Rule: Q[2, 84]

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)
297.89009957648145466 + 3.8578707854611683071e-2703j 4.43e-992, 4.43e-992j
282.99949042476965826 + 1.6547973171896611502e-2702j 1.93e-990, 1.93e-990j
316.49331882073379518 - 5.7717047568268404287e-2705j 3.19e-994, 3.19e-994j
211.95662043207600181 + 3.2844905451376592332e-2689j 1.54e-983, 1.54e-983j
204.12985620135420249 - 1.9176912604963198761e-2694j 6.17e-983, 6.17e-983j
238.07579050507659172 - 3.0783965968314657616e-2700j 7.73e-986, 7.73e-986j
258.51749942529532988 + 1.6397330617410672142e-2705j 7.52e-988, 7.52e-988j
70.804119767801304946 - 1.0115061471343855003e-2707j 1.06e-980, 1.06e-980j
30.025153341874955649 - 2.6657920163383471993e-2739j 2.17e-988, 2.17e-988j
28.112458863931849936 - 6.2847036421998763163e-2742j 4.6e-989, 4.6e-989j
103.70911653953249114 - 5.1387841031377382493e-2734j 5.06e-979, 5.06e-979j
247.91353194558501672 - 1.6695057054788518542e-2774j 8.83e-987, 8.83e-987j
182.64590627702763883 + 7.3056485719009088666e-2854j 2.13e-981, 2.13e-981j
157.66767210723440214 - 7.4326792113443068053e-2930j 5.48e-980, 5.48e-980j
21.139025615757242328 - 2.9773288230263805509e-2976j 6.44e-992, 6.44e-992j
34.059482637292639659 + 1.4888409836620694795e-2963j 4.11e-987, 4.11e-987j
26.268273915566076868 + 3.5281566920430895815e-2973j 1.03e-989, 1.03e-989j
45.409238942317452543 + 5.0054198510288733357e-2965j 2.5e-984, 2.5e-984j
189.50700920788761166 - 2.8761824236432094431e-3005j 7.25e-982, 7.25e-982j
141.08251814499079811 + 2.0745168330971265397e-3055j 2.28e-979, 2.28e-979j
270.09731175609306629 + 3.2097422326355895959e-3081j 4.77e-989, 4.77e-989j
176.0507296969445607 + 3.0181513527432391839e-3086j 5.54e-981, 5.54e-981j
61.580935794423781561 - 5.2711535505475342531e-3097j 1.04e-981, 1.04e-981j
19.561334067413062333 - 8.7524109258754812223e-3129j 1.07e-992, 1.07e-992j
88.044805898129258841 + 2.0404340245751926307e-3114j 1.62e-979, 1.62e-979j
220.18303823518337095 + 3.8475074846127034765e-3153j 3e-984, 3e-984j
135.90130783674603015 - 8.2218264777074482556e-3190j 3.31e-979, 3.31e-979j
10.304470292066903534 + 4.8989979790304619059e-3235j 1.09e-998, 1.09e-998j
24.491802268216786584 + 2.3162050271171422118e-3226j 1.9e-990, 1.9e-990j
146.43094121655903819 - 2.1256486289506714133e-3215j 1.52e-979, 1.52e-979j
163.57816903961027486 + 3.8004638090271095064e-3233j 2.77e-980, 2.77e-980j
5.5463769533629468053 - 4.6787241246312135426e-3278j 1.16e-1003, 1.16e-1003j
6.3770647817633966305 - 2.5586504293723150336e-3277j 1.3e-1002, 1.3e-1002j
3.4142135623730950488 - 3.0195793548594416237e-3281j 7.98e-1007, 7.98e-1007j
15.215512865298864596 - 1.727048518530441308e-3269j 4.03e-995, 4.03e-995j
107.91278006187195487 + 1.0517487802849352298e-3252j 6.14e-979, 6.14e-979j
36.182944087051845934 - 1.8889843999473072952e-3274j 1.63e-986, 1.63e-986j
2.8237425104108440586 + 8.1113296624616334243e-3296j 6.82e-1008, 6.82e-1008j
1.8277225295723206098 + 1.431562788114992769e-3299j 4.29e-1010, 4.29e-1010j
67.64072264733408836 - 1.5813744499154182818e-3268j 4.97e-981, 4.97e-981j
196.65854557623244531 - 1.1748897063385365128e-3267j 2.19e-982, 2.19e-982j
11.439032773712946859 + 1.2799040229812849501e-3291j 9.39e-998, 9.39e-998j
126.00813505165912239 + 2.7944745175340298555e-3271j 5.33e-979, 5.33e-979j
9.2313422710109254695 + 4.4453878400011305721e-3301j 1.1e-999, 1.1e-999j
