Rule: Q[5, 60]

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)
229.37975999167980877 - 7.0363165297469796957e-2688j 2.47e-1000, 2.47e-1000j
177.91142310137134854 + 5.1769739918482841864e-2677j 6.63e-995, 6.63e-995j
199.51067505150558787 + 1.5945809526310966484e-2682j 4.8e-997, 4.8e-997j
188.10073370832400599 - 3.7280422767642047061e-2680j 7.06e-996, 7.06e-996j
212.74785810808487887 + 3.0431675536297333402e-2687j 1.85e-998, 1.85e-998j
168.6266890606012042 - 3.2222824794292283723e-2680j 4.68e-994, 4.68e-994j
16.949707438726540375 - 4.6132658093828306784e-2693j 6.14e-998, 6.14e-998j
49.589110552562201265 + 3.8165129632774647702e-2685j 4.96e-991, 4.96e-991j
40.841407423488200999 - 9.031825649191798057e-2687j 3.96e-992, 3.96e-992j
11.460694742226287749 - 4.1663780138596678275e-2695j 1.8e-1000, 1.8e-1000j
52.742819284505171157 - 5.0318954528532646601e-2684j 9.45e-991, 9.45e-991j
22.261507129525551511 + 1.3472654850292724004e-2694j 4.3e-996, 4.3e-996j
46.556586489609501411 - 9.2505190711913353188e-2687j 2.45e-991, 2.45e-991j
56.021531048701858107 + 1.1026928325361886961e-2691j 1.72e-990, 1.72e-990j
26.296987546793526075 + 5.6533180782108813216e-2713j 5.5e-995, 5.5e-995j
160.0551058584461883 - 3.6905633923197951815e-2714j 2.74e-993, 2.74e-993j
15.38779517600537975 + 1.1176878169373696727e-2735j 1.51e-998, 1.51e-998j
28.463217934801592255 + 1.8232186224333717165e-2732j 1.8e-994, 1.8e-994j
20.39108155446524946 + 3.3575951380387267407e-2734j 1.06e-996, 1.06e-996j
35.572723783088370201 + 4.3811753315714032531e-2727j 6.14e-993, 6.14e-993j
12.640800844275782659 + 4.5267984125198226339e-2746j 7.98e-1000, 7.98e-1000j
4.3554147420486207635 + 5.3616025504798873283e-2753j 3.7e-1007, 3.7e-1007j
33.099277189623373976 + 2.161674319940739798e-2734j 2.07e-993, 2.07e-993j
6.1034249949475364792 - 1.7637043029798101897e-2758j 4.71e-1005, 4.71e-1005j
18.61957622757951676 + 3.3578015721893280005e-2751j 2.65e-997, 2.65e-997j
43.64175222724762241 - 2.255088432882457225e-2742j 1.04e-991, 1.04e-991j
0.48472377409294771799 - 1.1872888262925172328e-2802j 6.95e-1016, 6.95e-1016j
1.0755826213659163932 + 1.5911876182331583519e-2799j 3.39e-1013, 3.39e-1013j
7.0858100058588375569 - 1.2864417457160657058e-2788j 4.62e-1004, 4.62e-1004j
1.8187841719895005407 + 1.9555683841508886885e-2798j 3.13e-1011, 3.13e-1011j
3.5964257710407220812 + 1.45134391984003161e-2793j 3.58e-1008, 3.58e-1008j
152.06945309179653898 - 1.5967323900168318088e-2775j 1.28e-992, 1.28e-992j
1.4134030591065167922 + 1.8192855423670347924e-2820j 3.48e-1012, 3.48e-1012j
0.2635603197181409102 + 6.5246230127272105768e-2826j 2.81e-1017, 2.81e-1017j
30.730090338438538028 + 6.9629105186115851069e-2798j 6.3e-994, 6.3e-994j
9.2239175104104764419 - 3.3315733577074952607e-2826j 3.87e-1002, 3.87e-1002j
38.152623023357874924 + 1.7154741340562523858e-2818j 1.64e-992, 1.64e-992j
2.9173862528484075389 - 1.2422880974234296906e-2861j 3.61e-1009, 3.61e-1009j
10.338202765353457662 + 4.2304004173125606451e-2850j 2.68e-1001, 2.68e-1001j
24.230054045227535091 + 1.2399723290622333245e-2845j 1.62e-995, 1.62e-995j
5.1919284893683769564 - 7.6794961046373729245e-2873j 4.71e-1006, 4.71e-1006j
0.10774371486484895417 + 4.5927900355103961845e-2889j 6.95e-1019, 6.95e-1019j
0.020491481265066764251 - 2.1515545240439938765e-2890j 1.82e-1020, 1.82e-1020j
0.76224149512852183977 + 7.0393135168749088118e-2881j 1.76e-1014, 1.76e-1014j
13.946232520424064726 + 2.2837227873669811835e-2860j 3.6e-999, 3.6e-999j
8.1311912519434640889 + 2.7626269149837555156e-2868j 4.4e-1003, 4.4e-1003j
2.3222348970001147674 - 4.7108115968030864517e-2878j 3.18e-1010, 3.18e-1010j
92.004866323727173933 + 4.5523741746711725725e-2908j 1.34e-989, 1.34e-989j
96.851640177470888192 + 2.5240727126634029552e-2964j 1.12e-989, 1.12e-989j
87.351620070673042631 + 5.7534912255292215806e-2995j 1.64e-989, 1.64e-989j
78.583908402769968915 - 8.3732309522581941067e-3031j 1.45e-989, 1.45e-989j
118.44880166768740083 + 2.4789585093831248985e-3070j 1.89e-990, 1.89e-990j
130.83587058933634283 - 9.2252199862621341332e-3104j 3.54e-991, 3.54e-991j
59.429422803482331832 - 1.7660665352311588274e-3129j 2.96e-990, 2.96e-990j
137.5188891496904619 - 1.1514220618551843724e-3184j 1.37e-991, 1.37e-991j
70.476266721573463299 + 1.9323163002043023369e-3253j 9.23e-990, 9.23e-990j
101.90419870875355172 - 1.4766864616861324134e-3306j 7.7e-990, 7.7e-990j
74.451471071377018746 + 6.0343154579600923214e-3345j 1.23e-989, 1.23e-989j
66.651507211410134672 - 2.9453118578561599054e-3396j 7.18e-990, 7.18e-990j
112.68513435179142039 - 1.5961042345967216442e-3452j 3.54e-990, 3.54e-990j
124.49007890809680654 + 5.7701861089102751781e-3500j 8.29e-991, 8.29e-991j
62.971072111698920853 + 1.0040188766939254825e-3538j 4.84e-990, 4.84e-990j
107.17660543210427099 + 3.1898361818508964586e-3586j 5.77e-990, 5.77e-990j
144.5796475926076889 + 1.240501603727663479e-3633j 4.34e-992, 4.34e-992j
82.881138572472476721 - 1.3342136414581602315e-3660j 1.6e-989, 1.6e-989j

