
0.044593491350675255226 + 6.3842885644403365234e-1305j 5.78e-54, 8.26e-424j
6.0107763290816254867e-23 + 2.1805572095443123026e-1319j 1.03e-70, 1.46e-440j
0.17592750287559279364 - 2.3243785890011688451e-1304j 3.26e-55, 4.72e-425j
0.58106719515686628806 + 3.4494412455735252631e-1303j 7.37e-54, 1.1e-423j
0.00076013230242388068855 - 3.377589509268408828e-1306j 5.28e-58, 7.35e-428j

Download

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