Rule: Q[1, 3, 59]

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)
223.34118244205574621 + 3.6858108615062375844e-2550j 7.66e-1001, 7.66e-1001j
206.8569800357902966 - 2.2937145189739536719e-2548j 5.47e-999, 5.47e-999j
17.854863465502677227 + 1.5356588015656535912e-2548j 1.36e-998, 1.36e-998j
25.614364023320809347 - 1.241869346307981801e-2545j 5.31e-996, 5.31e-996j
193.74402107411594781 - 3.4986829641579669262e-2542j 1.34e-997, 1.34e-997j
182.44646581686868311 + 1.1883722967717485489e-2539j 1.89e-996, 1.89e-996j
30.086332274458079195 + 2.1643240438756100575e-2544j 7.34e-995, 7.34e-995j
8.9914623785490984949 - 3.1135380301032140487e-2553j 2.8e-1003, 2.8e-1003j
14.54071721116500806 - 3.3454003804342258074e-2551j 4.6e-1000, 4.6e-1000j
70.371758241711119856 + 7.9705487097576588643e-2539j 1.21e-990, 1.21e-990j
16.151861635235790921 - 3.2143442077500524468e-2548j 2.71e-999, 2.71e-999j
52.349929459426606076 - 4.1662872172130136171e-2542j 1.26e-991, 1.26e-991j
6.7414840647187201284 + 1.5188645653900382129e-2554j 4.98e-1005, 4.98e-1005j
40.298703859816490515 - 3.9121741237825236478e-2542j 5.67e-993, 5.67e-993j
34.974606746886531032 - 8.2818853366638134095e-2543j 7.39e-994, 7.39e-994j
49.153138144552942332 - 7.5792143455731996519e-2541j 6.54e-992, 6.54e-992j
55.676032839882652085 + 5.7058464646949672106e-2540j 2.46e-991, 2.46e-991j
46.0814943884979698 + 1.4656555993186144887e-2541j 3.09e-992, 3.09e-992j
66.478074332159011992 + 3.3395658725169511306e-2539j 8.81e-991, 8.81e-991j
10.24651044111103035 - 2.9739959521460833404e-2552j 1.89e-1002, 1.89e-1002j
7.8232631436879996743 + 3.4555169744383011277e-2553j 3.7e-1004, 3.7e-1004j
1.9178352539905620853 + 7.8109524527457588525e-2561j 2.46e-1011, 2.46e-1011j
62.734851087628581391 - 2.515878418428721017e-2540j 6.09e-991, 6.09e-991j
1.4229426138226924667 + 2.4027602166347390058e-2561j 1.11e-1012, 1.11e-1012j
5.7462942980991696734 - 1.9771000858852316545e-2555j 5.96e-1006, 5.96e-1006j
59.13600605620998254 - 8.566933252292652185e-2541j 3.84e-991, 3.84e-991j
32.477282874653207079 - 1.5509427542367154037e-2543j 2.32e-994, 2.32e-994j
1 + 8.4507401189140349889e-2563j 5.1e-1014, 5.1e-1014j
23.529174144107601592 - 2.1313450534294140044e-2545j 1.36e-996, 1.36e-996j
11.58912091442418844 + 5.6932726774302074694e-2551j 1.22e-1001, 1.22e-1001j
13.020182689484502194 + 3.6303217884006442274e-2550j 7.95e-1001, 7.95e-1001j
3.369839231310923141 + 1.8204741713681017354e-2557j 3.03e-1008, 3.03e-1008j
0.18188567320744303295 - 3.5343579376718013174e-2567j 3.39e-1018, 3.39e-1018j
2.9569571916949703462 - 2.9932459448597529406e-2558j 6.84e-1009, 6.84e-1009j
37.580834198246104751 - 1.9394262515239948502e-2542j 2.1e-993, 2.1e-993j
43.131183577253643495 - 2.6918900139734299972e-2541j 1.36e-992, 1.36e-992j
19.651080955519807975 + 4.1268301442743010278e-2547j 6.62e-998, 6.62e-998j
0.65226924910981971202 + 1.7366034128642762872e-2564j 2.16e-1015, 2.16e-1015j
2.4664483907250840311 - 9.0247415346309317756e-2559j 5.39e-1010, 5.39e-1010j
27.799414708411577817 - 9.1385189209054426907e-2545j 1.98e-995, 1.98e-995j
4.0300160234598798778 - 3.0149407329597614148e-2557j 1.31e-1007, 1.31e-1007j
0.056897625001077184683 + 1.5048178666159553201e-2568j 1.35e-1019, 1.35e-1019j
74.422647172989532389 - 5.6372360438071215205e-2538j 1.55e-990, 1.55e-990j
0.0035542023496789597174 + 5.3894903318674190428e-2570j 9.62e-1022, 9.62e-1022j
4.8395492246954389696 - 1.8078575962102178877e-2555j 9.26e-1007, 9.26e-1007j
0.37988301935463734018 - 7.6334894717780342209e-2566j 8.6e-1017, 8.6e-1017j
21.541986818890346772 - 6.3551539710405124054e-2546j 2.97e-997, 2.97e-997j
78.638251097711769776 - 6.7531477321787641563e-2539j 1.77e-990, 1.77e-990j
163.17717281495145004 - 1.7619389202926959529e-2540j 1.3e-994, 1.3e-994j
146.80895027972121986 - 3.7388063334731450972e-2557j 2.94e-993, 2.94e-993j
87.598259308608422764 - 4.9385518550071537392e-2590j 2e-990, 2e-990j
97.332778800192251836 - 9.7462596434472644785e-2642j 1.35e-990, 1.35e-990j
83.026971986197305004 - 1.1329115822537931425e-2732j 1.91e-990, 1.91e-990j
172.36211468572730423 + 6.8697009912524309638e-2875j 1.85e-995, 1.85e-995j
113.62648910640704564 + 4.3813967641842884806e-2969j 3.37e-991, 3.37e-991j
125.84232477355723914 + 5.5882305616956578723e-3033j 8.2e-992, 8.2e-992j
154.70156307249060638 - 1.9658114300989152957e-3102j 6.67e-994, 6.67e-994j
92.362803405209050591 + 3.599269973935631607e-3200j 1.72e-990, 1.72e-990j
119.58265770479778058 - 1.0610365434674492163e-3311j 1.87e-991, 1.87e-991j
102.52215441507067219 + 2.8741843861394584743e-3398j 1.02e-990, 1.02e-990j
132.43798283672475628 - 9.4417991023921364569e-3457j 3.01e-992, 3.01e-992j
107.94709496621272742 + 1.6897688139034252377e-3493j 6.44e-991, 6.44e-991j
139.4098715843123723 - 7.0919156159384233992e-3520j 1.04e-992, 1.04e-992j

