Rule: Q[6, 73]

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)
281.73090052383239933 + 1.271901637207959321e-2610j 1.43e-996, 1.43e-996j
226.19093958868171825 - 1.3514311340737667257e-2611j 1.5e-990, 1.5e-990j
206.71302403824374007 + 1.3697899877588072898e-2635j 1.07e-988, 1.07e-988j
249.59560147324272625 - 6.5493750152387691888e-2649j 6.08e-993, 6.08e-993j
20.626326063595255273 - 1.6190791216970668934e-2683j 2.17e-993, 2.17e-993j
63.739526054366988804 + 3.656581864471647611e-2671j 1.69e-984, 1.69e-984j
237.25144673633145088 - 1.8494777553439325864e-2751j 1.19e-991, 1.19e-991j
181.92563426030487063 + 1.5366064995263783777e-2877j 1.39e-986, 1.39e-986j
142.12580176898758949 - 1.188125965391991099e-2950j 4.69e-984, 4.69e-984j
48.921113974237036487 + 2.808524906607160277e-2982j 3.37e-986, 3.37e-986j
24.099371705287752788 + 3.6918977539610148743e-3012j 4.56e-992, 4.56e-992j
29.88754103035094017 + 2.2113872179469885683e-3005j 3.44e-990, 3.44e-990j
88.904805936059620621 + 1.0587366392107748513e-3013j 3.69e-983, 3.69e-983j
160.72791368800150941 - 8.8525627079242401709e-3053j 4.18e-985, 4.18e-985j
22.324788001605163607 - 3.1825406903994209552e-3077j 9.93e-993, 9.93e-993j
70.369062773996790358 + 2.3265500783448820129e-3066j 5.88e-984, 5.88e-984j
17.455640064466712352 + 8.3702923230282788495e-3079j 9.78e-995, 9.78e-995j
73.845183456984119102 + 3.0014538786773631527e-3066j 9.18e-984, 9.18e-984j
12.022820874432283746 - 4.0030956410559113721e-3090j 1.41e-997, 1.41e-997j
216.07905067097650081 - 3.2112023148789590442e-3075j 1.55e-989, 1.55e-989j
46.239798489787641306 + 1.0815096035501567172e-3090j 1.24e-986, 1.24e-986j
4.2737774048659358357 - 5.2784668040880114269e-3134j 2.46e-1005, 2.46e-1005j
106.01820383704506816 - 5.7798814523055975778e-3110j 4.73e-983, 4.73e-983j
154.27242122255900015 + 4.1374851112532665678e-3178j 1.03e-984, 1.03e-984j
125.55546531963600853 - 3.812935165039561024e-3238j 2.17e-983, 2.17e-983j
54.559751147197556068 - 6.6907863426339488652e-3272j 1.75e-985, 1.75e-985j
136.3973713899968512 + 3.2677813581526547767e-3299j 8.55e-984, 8.55e-984j
9.0052243196593361852 + 4.2902761166250220511e-3343j 2.12e-999, 2.12e-999j
120.41761706970756522 - 2.2354827597448229539e-3325j 3.13e-983, 3.13e-983j
14.585395144165952788 - 4.0137782196365893666e-3356j 3.54e-996, 3.54e-996j
263.86704822380705383 - 1.9630807024931097152e-3350j 1.52e-994, 1.52e-994j
6.601026410005029236 - 2.246031702522684623e-3361j 4.07e-1002, 4.07e-1002j
2.4403491826794756036 - 1.9880483910481189085e-3368j 9.7e-1009, 9.7e-1009j
34.142854238926103414 + 3.6096837662424922414e-3349j 4.56e-989, 4.56e-989j
92.978481844337053899 + 1.8207270571425804571e-3341j 4.46e-983, 4.46e-983j
67.001518254589193624 - 7.1898425405799968122e-3352j 3.15e-984, 3.15e-984j
51.693773001449691778 + 3.1317016602992901089e-3361j 7.95e-986, 7.95e-986j
1.1889321016726230307 + 6.3278609437161214509e-3395j 5.11e-1012, 5.11e-1012j
9.8374674183825899177 + 8.6162102043162720056e-3382j 7.32e-999, 7.32e-999j
197.95820015818447064 + 1.1824992022611122316e-3365j 6.4e-988, 6.4e-988j
