Rule: Q[5, 9, 39]

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)
140.45561297530206152 - 2.0568882462028218934e-1488j 3.35e-491, 3.35e-491j
167.0803899211161265 - 1.3492579500489730495e-1491j 4.42e-494, 4.42e-494j
121.46089105033294844 + 2.5610887168097589774e-1485j 2.18e-489, 2.18e-489j
130.39111883606317278 - 2.4324706602822944099e-1487j 3.35e-490, 3.35e-490j
152.20878820525735319 + 7.9563067231980213456e-1490j 2.05e-492, 2.05e-492j
8.2513526447863045039 + 3.0482603787868132602e-1491j 2.02e-493, 2.02e-493j
14.753354900255584282 - 5.1814099006406125853e-1487j 1.45e-489, 1.45e-489j
113.37561476393802014 - 2.4830602736771693403e-1483j 1.06e-488, 1.06e-488j
53.284804187059154585 - 3.7103507145502110441e-1488j 3.81e-486, 3.81e-486j
32.997525255688913646 - 1.2638705126618214967e-1496j 4.78e-487, 4.78e-487j
92.703926923082087706 - 9.1086827980754239807e-1502j 3.12e-487, 3.12e-487j
20.848284513111669175 + 6.4819084034915910848e-1514j 2.7e-487, 2.7e-487j
6.0614672980381884113 + 2.5157689738419491694e-1523j 3.19e-495, 3.19e-495j
27.532442987125322624 + 5.3267727553093819816e-1515j 1.96e-487, 1.96e-487j
2.3106347772255290763 - 1.5189691686569716671e-1527j 5.15e-500, 5.15e-500j
10.84374838722421369 - 6.7521373393787040556e-1520j 3.17e-491, 3.17e-491j
5.1777382646558372785 + 6.5026918434024568439e-1524j 3.97e-496, 3.97e-496j
1.8448022073844265402 + 1.4088621133026007784e-1528j 5.69e-501, 5.69e-501j
105.95983880809281759 - 8.3542966113413891314e-1514j 3.89e-488, 3.89e-488j
22.466610903822969323 - 7.2551081625453836239e-1526j 2.42e-487, 2.42e-487j
21.376453006750519738 - 1.1480384028057031085e-1528j 4.34e-487, 4.34e-487j
9.5251579906401413862 + 3.3091137853263262613e-1538j 2.14e-492, 2.14e-492j
45.81154949658495589 + 2.847003827160284339e-1531j 2.57e-486, 2.57e-486j
75.798852576075223446 + 8.6279505751070612914e-1569j 1.82e-486, 1.82e-486j
57.321709763592160754 - 7.7187125534812841561e-1617j 3.94e-486, 3.94e-486j
18.498132851110645756 - 9.4333409370536781703e-1646j 1.28e-488, 1.28e-488j
2.8933927053859570824 - 7.1488250899940195256e-1669j 4.35e-499, 4.35e-499j
7.0858100058588375569 + 7.2021477870965729143e-1669j 2.26e-494, 2.26e-494j
49.451806251030390576 + 9.8657920296087413508e-1669j 3.29e-486, 3.29e-486j
12.126437582454868669 + 1.8062619894173612706e-1700j 6.98e-490, 6.98e-490j
12.640800844275782659 + 1.305430565463513238e-1699j 2.13e-489, 2.13e-489j
13.163488878500400561 - 2.1491022430351085368e-1698j 1.91e-489, 1.91e-489j
1.4134030591065167922 - 6.7351327784734513882e-1711j 6.88e-502, 6.88e-502j
25.000830931607806788 - 2.0074495520545483249e-1718j 1.43e-487, 1.43e-487j
70.794921411657588837 - 1.0766348931431202094e-1775j 2.76e-486, 2.76e-486j
61.575357048374453948 + 2.6139129799958446767e-1820j 4.1e-486, 4.1e-486j
30.192803517488057918 + 2.4016187853420345136e-1837j 3.04e-487, 3.04e-487j
0.50570345274909796347 - 3.9096954818375150114e-1868j 2.24e-505, 2.24e-505j
0.016164262968590236822 + 5.9880459959644457695e-1885j 3.76e-510, 3.76e-510j
86.719726672671132166 - 3.3913093939548409427e-1849j 6.48e-487, 6.48e-487j
3.5964257710407220812 - 3.3784488035705947408e-1887j 4.51e-498, 4.51e-498j
16.533343203504277175 + 4.903313978263947874e-1877j 3.37e-489, 3.37e-489j
4.3694401283110748259 - 4.632351562250730938e-1887j 5.27e-497, 5.27e-497j
99.096844922602991347 - 3.3335521979677449897e-1876j 1.17e-487, 1.17e-487j
42.354238621533421086 - 1.7462476992910363582e-1909j 1.91e-486, 1.91e-486j
66.060623636188955025 + 3.309214750244908308e-1943j 3.33e-486, 3.33e-486j
0.77616217392612010956 - 2.2460906000421579474e-1975j 5.04e-504, 5.04e-504j
35.954676405957428881 + 2.9375823251527366068e-1956j 8.15e-487, 8.15e-487j
1.0447719743420423719 - 3.752116022797804847e-1983j 5.28e-503, 5.28e-503j
0.097850936687084069861 - 1.3112111944444541733e-1988j 1.17e-508, 1.17e-508j
0.2635603197181409102 + 8.2911244362249129366e-1987j 4.53e-507, 4.53e-507j
81.097107574746751657 + 3.0818784707152854943e-1967j 1.31e-486, 1.31e-486j
39.071204049396741948 + 7.271275849217951513e-1974j 1.31e-486, 1.31e-486j