Weights

Weight (ball center) Error (ball radius)
1.964136421698872271e-96 + 2.04215094801803952e-2601j 1.37e-172, 4.33e-920j
2.0935470249883451026e-89 - 8.2202491446137240678e-2598j 1.11e-170, 3.5e-918j
3.0804486057305595912e-08 - 7.5591941770388371632e-2555j 2.29e-108, 7.22e-856j
1.6039098845208333704e-11 - 1.5646099084449447073e-2556j 7.3e-118, 2.3e-865j
8.7008584007911814975e-84 + 6.3460869078280733508e-2595j 2.08e-169, 6.54e-917j
6.1767903160825314049e-79 - 1.9973957256790755074e-2592j 2.97e-168, 9.36e-916j
2.0073368291906534128e-13 - 3.2673626388954339429e-2557j 6.12e-124, 1.93e-871j
0.00015079577286621454975 - 2.0836676474045203926e-2552j 8.64e-96, 2.72e-843j
7.5812156945960376603e-07 - 7.9837179264017700773e-2554j 1.11e-106, 3.49e-854j
1.088541008840982649e-30 - 5.3764884179842244878e-2567j 9.18e-147, 2.89e-894j
1.6018446681298898446e-07 + 3.1026798750210155819e-2554j 2.37e-109, 7.47e-857j
5.9983014578854834959e-23 + 2.4207927808926676995e-2562j 1.76e-139, 5.55e-887j
0.0012264669276526909916 - 9.9876363788021440288e-2552j 1.82e-93, 5.73e-841j
8.7438969089952349632e-18 + 8.6334369567299191864e-2560j 2.86e-133, 9.02e-881j
1.6500197786435623449e-15 + 7.3992250722983398075e-2558j 8.34e-130, 2.63e-877j
1.409614994365557131e-21 - 7.9552191264714605297e-2562j 2.25e-138, 7.09e-886j
2.2422972344033909405e-24 - 3.2540922247917418636e-2563j 5.37e-142, 1.69e-889j
2.9220050509361881623e-20 + 6.1922320065776579036e-2561j 2.48e-137, 7.8e-885j
5.1369511036378424269e-29 + 4.4477761973662387831e-2566j 9.44e-148, 2.98e-895j
4.6079076906276857116e-05 + 9.4119335695862954828e-2553j 2.69e-110, 8.49e-858j
0.00045033290110703169137 + 4.5639113802839958031e-2552j 1.19e-105, 3.76e-853j
0.077524792088584680413 + 3.3895559546231436303e-2550j 3.09e-84, 9.74e-832j
2.0858103396810574762e-27 - 3.5532922435414974012e-2565j 2.61e-146, 8.23e-894j
0.11085035628215201659 - 3.1057944663082849379e-2550j 1.57e-81, 4.94e-829j
0.0030397680415769851687 + 2.220322078269679938e-2551j 5.18e-103, 1.63e-850j
7.3308341139374899508e-26 + 2.6699994949328341265e-2564j 1.32e-144, 4.16e-892j
1.9202104240433213265e-14 - 3.3297189425997885742e-2558j 1.34e-132, 4.23e-880j
0.14181867227719541267 + 3.0369065646017627356e-2550j 2.73e-86, 8.62e-834j
1.230733307363925773e-10 + 3.1811536119262775052e-2555j 1.67e-127, 5.26e-875j
1.2849427066511759576e-05 - 4.1720080632439674603e-2553j 8.6e-116, 2.71e-863j
3.2687404332843031059e-06 + 1.8182722606898040432e-2553j 1.34e-117, 4.21e-865j