148.07841657238814693 - 1.0053382435886951646e-3392j 2.27e-984, 2.27e-984j
130.87825010040290072 - 5.1411968328691957799e-3415j 1.41e-983, 1.41e-983j
7.4590667988105025505 - 1.7040881272893862329e-3447j 4.73e-1001, 4.73e-1001j
1.532914790058785739 - 2.7922332165627947388e-3458j 5.7e-1011, 5.7e-1011j
4.9978982246509063273 + 8.4507947398505175031e-3451j 2.92e-1004, 2.92e-1004j
27.879869702406188252 + 1.8316657161963121191e-3437j 7.81e-991, 7.81e-991j
43.647980787155394797 + 4.0058384784603017732e-3434j 4.48e-987, 4.48e-987j
15.982873980601701783 + 5.0138034396546837457e-3442j 1.79e-995, 1.79e-995j
0.63988374372526205578 - 6.2972847168554485197e-3461j 2.35e-1014, 2.35e-1014j
3.6047530780766056631 + 4.6916606378608052532e-3453j 1.67e-1006, 1.67e-1006j
60.580278351726299775 - 1.42048409064403037e-3430j 9.15e-985, 9.15e-985j
13.264328566595607876 + 2.4491499633617180813e-3443j 6.76e-997, 6.76e-997j
101.52952379451105057 + 1.2084992326749182557e-3428j 5.13e-983, 5.13e-983j
1.9516149959279983986 + 4.2120816925305066231e-3474j 6.46e-1010, 6.46e-1010j
10.870087046464081553 - 2.956704379065651484e-3463j 3e-998, 3e-998j
19.003409786100261102 - 7.8805097335477497106e-3459j 4.38e-994, 4.38e-994j
174.52302435066613188 + 1.3673789772149980011e-3447j 4.92e-986, 4.92e-986j
84.958971232789569982 + 1.5878232933007685164e-3458j 2.88e-983, 2.88e-983j
31.974829575824589133 + 4.2485787124204347806e-3481j 1.22e-989, 1.22e-989j
0.40851556554686224445 - 8.0491677684833023548e-3507j 8.97e-1016, 8.97e-1016j
189.71928176777319175 - 7.087505031204934844e-3474j 3.17e-987, 3.17e-987j
115.45461909881259215 - 7.8435040536978996587e-3503j 3.68e-983, 3.68e-983j
5.7751435691045105018 - 1.4822945496836234526e-3555j 3.53e-1003, 3.53e-1003j
38.726052929295270069 - 4.5903504330257121309e-3539j 5.02e-988, 5.02e-988j
2.9927363260593140777 + 2.4779656820664072991e-3559j 1.24e-1007, 1.24e-1007j
0.90134521535501762145 + 1.7387453650888708336e-3566j 4.12e-1013, 4.12e-1013j
36.39282670598436129 - 4.8440310120534730865e-3540j 1.52e-988, 1.52e-988j
167.46863906095512648 - 2.1766488665183805805e-3534j 1.56e-985, 1.56e-985j
81.136465349100494112 - 3.2095983916855653383e-3545j 1.9e-983, 1.9e-983j
8.2858457419844448306 - 1.7877056515556499884e-3574j 4.24e-1000, 4.24e-1000j
0.22284660417926068946 - 8.2481923153399812377e-3591j 3.02e-1017, 3.02e-1017j
41.143936083138738723 + 1.0311652647371377212e-3561j 1.5e-987, 1.5e-987j
57.521163928479491569 - 1.12673401369485908e-3557j 4.26e-985, 4.26e-985j
110.65749319788395664 + 1.9975021170224258038e-3555j 4.59e-983, 4.59e-983j
77.433142382168613612 - 2.3216784325534232665e-3567j 1.42e-983, 1.42e-983j
0.09130017312091335529 - 1.4256374600633688243e-3614j 7.85e-1019, 7.85e-1019j
25.950789843401596251 - 6.6962983171048248676e-3588j 2.04e-991, 2.04e-991j
97.184923911389518254 + 1.3162197637078474262e-3577j 4.7e-983, 4.7e-983j
0.017384863216147324347 - 6.676816432205650782e-3683j 1.99e-1020, 1.99e-1020j

Weights

Weight (ball center) Error (ball radius)
9.3064818349115958436e-122 - 1.0503941755596880419e-2722j 2.44e-151, 5.73e-894j
