Rule: Q[2, 4, 70]

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)
226.36092839478484065 - 1.8366337280662922665e-2705j 1.39e-992, 1.39e-992j
252.56215850450859523 - 3.6050381679238208944e-2714j 2.08e-995, 2.08e-995j
270.16619520560549743 - 1.4839310068847445879e-2718j 2.29e-997, 2.29e-997j
215.48349898736262002 - 6.1803380448645786642e-2706j 1.73e-991, 1.73e-991j
238.5085485449005926 + 5.1979701315840523718e-2714j 7.19e-994, 7.19e-994j
164.77733527509056637 + 1.3572800583498043163e-2715j 3.74e-987, 3.74e-987j
187.75215276611139823 - 8.4385419298576934254e-2723j 5.93e-989, 5.93e-989j
85.334055928757234647 - 2.2507286610057609611e-2723j 1.18e-984, 1.18e-984j
81.397173241365518059 + 8.4296618807939031326e-2724j 8.59e-985, 8.59e-985j
19.859350560854749989 + 5.1592549171317149605e-2734j 1.13e-994, 1.13e-994j
12.486507079040894342 - 2.6452462065556973617e-2738j 1.74e-998, 1.74e-998j
40.539224746797960776 - 4.8764702830846624468e-2728j 9.3e-989, 9.3e-989j
205.54525147193203054 + 5.0536948832384101154e-2726j 1.54e-990, 1.54e-990j
70.336754676198381618 + 2.6963144250736638467e-2724j 2.68e-985, 2.68e-985j
21.56170305749718165 + 1.6642032365637509368e-2734j 6.15e-994, 6.15e-994j
89.403744305436061994 - 1.4649594439027821028e-2722j 1.43e-984, 1.43e-984j
48.434827142330530379 - 1.7154024478830192545e-2733j 1.84e-987, 1.84e-987j
23.342231978271849809 + 5.3201105436811565503e-2739j 2.59e-993, 2.59e-993j
66.886357374431463433 - 1.689097821248422921e-2730j 1.63e-985, 1.63e-985j
93.611560772845363098 - 2.1621931747403595207e-2728j 1.64e-984, 1.64e-984j
60.318849123212608738 - 2.5483649429727699407e-2738j 4.92e-986, 4.92e-986j
15.211605840957686646 + 1.6542966416182832892e-2749j 6.82e-997, 6.82e-997j
63.548126528225785563 - 2.9006271420904617268e-2738j 9.46e-986, 9.46e-986j
196.34583059125643826 - 1.1058439392743134922e-2736j 1.05e-989, 1.05e-989j
73.902792693399688441 + 2.9343668281683698186e-2750j 4.41e-985, 4.41e-985j
43.078441954441360553 + 5.6794106176537885708e-2762j 2.78e-988, 2.78e-988j
8.9398109063601558453 + 7.1533836583581646119e-2775j 5.35e-1001, 5.35e-1001j
31.267774725463357241 - 4.5103259643208436758e-2765j 7.72e-991, 7.72e-991j
54.175460281201165012 - 2.1653922502070862373e-2758j 1.08e-986, 1.08e-986j
172.02962391827567397 - 2.3883251513523680736e-2793j 1.09e-987, 1.09e-987j
107.12535153897569545 - 3.0069907615491696776e-2853j 1.54e-984, 1.54e-984j
18.23418324815800885 + 2.1137532098334901524e-2909j 2.29e-995, 2.29e-995j
1.8998162242971575852 + 7.3860903585997880962e-2925j 3.61e-1010, 3.61e-1010j
51.25601701231317251 - 4.7879068714924232866e-2899j 4.93e-987, 4.93e-987j
33.456009679419150607 - 3.7298855171058020792e-2927j 2.91e-990, 2.91e-990j
122.13430560174064995 - 1.8471969803157538611e-2948j 6.51e-985, 6.51e-985j
25.2019756575098219 - 2.6176537772318818454e-3006j 1.2e-992, 1.2e-992j
2.4183163745933149701 + 2.092145482923001005e-3027j 7.92e-1009, 7.92e-1009j
13.812337970630723749 - 4.1136771888858175212e-3016j 1.1e-997, 1.1e-997j
