Rule: Q[7, 83]

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)
335.31049514991220185 - 1.163687957911616415e-2508j 2.42e-994, 2.42e-994j
295.73528395794611396 - 4.2818266232120934013e-2497j 4.15e-990, 4.15e-990j
312.18621059943243358 + 1.1145262155184985426e-2503j 7.15e-992, 7.15e-992j
281.89958945408503055 - 7.1815189434395401918e-2508j 1.27e-988, 1.27e-988j
22.544224033911541575 + 5.3210509435864689963e-2542j 3.33e-990, 3.33e-990j
33.584988050881436268 - 3.0364477796549934936e-2530j 2.35e-986, 2.35e-986j
89.989871574014087913 + 2.8551398592003737655e-2566j 1.94e-978, 1.94e-978j
142.94760145826676598 + 6.4962165446688926272e-2653j 2.88e-978, 2.88e-978j
109.86717353214414636 - 5.095058596355973015e-2709j 6.34e-978, 6.34e-978j
69.521372914311646347 + 8.2468008463868252331e-2748j 6.53e-980, 6.53e-980j
248.27515160826353603 - 5.7576610951339188748e-2823j 2.7e-985, 2.7e-985j
171.37915343142821184 + 2.5090579764583954759e-2910j 1.78e-979, 1.78e-979j
31.575291873484806736 + 6.2511393146508398654e-2953j 5.94e-987, 5.94e-987j
19.395727862262540312 - 4.0333705795972698064e-2958j 1.27e-991, 1.27e-991j
25.955884706502290503 - 4.0301776996433506676e-2956j 7.26e-989, 7.26e-989j
47.138191888075219457 + 2.8752510365362719937e-2944j 4.42e-983, 4.42e-983j
205.41536063780608669 + 1.0403730345320944347e-2964j 1.23e-981, 1.23e-981j
148.26928801428269937 - 1.3623449504153958458e-2994j 1.93e-978, 1.93e-978j
37.814101496549529346 - 5.0294743688576807687e-3021j 3.48e-985, 3.48e-985j
269.65594100573496378 + 3.1961533450619916108e-3019j 2.21e-987, 2.21e-987j
15.169611063664827808 + 9.8327814674464172312e-3030j 9.94e-994, 9.94e-994j
27.761475251560641652 + 1.5631293433488452421e-3024j 3.38e-988, 3.38e-988j
20.937212665657050677 - 2.3823877476065323096e-3028j 6.63e-991, 6.63e-991j
16.510426335321076513 - 6.9448581810799239187e-3029j 4.68e-993, 4.68e-993j
177.67208711993232511 - 4.8360645720058295854e-3013j 8.01e-980, 8.01e-980j
66.432367335167668042 + 5.0053017616863466796e-3021j 3.3e-980, 3.3e-980j
213.11954700598506064 - 1.4772716965392183885e-3018j 2.91e-982, 2.91e-982j
75.966835705756814274 - 1.0991887019214897725e-3020j 2.49e-979, 2.49e-979j
123.21592245037089853 - 1.2578673108674134729e-3020j 6.97e-978, 6.97e-978j
29.634376978892445836 - 1.8008827533290706424e-3046j 1.43e-987, 1.43e-987j
190.98574178980757593 - 2.5646377792946969153e-3035j 1.21e-980, 1.21e-980j
9.1321111935817014003 + 9.0012770242670134728e-3073j 3.49e-998, 3.49e-998j
63.429905061708730507 + 2.4210593753550269455e-3052j 1.42e-980, 1.42e-980j
12.734180291797813758 - 1.4677661366298407561e-3071j 4.55e-995, 4.55e-995j
153.7627945912881367 - 1.8707270838307057472e-3052j 1.29e-978, 1.29e-978j
93.746303888682999661 + 3.7119925706937894888e-3077j 2.69e-978, 2.69e-978j
44.696298824167552346 + 8.4898805359980691987e-3113j 1.43e-983, 1.43e-983j
5.6320343138366162375 - 7.7426612102480452581e-3146j 2.45e-1002, 2.45e-1002j
127.92988838909164932 + 4.8872719436018364075e-3120j 6e-978, 6e-978j
60.512175959859020348 + 1.2111049096519818623e-3151j 6.51e-981, 6.51e-981j
132.78541037846358737 + 1.0744656717101024874e-3165j 5.17e-978, 5.17e-978j
137.78894070570827439 - 5.8832203733469780009e-3192j 4.11e-978, 4.11e-978j
17.919880352435447639 - 8.4664116540773500954e-3222j 2.52e-992, 2.52e-992j
11.734764085675378304 - 7.6687085391061030041e-3225j 1.13e-995, 1.13e-995j
57.677475874805182041 - 1.0499727984392296562e-3209j 2.61e-981, 2.61e-981j
238.70425659073893557 - 3.4933318318906307861e-3212j 2.01e-984, 2.01e-984j
221.20036607813533416 - 3.3876861266861837965e-3208j 6.13e-983, 6.13e-983j
13.9038434198866839 - 3.2732917788729631933e-3224j 1.77e-994, 1.77e-994j
0.77173781719034800365 + 8.7340735123964240425e-3242j 3.78e-1013, 3.78e-1013j
3.0706746051602605828 + 4.8785683335330024392e-3236j 1.86e-1006, 1.86e-1006j
229.70739749339109402 + 6.0597362017656613185e-3211j 1.25e-983, 1.25e-983j