Weights

Weight (ball center) Error (ball radius)
4.7251005352883917028e-99 + 9.0706287081787062238e-2748j 6.63e-170, 2.32e-918j
5.2567466659562788435e-77 + 2.2621210903066341273e-2736j 2.83e-163, 9.93e-912j
2.750027397291497856e-86 + 3.495798929175575426e-2741j 1.38e-166, 4.84e-915j
2.1854747804311454724e-81 - 1.2043929684630501078e-2738j 4.91e-165, 1.72e-913j
5.8411655106088585805e-92 - 4.1017399581898050189e-2744j 8.65e-169, 3.03e-917j
5.1986194381200498917e-73 - 2.7096986330559560101e-2734j 5.14e-163, 1.8e-911j
7.0411579183310818691e-08 - 9.1593429830900096012e-2699j 5.84e-109, 2.04e-857j
8.9956750657466134402e-22 - 4.8058532910341557712e-2706j 8.94e-136, 3.13e-884j
5.0257600479017923939e-18 + 4.1414402436049478101e-2704j 1.43e-131, 5e-880j
1.1984415954177641601e-05 - 3.7498977809942684123e-2697j 3.07e-102, 1.08e-850j
3.9933672335364109367e-23 + 8.2253866675322155571e-2707j 1.1e-137, 3.86e-886j
4.1223139345404654175e-10 + 3.6444505133466304882e-2700j 8.15e-119, 2.86e-867j
1.7945027823654455062e-20 + 1.242097323217788748e-2705j 7.76e-135, 2.72e-883j
1.5640088091664716893e-24 + 1.3189716294772629362e-2707j 8.72e-140, 3.06e-888j
8.0345017776109242658e-12 + 3.7928548942572162272e-2701j 1.17e-123, 4.12e-872j
2.5467685325763356457e-69 + 2.2774437009482644019e-2732j 2.68e-166, 9.4e-915j
3.1227044194624458405e-07 + 2.6182649558593490788e-2698j 3.96e-113, 1.39e-861j
9.6429421952654575054e-13 - 1.190458282624122968e-2701j 1.08e-125, 3.79e-874j
2.5387976779774446333e-09 - 1.1003551583986330837e-2699j 5.33e-119, 1.87e-867j
8.9834905069642537533e-16 + 3.6039346336146510491e-2703j 4.07e-131, 1.43e-879j
4.0009752067148400246e-06 + 1.8103061306224484971e-2697j 4.81e-112, 1.69e-860j
0.01024557337218226972 + 8.357716521302482254e-2696j 7.38e-96, 2.59e-844j
1.0213067830390839744e-14 - 1.137315591353042978e-2702j 9.72e-130, 3.4e-878j
0.0021186132446627049421 + 3.5114870096502493648e-2696j 1.46e-102, 5.13e-851j
1.4108922928075020903e-08 + 3.2888899533887236164e-2699j 1.47e-118, 5.13e-867j
3.1809009192203745997e-19 - 1.293310320249690979e-2705j 6.72e-136, 2.36e-884j
0.15497449681986441965 + 3.1377270882898870088e-2695j 1.14e-78, 3.99e-827j
0.1102628200919632147 + 6.2868914895548873631e-2695j 1.14e-78, 3.99e-827j
0.00085001968248154272616 - 2.2932115072898962843e-2696j 4.83e-106, 1.69e-854j
0.073660727296987006318 + 4.8593725391572476105e-2695j 3.75e-87, 1.31e-835j
0.019729187625732456626 - 1.2961648343017964095e-2695j 1.51e-96, 5.29e-845j
6.9979910157806677204e-66 - 1.4314157055877664723e-2730j 1.53e-169, 5.37e-918j
0.088026766961560005523 - 6.3740769397764668611e-2695j 8e-86, 2.8e-834j