27.142028947015752249 - 5.1920568277862338192e-3003j 5.22e-992, 5.22e-992j
102.46557024489394454 + 1.6409314285828813086e-3000j 1.69e-984, 1.69e-984j
1.4402805525273090019 + 2.7642361492600815391e-3074j 2.04e-1011, 2.04e-1011j
138.91319133308506102 - 4.6142379827830272212e-3046j 1.37e-985, 1.37e-985j
7.897715395350053879 - 3.5917169296907916131e-3103j 6.84e-1002, 6.84e-1002j
179.670024906429477 - 1.6991068252337455206e-3085j 2.81e-988, 2.81e-988j
77.588236026170312401 + 2.4797137428174632774e-3116j 6.47e-985, 6.47e-985j
45.709661979300971195 - 9.5310338177702464567e-3153j 7.57e-988, 7.57e-988j
111.95063675830084872 - 1.0931935179594324642e-3202j 1.26e-984, 1.26e-984j
0.47193845768537280597 + 3.5821959831991598809e-3309j 1.05e-1014, 1.05e-1014j
5.1788322725793102764 + 2.0105365023012082405e-3294j 1.68e-1004, 1.68e-1004j
151.27593948282694718 - 3.388379994761580147e-3278j 2.93e-986, 2.93e-986j
3.7405574569087369047 - 2.4594614284690395564e-3365j 6.33e-1006, 6.33e-1006j
11.233150964500157666 - 1.3404189639001355684e-3346j 2.6e-999, 2.6e-999j
6.0177132910765452722 - 1.3751695929999125581e-3359j 1.21e-1003, 1.21e-1003j
2.983179817722995532 - 8.2039591783955374145e-3369j 2.16e-1007, 2.16e-1007j
97.963353205365308951 + 8.4115585553370522728e-3358j 1.69e-984, 1.69e-984j
133.10198664049595423 + 3.7410758179251265458e-3446j 2.52e-985, 2.52e-985j
38.090194658484202968 - 2.9326487794021225983e-3493j 3.06e-989, 3.06e-989j
144.96455184107457405 + 2.085892996917724626e-3537j 6.89e-986, 6.89e-986j
1.0406748406401594478 - 3.73729169143535462e-3639j 1.23e-1012, 1.23e-1012j
10.051267193763907511 - 3.9608949647523480737e-3617j 3.85e-1000, 3.85e-1000j
127.51392687077237614 + 7.6599470465842904496e-3610j 4.32e-985, 4.32e-985j
157.87083180568366307 - 9.219878016925522985e-3660j 1.15e-986, 1.15e-986j
6.9239565457104964806 - 9.8651344908375894664e-3697j 9.25e-1003, 9.25e-1003j
29.163551409988713763 + 5.1366291256327890982e-3685j 2.07e-991, 2.07e-991j
4.4099626576024234506 - 1.874945109148916453e-3699j 2.71e-1005, 2.71e-1005j
16.685245850252006032 - 7.3606531745373933268e-3691j 4.16e-996, 4.16e-996j
0.018882491139866418489 + 5.3755727591680634376e-3714j 1.53e-1020, 1.53e-1020j
57.19554810081711874 - 1.080178663069101492e-3678j 2.59e-986, 2.59e-986j
0.68375466082899932417 - 3.3273543927097860362e-3713j 1.67e-1013, 1.67e-1013j
0.5857864376269049512 + 5.9100395342071109762e-3713j 8.46e-1014, 8.46e-1014j
35.729653052484682017 + 3.4738214894678529575e-3689j 9.49e-990, 9.49e-990j
116.95029846259003806 - 8.1193633454089286239e-3684j 9.23e-985, 9.23e-985j
0.099638285724864144836 + 1.8741983212887531924e-3728j 8.89e-1019, 8.89e-1019j
0.24603012782415396459 + 6.7611610645440807405e-3727j 6.1e-1017, 6.1e-1017j
3.4142135623730950488 - 1.250353918390934746e-3716j 2.12e-1006, 2.12e-1006j

Weights

Weight (ball center) Error (ball radius)
5.6385037509981196605e-98 - 1.8669403406185661021e-2789j 9.93e-146, 5.01e-891j