80.854025186270323412 - 9.5666490507161390138e-3279j 6.21e-980, 6.21e-980j
91.795697509642405367 - 3.4549356905249739311e-3287j 2.36e-979, 2.36e-979j
74.059281783869317648 - 2.3938266236715707495e-3299j 1.97e-980, 1.97e-980j
95.654398724678924905 + 2.0573956446864430898e-3310j 3.13e-979, 3.13e-979j
0.82449638631799931346 - 1.5931958708285524915e-3359j 2.85e-1013, 2.85e-1013j
58.680713044593445598 + 1.2623306635325930315e-3325j 4.61e-982, 4.61e-982j
22.782290418901789729 - 5.4926308469922134031e-3336j 3.81e-991, 3.81e-991j
77.408451918451056685 + 2.8966123050911254546e-3324j 3.64e-980, 3.64e-980j
64.566986540277740406 + 4.4061840762362286211e-3332j 2.32e-981, 2.32e-981j
169.70073667983094974 + 3.7666784899109495937e-3350j 1.21e-980, 1.21e-980j
18.048579331418976185 - 7.2956191727245088562e-3385j 1.97e-993, 1.97e-993j
55.864570290838386192 - 8.1023562756254937954e-3371j 1.78e-982, 1.78e-982j
112.23961260407421477 + 2.6076508752541704687e-3395j 6.11e-979, 6.11e-979j
40.647418378006610697 + 2.4681107971253147034e-3442j 2.35e-985, 2.35e-985j
42.990583846920064594 + 1.4620406819689695172e-3441j 7.52e-985, 7.52e-985j
4.0649695587876138729 - 1.3128288853845697857e-3468j 9.7e-1006, 9.7e-1006j
12.635432056581903119 - 1.4832243207195401537e-3459j 7.82e-997, 7.82e-997j
99.624313865765438348 + 1.8997920908356217566e-3440j 4.08e-979, 4.08e-979j
16.600160882118928072 - 7.9057526809510705361e-3492j 2.78e-994, 2.78e-994j
13.894103056756241938 - 1.5864378015978477381e-3493j 5.48e-996, 5.48e-996j
2.2943348462692131684 + 1.1883023309205679943e-3506j 4.94e-1009, 4.94e-1009j
7.2679515326364900188 + 1.1541881897774453648e-3499j 1.14e-1001, 1.14e-1001j
116.69429799766871934 + 6.1587548594874156831e-3475j 6.29e-979, 6.29e-979j
8.2192801392993628214 - 2.5546593651977710929e-3520j 1.16e-1000, 1.16e-1000j
4.7757083665807618298 - 1.9810885658086450444e-3522j 1.08e-1004, 1.08e-1004j
0.5857864376269049512 + 2.8004640750399162361e-3533j 1.64e-1014, 1.64e-1014j
0.37520509215909064192 + 2.1097141396590254304e-3534j 7.44e-1016, 7.44e-1016j
50.47803223221283115 - 3.0373919791148252493e-3501j 2.4e-983, 2.4e-983j
32.007198470765812687 - 9.1933757899792311678e-3506j 9.94e-988, 9.94e-988j
84.398562389225101923 + 4.1933202637156346306e-3496j 1.04e-979, 1.04e-979j
47.904619374009117347 - 3.923393234667992835e-3521j 7.66e-984, 7.66e-984j
1.096273115787871182 + 1.5772324878509719812e-3558j 3.63e-1012, 3.63e-1012j
0.2051012332837143157 + 1.3342243404939516601e-3562j 2.35e-1017, 2.35e-1017j
228.8651103915929794 + 6.6236463483377058726e-3526j 5.34e-985, 5.34e-985j
151.95585331561759704 - 6.6408988708862084137e-3570j 1e-979, 1e-979j
53.130860872677870031 + 2.5424088758471495994e-3601j 6.54e-983, 6.54e-983j
0.08411597676022220434 - 4.7252716361117754379e-3654j 6.88e-1019, 6.88e-1019j
1.427284627072316302 - 1.6075684028395419675e-3645j 3.53e-1011, 3.53e-1011j
38.378573758264586899 - 5.2122239106131389168e-3614j 6.54e-986, 6.54e-986j
0.016023852655641129364 + 8.9349444816929198506e-3669j 1.72e-1020, 1.72e-1020j
130.87900469313733424 - 5.304065507895597172e-3625j 4.61e-979, 4.61e-979j
121.28194336626035546 + 1.8226545424814581928e-3661j 5.86e-979, 5.86e-979j

Weights

Weight (ball center) Error (ball radius)
6.9130597158950259386e-129 - 1.3520520443794666829e-2789j 2.25e-130, 2.63e-872j