0.14546210626484970761 - 1.8793150669089829471e-2695j 7.22e-83, 2.53e-831j
1.0450897919724109453e-13 + 3.6851011850562102849e-2702j 1.1e-128, 3.86e-877j
0.00010933994324886029797 - 1.0015971953222866832e-2696j 1.88e-111, 6.6e-860j
7.0978749143942923107e-17 - 1.3122284032363651769e-2703j 2.99e-133, 1.05e-881j
0.034499227002747620972 + 2.0227916263944312458e-2695j 2e-98, 7.01e-847j
3.6149116023370629113e-05 + 6.4597104577986580672e-2697j 5.98e-113, 2.1e-861j
6.0515045437544061097e-11 - 1.186910356806255692e-2700j 6.81e-125, 2.39e-873j
0.0048633558412722886374 - 5.4083686538080031901e-2696j 5.43e-106, 1.9e-854j
0.10937725144137083279 + 9.3174780663098411133e-2696j 1.86e-90, 6.53e-839j
0.051497905395686214632 - 2.6307411822739404451e-2696j 8.66e-91, 3.03e-839j
0.1399231555154224585 - 4.7576109462603297312e-2695j 6.6e-92, 2.31e-840j
1.2070715239963188363e-06 - 7.2617407113861090869e-2698j 6.01e-117, 2.11e-865j
0.0003155660837453798069 + 1.5113776776199744857e-2696j 5.66e-111, 1.98e-859j
0.054030146025912089893 - 3.1759171208591509101e-2695j 1.93e-100, 6.77e-849j
5.2397936437546259283e-40 - 8.6859229675008952261e-2717j 3.8e-161, 1.33e-909j
4.2879681755719427761e-42 + 6.3082895331130057288e-2718j 1.05e-162, 3.67e-911j
5.2802627935023801249e-38 + 1.0972817471438818056e-2715j 3.39e-160, 1.19e-908j
3.1339032083602019564e-34 + 1.3944595673007711129e-2713j 3.44e-158, 1.2e-906j
2.1334032250235909569e-51 + 6.2823954053319564356e-2723j 3.08e-169, 1.08e-917j
9.8214687984856637619e-57 + 9.2638215655521941676e-2726j 8.26e-172, 2.89e-920j
5.382151403459808947e-26 - 1.1432783294904204026e-2708j 1.29e-152, 4.53e-901j
1.2968962491451564813e-59 - 2.8018840513056861683e-2727j 4.57e-173, 1.6e-921j
9.6269650631219329651e-31 + 1.3847702149471022696e-2711j 9.23e-158, 3.23e-906j
2.8590119920275369562e-44 - 4.1707420333656556465e-2719j 2.56e-166, 8.97e-915j
1.8787707500578079148e-32 - 1.4259787745197692738e-2712j 4.39e-159, 1.54e-907j
4.2446121494001360912e-29 - 1.2955888391925557787e-2710j 4.96e-157, 1.74e-905j
6.4890651166118241609e-49 - 1.3291350240968330045e-2721j 1.2e-169, 4.2e-918j
5.3240181949890552815e-54 - 2.59758386384379903e-2724j 2.84e-172, 9.96e-921j
1.6200848829103846023e-27 + 1.19573896704409689e-2709j 2.78e-157, 9.74e-906j
1.5317319242345564238e-46 + 2.4894104645179517518e-2720j 1.43e-168, 5.01e-917j
1.1779595977955805055e-62 + 7.0396046433665937922e-2729j 4.98e-177, 1.74e-925j
4.4349354821483516679e-36 - 1.2815015512235137977e-2714j 5.43e-163, 1.9e-911j

Download

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