6.1595388713953586921e-98 + 4.2565148242296674146e-2709j 3.1e-144, 7.3e-887j
1.5203176509788200372e-89 + 8.4615277395256227812e-2706j 9.56e-142, 2.25e-884j
5.2624234636420151553e-108 - 2.5543783806892065931e-2715j 5.01e-148, 1.18e-890j
1.8296458120048046357e-09 - 5.8564626725561840436e-2664j 5.25e-71, 1.23e-813j
6.6804150825783319662e-28 - 1.5038421919682694453e-2674j 3.99e-107, 9.39e-850j
1.0680339098013598597e-102 + 2.7728329096024529166e-2712j 3.95e-146, 9.29e-889j
7.4293778537824800797e-79 - 1.1438942128229656934e-2700j 2.67e-139, 6.28e-882j
1.1010388180411857987e-61 - 4.3987090674710350606e-2692j 8.41e-133, 1.98e-875j
1.5469012598082719201e-21 + 4.3836710603651513886e-2671j 2.28e-101, 5.36e-844j
6.1964508231129650003e-11 - 6.501820093533655119e-2665j 1.47e-80, 3.46e-823j
2.1438163911348163812e-13 + 1.9885702077256073207e-2666j 3.61e-87, 8.49e-830j
9.8212378741576264808e-39 + 2.7712808271773854669e-2680j 4.93e-120, 1.16e-862j
1.0372653405586780087e-69 + 3.9823093145056067577e-2696j 7.4e-137, 1.74e-879j
3.5004280680749717235e-10 + 1.9733762810915868925e-2664j 7.49e-80, 1.76e-822j
9.4036555358655574872e-31 - 4.4879036083892785079e-2676j 4.05e-113, 9.51e-856j
3.9643034580379133717e-08 - 4.8802992924218724734e-2663j 8.54e-76, 2.01e-818j
3.0019292509853317728e-32 + 7.194694449262646833e-2677j 1.13e-114, 2.66e-857j
7.2042278582246184232e-06 - 3.1683991682771756555e-2661j 2.42e-68, 5.7e-811j
1.3975781335426297121e-93 - 1.3944862351027514507e-2707j 6e-146, 1.41e-888j
2.1842404595470483963e-20 - 1.9045509691397058593e-2670j 6.77e-103, 1.59e-845j
0.0097065944273767160622 + 2.7394026293956654296e-2659j 8.07e-47, 1.9e-789j
4.1315640583065977595e-46 + 4.0669794816448713719e-2684j 7.24e-127, 1.7e-869j
6.3260564704321682997e-67 - 9.9566668527038455717e-2695j 6.91e-137, 1.62e-879j
1.550008731941904875e-54 + 1.906026316399528483e-2688j 3.84e-132, 9.03e-875j
5.8801840896820876297e-24 + 2.0542372034921348389e-2672j 1.8e-110, 4.24e-853j
3.2600478123904732642e-59 + 7.8887011112621021068e-2691j 2.83e-134, 6.65e-877j
8.8844005352110862406e-05 + 6.6451857284603797715e-2660j 1.41e-73, 3.31e-816j
2.5496762271735347846e-52 - 2.595228215649265738e-2687j 2.25e-131, 5.3e-874j
6.2956996897705537319e-07 - 3.8911550442417513039e-2662j 9.14e-84, 2.15e-826j
3.9594277809725080762e-114 + 1.1939370432776610735e-2718j 1.83e-157, 4.3e-900j
0.0011506935067806313306 - 1.2925722290694256149e-2659j 3.16e-70, 7.42e-813j
0.045429776953273590514 - 6.3442756830084854961e-2659j 2.49e-52, 5.86e-795j
3.2817160910355542158e-15 + 1.6775600527732248557e-2667j 8.53e-103, 2.01e-845j
1.7253409854189341717e-40 - 3.3588252456687553985e-2681j 1.81e-125, 4.26e-868j
2.6424084066664003499e-29 + 2.6619949623443821193e-2675j 8.43e-117, 1.98e-859j
9.9947359882388324513e-23 - 9.6896225016924462415e-2672j 2.61e-111, 6.13e-854j
0.094328638160909182201 + 1.3370511299134962626e-2658j 2.13e-48, 5.01e-791j
5.0650891674197739972e-05 - 2.8605665606469808041e-2660j 1.66e-81, 3.91e-824j
9.0451481671868981243e-86 - 5.0332362194126208982e-2704j 2.97e-147, 6.98e-890j