1.7096237363914637028e-122 + 2.3348643045915376999e-2786j 1.04e-128, 1.21e-870j
7.7417568968623519755e-137 + 1.2827945712278891849e-2793j 5.01e-133, 5.86e-875j
7.1202568892793853842e-92 - 8.2851768575810035787e-2771j 6.98e-120, 8.17e-862j
1.701231781867417614e-88 + 4.3696392632625720907e-2769j 9.01e-119, 1.05e-860j
3.8278376497987886113e-103 + 1.5288912502542540793e-2776j 2.39e-124, 2.8e-866j
5.8964376766868735769e-112 + 5.1299729318558175221e-2781j 2.62e-127, 3.06e-869j
5.7084745306211571551e-31 + 2.9288128698776046192e-2738j 2.36e-87, 2.76e-829j
1.7768791512118861457e-13 + 1.2327563802758381237e-2730j 3.1e-59, 3.62e-801j
1.1605930728625028725e-12 - 3.1160366397097805986e-2730j 4.06e-57, 4.76e-799j
3.7763735152080675917e-45 + 1.1749162423450091613e-2746j 1.13e-100, 1.32e-842j
2.1919436502617228539e-107 - 1.070638478957902239e-2778j 3.49e-126, 4.09e-868j
3.2029062982583053237e-79 - 2.3905701005848085025e-2764j 3.72e-118, 4.36e-860j
1.9494257666209135508e-68 - 8.1789035104380583356e-2759j 1.52e-114, 1.78e-856j
1.0625839086282644614e-09 - 9.4394254577179800299e-2729j 8.85e-54, 1.04e-795j
3.3715162023503003131e-15 + 1.7635499836861554132e-2731j 5.86e-68, 6.86e-810j
7.072288415723518519e-12 + 7.6440420327846692452e-2730j 1.05e-59, 1.23e-801j
4.6707752182855584338e-20 - 8.1751422681346889843e-2734j 6.67e-78, 7.8e-820j
3.4943460058544752044e-82 + 7.3025766821136206243e-2766j 1.18e-119, 1.38e-861j
2.817757889953973528e-61 + 4.0654864711661002919e-2755j 5.67e-113, 6.64e-855j
6.0726918615254622432e-117 - 1.5168366737279077358e-2783j 4.45e-132, 5.2e-874j
2.2542571957579097842e-76 + 6.8657336386236048936e-2763j 3.76e-118, 4.4e-860j
5.3028035720726267619e-27 - 6.481443161876595248e-2737j 2.79e-91, 3.27e-833j
4.9383606085389392081e-09 + 2.0569401928087851842e-2728j 5.49e-60, 6.42e-802j
2.1409205600568930204e-38 + 5.8030005121561573003e-2743j 1.33e-101, 1.56e-843j
2.0056489190380840994e-95 + 1.2889878742499799282e-2772j 3.65e-125, 4.28e-867j
4.8575812441656638501e-59 - 5.8728981088119647562e-2754j 5.41e-113, 6.34e-855j
3.6957987010874362384e-05 - 2.1600691443274240043e-2726j 8.72e-51, 1.02e-792j
4.0235585326297360863e-11 - 1.8200288288361379295e-2729j 2.9e-68, 3.39e-810j
1.3837333669630146803e-63 - 2.598123742566271654e-2756j 1.21e-114, 1.41e-856j
5.4711427411116831314e-71 + 3.9821533737375147069e-2760j 2.28e-117, 2.67e-859j
0.003123807695832704029 + 2.7012335068169548319e-2725j 1.65e-40, 1.93e-782j
0.001463368532461653101 - 1.7100810710491643804e-2725j 1.4e-43, 1.64e-785j
0.020422210107796046898 - 9.4521776128383704435e-2725j 6.22e-31, 7.28e-773j
3.3363085813042798346e-07 - 1.7892307361157334568e-2727j 2.03e-62, 2.37e-804j
5.806885031492872697e-47 - 1.2660888936182550299e-2747j 3.14e-109, 3.68e-851j
4.1713370854790249918e-16 - 6.3782922956806880633e-2732j 4.84e-82, 5.66e-824j
0.033262174244872347072 + 1.392456855252016599e-2724j 7.11e-31, 8.32e-773j
0.069817812831553077707 + 2.9473148292352217118e-2724j 3.44e-23, 4.02e-765j
1.3119434944018708989e-29 - 8.9576972949975465546e-2738j 3.83e-98, 4.49e-840j
2.8573427151333664717e-85 - 1.9330999935116090068e-2767j 2.11e-123, 2.47e-865j
1.2547879323611798375e-05 + 1.2073107594666847152e-2726j 5.62e-61, 6.58e-803j
9.0442716285137858742e-55 - 9.8184166088751126621e-2752j 3.51e-113, 4.1e-855j
0.00010208696293727202537 + 3.7636274010701237349e-2726j 3.96e-58, 4.64e-800j