0.018304233248057637956 - 3.6679457174289682536e-2550j 1.64e-101, 5.18e-849j
0.13443573443032244333 - 2.629855855360380498e-2550j 5.1e-91, 1.61e-838j
0.020318102030704257979 + 5.203067295527762812e-2550j 6.37e-100, 2.01e-847j
1.270543646477787915e-16 + 2.0980168257122825406e-2558j 2.4e-136, 7.57e-884j
5.3627608535665872566e-19 + 9.7420144839892959398e-2560j 3.8e-139, 1.2e-886j
5.3856920049709223958e-09 + 1.0227659333623510317e-2555j 1.71e-126, 5.38e-874j
0.16144672172129997349 - 3.004976637625693836e-2550j 7.48e-97, 2.36e-844j
0.047120800939632106258 - 4.3164431917575375985e-2550j 8.88e-103, 2.8e-850j
1.8891605005239134248e-12 + 2.1830145632585152821e-2556j 1.37e-131, 4.33e-879j
0.013369542651885829662 + 1.3377683902278350294e-2550j 9.71e-109, 3.06e-856j
0.084027193956543896673 + 2.0711742913157078511e-2550j 5.23e-99, 1.65e-846j
1.9715483958343911119e-32 + 5.7886114390909455018e-2568j 8.58e-156, 2.71e-903j
0.018330732538076356494 - 8.5143446963963947243e-2551j 3.85e-100, 1.21e-847j
0.006809714221227672061 - 5.1718281988412259719e-2551j 3.94e-112, 1.24e-859j
0.16071288723428224286 + 2.9016974942103201553e-2550j 1.61e-100, 5.07e-848j
8.5498883110879767512e-10 - 3.2010322474531858838e-2555j 5.97e-129, 1.88e-876j
3.0295537660423793332e-34 - 5.788689244424383021e-2569j 2.9e-158, 9.14e-906j
1.1961627516976496886e-70 - 3.8015795804340174494e-2588j 4.03e-181, 1.27e-928j
1.3316469268509718561e-63 - 1.7148118417771457844e-2584j 9.48e-179, 2.99e-926j
4.221880115056380781e-38 - 4.7204938485009658071e-2571j 9.41e-164, 2.97e-911j
2.7197800348429682329e-42 - 2.6820561515375443998e-2573j 7.7e-168, 2.43e-915j
3.9170633702382388389e-36 + 5.4541809874747740953e-2570j 8.09e-162, 2.55e-909j
1.33707134300426214e-74 + 3.4447847959271661261e-2590j 1.12e-183, 3.52e-931j
2.6127496336558983465e-49 + 5.1246363861466414679e-2577j 1.47e-173, 4.65e-921j
1.4289645632237073098e-54 + 8.813507287289013911e-2580j 9.11e-177, 2.87e-924j
5.321242611760468463e-67 + 2.950294128190087675e-2586j 7.66e-182, 2.41e-929j
3.7534901013077957761e-40 + 3.7343778416262996904e-2572j 8.64e-168, 2.72e-915j
7.1032585300556431607e-52 - 2.2888746937198772426e-2578j 1.49e-175, 4.71e-923j
1.5842314557510620645e-44 + 1.7354043817521973016e-2574j 1.32e-171, 4.17e-919j
2.0601892272383787793e-57 - 2.8776972538194161636e-2581j 5.12e-179, 1.61e-926j
7.3007637847588863984e-47 - 1.002863978228655879e-2575j 1.61e-173, 5.08e-921j
2.0461550102610158843e-60 + 7.8064584423862493912e-2583j 1.42e-180, 4.47e-928j

Download

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