2.9755373677064872057e-64 + 2.2116109162819505567e-2693j 1.83e-137, 4.31e-880j
7.8381190182332147711e-57 - 1.2837023736171459285e-2689j 5.12e-134, 1.2e-876j
0.00049557647600125430875 + 1.1018903945989594208e-2659j 9.64e-82, 2.27e-824j
0.0823011267640978251 - 1.1328908106106117127e-2658j 1.69e-60, 3.97e-803j
0.0050714271469642398588 - 2.0939602844367053423e-2659j 1.06e-76, 2.49e-819j
1.5346113844382500982e-12 - 6.5391046861373568256e-2666j 2.64e-103, 6.2e-846j
2.8187927420005479529e-19 + 7.9562665406757070064e-2670j 1.77e-111, 4.15e-854j
1.6430254578119016498e-07 + 1.3815685044277293219e-2662j 1.62e-94, 3.81e-837j
0.13150713356978348138 + 9.0650004501736761691e-2659j 5.84e-64, 1.37e-806j
0.017428219780688782056 - 3.6006502018913344902e-2659j 2.63e-76, 6.18e-819j
1.5237256708950716267e-26 + 8.1038499243904160522e-2674j 2.47e-117, 5.82e-860j
2.2248208071624663775e-06 + 1.1004661848231639987e-2661j 2.13e-92, 5e-835j
3.558592772581597973e-44 - 4.0799884851010801766e-2683j 5.45e-130, 1.28e-872j
0.064629285708267167643 + 8.5449994611210432095e-2659j 4.29e-74, 1.01e-816j
2.0948517627886500829e-05 + 9.4482457714589261494e-2661j 1.58e-90, 3.7e-833j
8.8518464568130928013e-09 + 1.7042621564314738955e-2663j 4.86e-98, 1.14e-840j
1.1595222495851341315e-75 + 4.3102892327422269221e-2699j 2.68e-145, 6.29e-888j
4.9204559045478801454e-37 - 2.15316228248972027e-2679j 1.37e-126, 3.21e-869j
2.7629298017930873465e-14 - 5.8677614311663122344e-2667j 4.4e-109, 1.03e-851j
0.13993404385630820092 - 5.7032004199085911301e-2659j 9.25e-81, 2.18e-823j
3.2313421431682363235e-82 + 2.5983801728490086412e-2702j 3.09e-148, 7.26e-891j
3.523672963645457981e-50 + 3.2550892381674331415e-2686j 1.62e-133, 3.81e-876j
0.002491616272191544172 + 1.6193568038560289559e-2659j 4.46e-93, 1.05e-835j
3.607527639377109595e-17 + 1.2403946424656983263e-2668j 1.01e-113, 2.38e-856j
0.029223687684627994459 + 4.7575359222964902248e-2659j 3.01e-91, 7.08e-834j
0.11042516286316935402 - 1.2444684918450237028e-2658j 1.58e-87, 3.72e-830j
3.5883277671951060192e-16 - 4.6404794358139219818e-2668j 1.18e-112, 2.77e-855j
1.281333934662453599e-72 - 1.4027521704311312012e-2697j 2.05e-144, 4.83e-887j
2.1793585624110720704e-35 + 1.5788530496251727693e-2678j 5.86e-127, 1.38e-869j
0.00019392225042717655543 - 9.6911104249587581225e-2660j 2.26e-100, 5.32e-843j
0.12761727168241356807 + 3.2523998191227333006e-2659j 1.03e-95, 2.42e-838j
3.3302363033692685767e-18 - 3.1997866890746938614e-2669j 2.18e-115, 5.13e-858j
3.1435763615923761848e-25 - 4.1716322069315312161e-2673j 2.08e-120, 4.89e-863j
4.1278285807214988965e-48 - 3.7762453735150631104e-2685j 6.29e-134, 1.48e-876j
8.5686942561488530146e-34 - 1.0948985671665095879e-2677j 1.59e-126, 3.73e-869j
0.094080778216082889089 - 1.551250361633117135e-2659j 1.42e-105, 3.35e-848j
1.014379532952130682e-11 + 2.0897504427480030594e-2665j 1.2e-113, 2.82e-856j
2.654711414135653982e-42 + 3.8243351246950679296e-2682j 3.83e-131, 9e-874j
0.043814327596343799676 + 4.2812235643734197978e-2660j 1.23e-106, 2.9e-849j

Download

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