2.6849871855291809562e-35 + 3.6819831258949668822e-2741j 1.28e-103, 1.5e-845j
5.1749262866989775181e-40 - 7.2541590817218653593e-2744j 1.6e-106, 1.87e-848j
2.2657433780787871278e-32 + 3.4536350729482703139e-2739j 6e-102, 7.02e-844j
1.1230837342824527833e-41 + 8.8400553353819677418e-2745j 7.1e-108, 8.31e-850j
0.11028005964876819121 - 5.5409679169193323076e-2724j 1.67e-42, 1.96e-784j
9.3613218481931077374e-26 + 2.1237808863451704677e-2736j 7.82e-99, 9.16e-841j
2.1385612520569154468e-10 + 4.2065626448576847025e-2729j 1.91e-80, 2.23e-822j
8.1851531774614348971e-34 - 3.1630980445573473839e-2740j 2.85e-103, 3.33e-845j
2.7561042675079115541e-28 + 2.1325968314001733319e-2737j 4.99e-100, 5.84e-842j
1.2434864881223817975e-73 - 1.7481793497721715081e-2761j 9.77e-124, 1.14e-865j
2.1478646087364217948e-08 - 4.3536816084966496485e-2728j 1.06e-80, 1.24e-822j
1.5189207578035349214e-24 - 7.1201053112094046097e-2736j 4.46e-99, 5.22e-841j
7.8961365741014428711e-49 + 1.2960961985199733913e-2748j 8.35e-114, 9.77e-856j
5.1271387577186927788e-18 - 7.6400021574493661451e-2733j 5.18e-95, 6.06e-837j
5.0831528220968581089e-19 + 2.5333356266535785521e-2733j 7.32e-96, 8.56e-838j
0.011684440005386730683 + 6.3350127567366029401e-2725j 1.32e-69, 1.54e-811j
3.9949276603679255663e-06 - 6.5679610347744832855e-2727j 7.13e-81, 8.34e-823j
2.1810315760206667904e-43 - 1.0404800648262250594e-2745j 5.54e-111, 6.48e-853j
8.7466238846498486252e-08 + 8.9528906997434846832e-2728j 1.1e-83, 1.29e-825j
1.192460255512399325e-06 + 3.4761948668036926292e-2727j 3.62e-82, 4.24e-824j
0.050254308113204911366 - 2.0335813453296593838e-2724j 1.66e-69, 1.94e-811j
0.00064247759597921482378 + 1.0580551368412120698e-2725j 3.97e-78, 4.65e-820j
9.4509461703989113627e-51 - 1.2552955101756206994e-2749j 2.57e-116, 3e-858j
0.00026446343853490938687 - 6.3901262020443786334e-2726j 2.52e-79, 2.95e-821j
0.0062456488239456466485 - 4.1767017793308762595e-2725j 3.05e-76, 3.57e-818j
0.12601717214223839522 + 4.4743191831648674941e-2724j 2.25e-71, 2.63e-813j
0.13216156153537731168 - 3.0033561537174224074e-2724j 1.07e-71, 1.25e-813j
3.1245624049542878858e-22 - 7.9087245900735131286e-2735j 1.92e-100, 2.25e-842j
2.536056452247981735e-14 - 4.7329599748602378286e-2731j 1.72e-93, 2.02e-835j
7.9773560983595825451e-37 - 4.5902512975555310293e-2742j 2.58e-108, 3.02e-850j
3.9730528408043083774e-21 + 2.5718776083835559455e-2734j 1.13e-99, 1.32e-841j
0.099409245131760294626 + 5.3442288456567880844e-2724j 1.43e-79, 1.68e-821j
0.11931460847312915367 + 1.7741968093531838141e-2724j 1.01e-79, 1.19e-821j
3.5984569554052176042e-99 - 1.6002370025080582162e-2774j 1.65e-140, 1.93e-882j
5.7000550425694691306e-66 + 1.5251743498515865073e-2757j 8.5e-125, 9.95e-867j
2.2688172942408731363e-23 + 2.3870855613789888431e-2735j 3.93e-102, 4.6e-844j
0.087250805086687540205 - 8.635012556616443264e-2725j 5.06e-86, 5.92e-828j
0.087793084157953853155 - 4.1673839828604503232e-2724j 7.16e-86, 8.38e-828j
4.7984684673691816046e-17 + 2.239776800181265028e-2732j 1.51e-98, 1.77e-840j
0.040435523378111315737 + 2.4081310415132147393e-2725j 6.52e-88, 7.64e-830j
7.147797590999779708e-57 + 7.8682179792916593755e-2753j 4.95e-121, 5.8e-863j
9.9067003940946120073e-53 + 1.1457816978317629537e-2750j 6.54e-119, 7.65e-861j

Download

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