Weights

Weight (ball center) Error (ball radius)
1.0802053498810937829e-60 + 4.260748168301629067e-1530j 4.28e-192, 7.45e-433j
4.8268148072701392975e-72 + 2.3765867737505567298e-1536j 2.01e-196, 3.5e-437j
1.5072135519397988335e-52 + 1.5530083823664026388e-1525j 1.28e-189, 2.22e-430j
2.2212426738342675971e-56 - 1.0859118648498170514e-1527j 5.59e-191, 9.72e-432j
1.0187368005413577674e-65 - 7.049771785046659912e-1533j 1.07e-194, 1.86e-435j
0.00032001165616592264477 + 2.1078052570908292247e-1492j 1.92e-138, 3.34e-379j
6.5778151590087700093e-07 + 4.6458361878188764404e-1493j 2.27e-150, 3.95e-391j
4.462973192557393015e-49 - 1.4483006233427757526e-1523j 4.98e-189, 8.67e-430j
2.8406871071306478996e-23 + 5.9260200334061451518e-1508j 8.33e-177, 1.45e-417j
1.3449698726186787618e-14 + 1.4192070977692306535e-1501j 6.29e-168, 1.09e-408j
3.3897151513214178237e-40 + 1.9669281035919307433e-1518j 1.17e-186, 2.04e-427j
3.5308745744393741991e-09 + 1.2955374060366975222e-1495j 9.14e-160, 1.59e-400j
0.0022108036711691861257 + 6.4697376533492190181e-1492j 2.24e-139, 3.9e-380j
2.8604351909066681632e-12 + 1.9091461748015234675e-1499j 2.96e-165, 5.15e-406j
0.050894336873244039306 - 8.1525942911264998977e-1491j 2.71e-125, 4.71e-366j
2.5444129674651847659e-05 + 1.9384199098701884952e-1492j 1.72e-149, 2.99e-390j
0.0046940198558606638184 - 1.1231781020581523e-1491j 6.98e-138, 1.21e-378j
0.069425034976826933678 + 1.1695975130710328668e-1490j 2.63e-123, 4.59e-364j
6.8376870893630157854e-46 + 9.6531673595530085205e-1522j 1.69e-189, 2.94e-430j
5.213828252125421726e-10 + 1.2743634214933820609e-1496j 8.97e-162, 1.56e-402j
-1.4375312127363262219e-09 - 1.0035747176449050635e-1495j 1.54e-160, 2.68e-401j
9.5734062248492134642e-05 - 1.6486233440634549246e-1492j 1.76e-149, 3.06e-390j
4.5101290643005911929e-20 + 9.3544425506598843551e-1506j 1.23e-176, 2.14e-417j
6.2014818197817328432e-33 - 4.3151516569817560735e-1514j 2.01e-186, 3.49e-427j
5.282149965683484796e-25 - 4.2387869185234031745e-1509j 4.67e-181, 8.13e-422j
1.909683427187054146e-08 - 2.5697412738056737248e-1495j 8.35e-162, 1.45e-402j