3.1677427417064384325e-109 - 2.9420906628676559348e-2795j 1.21e-149, 6.1e-895j
9.6621757353742160122e-117 + 4.0032843551482270589e-2799j 2.85e-152, 1.44e-897j
2.7060913708567727965e-93 + 4.919231269423594912e-2787j 3.3e-145, 1.67e-890j
3.3837671478631823224e-103 + 3.7624485349187858177e-2792j 5.89e-148, 2.97e-893j
1.9396465855393319828e-71 + 1.1553208079666016436e-2775j 2.55e-139, 1.29e-884j
2.4023622822687459491e-81 - 7.8004751734562999023e-2781j 1.77e-142, 8.93e-888j
3.4850988762094899644e-37 - 2.263137985422701945e-2757j 3.72e-122, 1.88e-867j
1.7282532306835940247e-35 + 1.948421718832867743e-2756j 6.03e-121, 3.04e-866j
3.946772128987682704e-09 + 2.2967577549725063513e-2741j 5.69e-83, 2.87e-828j
4.8705351583026471064e-06 - 2.1030540107152058914e-2739j 3.52e-70, 1.78e-815j
6.1788183352400176929e-18 + 1.7002382877497723675e-2745j 3.08e-103, 1.55e-848j
5.1580618379352714072e-89 - 8.1123578360865876492e-2785j 6.15e-146, 3.1e-891j
9.9574364837783446194e-31 - 1.1145332032374851108e-2753j 3.92e-118, 1.97e-863j
7.5290111000817524555e-10 - 9.7037148614941214938e-2742j 2.16e-87, 1.09e-832j
6.1548742728807288927e-39 + 2.4638218281013547494e-2758j 2.18e-124, 1.1e-869j
2.5582521503481406795e-21 + 4.8956927165489369054e-2748j 1.1e-109, 5.54e-855j
1.3263526793400686711e-10 + 3.5024835956049898507e-2742j 6.5e-91, 3.28e-836j
3.0360219724781830876e-29 + 7.3896787986659479475e-2753j 2.19e-117, 1.1e-862j
9.4696934939512353137e-41 - 2.4988486925382084582e-2759j 7.9e-127, 3.98e-872j
2.0216752510897169639e-26 + 3.1549194165009022157e-2751j 6.96e-116, 3.51e-861j
3.5557279910637732982e-07 - 3.7052272577342182951e-2740j 9.72e-86, 4.9e-831j
8.2737390800871413755e-28 - 4.8562677607894273151e-2752j 9.03e-117, 4.55e-862j
4.7469691616654322558e-85 + 9.25242900776705363e-2783j 2.71e-149, 1.37e-894j
2.9089980064132959378e-32 + 1.1905947470533680027e-2754j 1.17e-120, 5.88e-866j
5.0549293303754264183e-19 + 2.8978081575918884562e-2746j 3.12e-110, 1.57e-855j
0.00014110526530211453061 + 2.4653311998036697191e-2738j 1.39e-80, 6.99e-826j
5.6520819326073329451e-14 + 6.1425435472473904243e-2744j 8.26e-105, 4.16e-850j
8.8015333765353345304e-24 + 1.2482827435110672391e-2749j 5.88e-115, 2.97e-860j
1.44533204122885874e-74 - 2.6721839329979456733e-2777j 1.78e-147, 8.99e-893j
1.4188401536661679894e-46 + 1.7350982063591527668e-2762j 9.05e-135, 4.56e-880j
1.9122433830535565278e-08 - 5.8374429124233070878e-2741j 2.62e-96, 1.32e-841j
0.073237448512516477549 + 6.160982846643163958e-2736j 2.37e-60, 1.2e-805j
1.5763994040971346987e-22 - 7.7418473263642898858e-2749j 1.57e-114, 7.9e-860j
6.5868921671995001961e-15 - 2.2965197637186239926e-2744j 5.52e-108, 2.79e-853j
4.7903121496304297773e-53 - 5.9021781662926875386e-2766j 1.02e-139, 5.14e-885j
2.1558003962505123744e-11 - 1.28722206801930561e-2742j 2.67e-103, 1.35e-848j
0.048645848325433376977 - 6.142222638065056844e-2736j 3.17e-71, 1.6e-816j
1.3667209807361230133e-06 + 8.9265220897777462677e-2740j 3.15e-95, 1.59e-840j