0.036024428155729333343 + 4.6546279046702400637e-1491j 1.77e-141, 3.08e-382j
0.00091979741651710142102 - 3.4974667806678883756e-1492j 3.01e-150, 5.24e-391j
1.2463245999364122473e-21 - 7.6808466399070156993e-1507j 2.7e-178, 4.69e-419j
7.6454947719207563201e-06 - 5.6495992900623110796e-1492j 5.48e-157, 9.54e-398j
-1.9752596017830405714e-06 + 8.0793444854469269169e-1492j 9.43e-158, 1.64e-398j
3.149433076522476024e-06 - 4.0651517515800773357e-1492j 1.51e-158, 2.62e-399j
0.10112976270866277228 - 1.4335925302577063168e-1490j 1.13e-143, 1.96e-384j
3.4414439175507857926e-11 - 2.8471419051300390011e-1498j 1.11e-168, 1.93e-409j
8.7351949660795744421e-31 + 9.0216182254732636031e-1513j 4.49e-188, 7.81e-429j
7.9126873379315561895e-27 + 2.7932715176894337001e-1510j 2.13e-185, 3.71e-426j
2.1074073133052270911e-13 - 1.5807063865766921512e-1500j 5.92e-174, 1.03e-414j
0.16248122381135837976 + 8.1611933445140397918e-1491j 5.55e-152, 9.66e-393j
0.042932212196545571415 - 6.8364491159314596896e-1492j 3.5e-152, 6.09e-393j
1.2626019055958326578e-37 - 6.4936274566824168546e-1517j 1.64e-192, 2.85e-433j
0.020475855161568054783 - 2.7108420292401899586e-1491j 3.63e-158, 6.32e-399j
1.2367769424067255081e-07 + 2.6215883199636590646e-1494j 1.13e-166, 1.96e-407j
0.010026080950730518559 + 1.7477209849558369508e-1491j 2.35e-159, 4.09e-400j
6.0729428392163723904e-43 - 4.8897670144876069474e-1520j 4.44e-195, 7.72e-436j
1.359140788662173822e-18 - 1.0822457416724835827e-1504j 6.89e-181, 1.2e-421j
9.4106564151469754674e-29 - 1.6741531039091279244e-1511j 1.47e-187, 2.57e-428j
0.11898716851855615569 - 1.4420443114252704326e-1490j 2.53e-163, 4.4e-404j
7.3678284214875392367e-16 - 1.3094404119752154943e-1502j 4.01e-179, 6.98e-420j
0.10854911867973752646 + 1.6787776715166182183e-1490j 1.48e-163, 2.57e-404j
0.11139889232930324634 + 2.1558975317121120294e-1491j 1.73e-164, 3e-405j
0.15940045196958435249 - 4.1988751237196492626e-1491j 1.71e-164, 2.98e-405j
3.2867062417786716106e-35 + 1.8053231651766551798e-1515j 4.92e-192, 8.57e-433j
3.4398917080748898728e-17 + 1.2044620214064251447e-1503j 2.47e-180, 4.3e-421j

Download

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