3.2296906709249666581e-12 + 4.6769162651295888655e-2743j 7.02e-105, 3.54e-850j
1.4474704334822997263e-44 - 2.1087305301715786397e-2761j 7.5e-134, 3.78e-879j
0.10169802387433955565 - 7.4029473212292330308e-2736j 4.16e-69, 2.1e-814j
2.7777464842444250973e-60 + 8.5075233600561192085e-2770j 1.32e-144, 6.68e-890j
0.00037447713169649217975 - 5.4717977326474774858e-2738j 9.55e-94, 4.81e-839j
7.3322060148013301554e-78 + 5.0962042972710562477e-2779j 7.88e-151, 3.97e-896j
7.5418979447439430088e-34 - 1.5874322346592106823e-2755j 2.52e-126, 1.27e-871j
3.7699322514733366497e-20 - 3.3327239127747629192e-2747j 5.88e-117, 2.97e-862j
1.1792832499378347561e-48 - 1.3192774835912968952e-2763j 9.26e-138, 4.67e-883j
0.19623563882781932737 - 3.240578166278193254e-2735j 4.17e-82, 2.1e-827j
0.0045348509355873051699 + 6.6347101419915675285e-2737j 3.09e-96, 1.56e-841j
1.2917504086406240153e-65 + 1.3132981278754788798e-2772j 1.47e-147, 7.4e-893j
0.013412365313929076659 + 7.3121886756420531504e-2736j 3.2e-94, 1.61e-839j
1.6104800405639575653e-05 + 4.8563889059245015085e-2739j 8.99e-104, 4.53e-849j
0.0021250789090648464995 - 2.7617376765444870675e-2737j 9.17e-99, 4.62e-844j
0.028815995215892444667 + 8.5534593654765236774e-2736j 6.43e-93, 3.24e-838j
1.2619887509532977279e-42 + 2.3783991788552295264e-2760j 7.11e-134, 3.58e-879j
8.9163740743262299227e-58 - 1.8051531661986562629e-2768j 3.86e-144, 1.95e-889j
6.8970853908072753458e-17 - 4.8365616841908548622e-2745j 1.07e-119, 5.38e-865j
6.8159788158412154646e-63 - 3.5636088143066187028e-2771j 9.32e-147, 4.7e-892j
0.13094724710008860722 + 1.10287604813664456e-2735j 7.39e-98, 3.73e-843j
4.9449450730565504976e-05 - 1.1018665885716094319e-2738j 2.71e-109, 1.36e-854j
2.2924995096594573969e-55 + 3.4341343840282884322e-2767j 3.37e-143, 1.7e-888j
1.8475116801571161551e-68 - 4.2075764579105433368e-2774j 1.37e-149, 6.88e-895j
0.00092479027352941866613 + 1.216918645383905454e-2737j 6.87e-110, 3.46e-855j
4.4551102816986479175e-13 - 1.6900541892177451634e-2743j 1.29e-119, 6.5e-865j
0.0088791900058974023024 - 1.842831946334112759e-2736j 4.04e-109, 2.04e-854j
8.5702383757110162212e-08 + 1.4993929619567536767e-2740j 2.38e-115, 1.2e-860j
0.047565983672979714786 + 4.8895054777601904706e-2737j 1.52e-109, 7.66e-855j
4.4422637430752607681e-25 - 2.0024125605831703196e-2750j 2.8e-127, 1.41e-872j
0.20973508494009762468 - 4.8023206247272173849e-2735j 5.13e-109, 2.59e-854j
-0.11820597713928171912 + 6.9513002746067761492e-2735j 6.33e-109, 3.19e-854j
7.0421317403898613566e-16 + 9.3045886985371138337e-2745j 5.16e-122, 2.6e-867j
8.2386235799123949644e-51 + 9.2256367835902807731e-2765j 2.83e-141, 1.43e-886j
0.10247852392661379317 - 1.9811779634050270107e-2736j 4.23e-112, 2.13e-857j
0.14108032161642038131 + 5.5473789514769541156e-2736j 7.59e-112, 3.81e-857j
0.007301746529576221652 - 1.1277844467175423685e-2735j 3.83e-112, 1.96e-857j

Download

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