1.6956635708255522545 + 1.6350193839838576767e-3238j 8.15e-1010, 8.15e-1010j
35.664294988654106916 - 6.6870069127461448969e-3215j 9.29e-986, 9.29e-986j
2.1092177761241466456 - 4.8458033255661648652e-3238j 1.15e-1008, 1.15e-1008j
3.6225720110045415576 - 9.0132765319555993465e-3235j 1.99e-1005, 1.99e-1005j
54.924199112180966806 - 9.9620471829858831017e-3211j 9.9e-982, 9.9e-982j
10.09185618413332224 - 3.4630105222607665208e-3226j 3.84e-997, 3.84e-997j
258.53612289414300454 + 7.6665135097010180358e-3215j 3.06e-986, 3.06e-986j
72.698846297006463809 - 3.2065217613902765285e-3208j 1.29e-979, 1.29e-979j
1.3328625660851441887 - 2.9188855871462921048e-3240j 6.18e-1011, 6.18e-1011j
79.327523556447616359 + 2.6468533527704073671e-3208j 4.48e-979, 4.48e-979j
114.18969637317270029 - 4.2341172300830769603e-3207j 7.48e-978, 7.48e-978j
184.20121880217266867 - 2.353264223180153462e-3225j 3.38e-980, 3.38e-980j
4.9003530845264845681 + 6.8429610696530432496e-3276j 2.28e-1003, 2.28e-1003j
10.951817421400228782 - 6.7169657341255830835e-3269j 2.89e-996, 2.89e-996j
0.54863077195885881332 - 6.7701870621982999863e-3287j 2.29e-1014, 2.29e-1014j
49.65594530358713701 + 9.4616748377320172388e-3255j 1.32e-982, 1.32e-982j
165.30589759283390322 + 4.2062928952822699232e-3250j 4e-979, 4e-979j
198.04819282327304334 - 2.5806868743184387332e-3275j 3.96e-981, 3.96e-981j
2.5678767449507462069 + 2.5355967024962739429e-3332j 1.47e-1007, 1.47e-1007j
0.35228963787527798604 + 3.9268839919418267085e-3340j 9.14e-1016, 9.14e-1016j
8.1821534445628607911 + 4.0598128939044684323e-3324j 2.96e-999, 2.96e-999j
24.216978826638513326 - 1.6534626712465386644e-3314j 1.6e-989, 1.6e-989j
118.6376440474194644 - 6.9189006928531074614e-3301j 7.67e-978, 7.67e-978j
7.2762756781710311308 + 7.7088002419509836028e-3352j 2.69e-1000, 2.69e-1000j
6.4248021925679197609 + 1.5951809201715109182e-3353j 2.46e-1001, 2.46e-1001j
42.329064666632473597 - 4.2945109383941622756e-3336j 4.39e-984, 4.39e-984j
159.43796796437987574 + 1.846637152550955411e-3329j 7.29e-979, 7.29e-979j
105.66556891484745 - 4.4325167276878815397e-3352j 5.69e-978, 5.69e-978j
52.250831692606526097 - 2.8315011504854478136e-3380j 3.69e-982, 3.69e-982j
1.0266648953391919503 - 3.891670553794090452e-3412j 5.24e-1012, 5.24e-1012j
0.015120759473525234328 + 1.3014923453426861411e-3418j 1.32e-1020, 1.32e-1020j
97.608825938035109776 + 4.1077714487946239882e-3376j 3.61e-978, 3.61e-978j
86.336467060095082537 + 1.7226169661584891326e-3390j 1.2e-978, 1.2e-978j
0.19304367656036241384 - 1.1298349296827070477e-3453j 2.86e-1017, 2.86e-1017j
40.035355439916946598 + 5.7364779579269698977e-3421j 1.23e-984, 1.23e-984j
0.079303878084330424251 + 9.903474951196394005e-3456j 7.19e-1019, 7.19e-1019j
4.2308887029025461017 + 4.040398423504262228e-3441j 2.16e-1004, 2.16e-1004j
82.783238191115045566 - 7.0305159802617882315e-3414j 7.39e-979, 7.39e-979j
101.58073109438542214 - 9.9376110667389299745e-3452j 4.91e-978, 4.91e-978j

Weights

Weight (ball center) Error (ball radius)
7.8413396134208632871e-145 + 6.3257902375418301605e-2614j 1.57e-130, 4.29e-869j
5.4531017837232641472e-128 + 1.3219194183942574135e-2605j 4.99e-126, 1.36e-864j
4.847698210917486403e-135 - 3.8941440814992763776e-2609j 3.6e-128, 9.85e-867j
4.8342482389486900532e-122 - 1.3217199123845766371e-2602j 1.26e-124, 3.45e-863j
2.6543991280104575815e-10 + 1.209887496758975305e-2542j 5.72e-34, 1.56e-772j
5.3061807003212004216e-15 + 9.5194091782181365461e-2545j 9.1e-49, 2.49e-787j
3.0663117066902638057e-39 - 1.4546182790080102257e-2559j 2.25e-85, 6.16e-824j
4.3438644490493296404e-62 - 9.3247698556139097233e-2572j 1.72e-102, 4.71e-841j
8.2193854008196904426e-48 + 3.4070218094837009797e-2564j 5.19e-93, 1.42e-831j
2.0100141497681723149e-30 - 1.1323592786057902319e-2554j 2.3e-77, 6.3e-816j
1.4818543039461445473e-107 + 3.0191435299128876483e-2595j 2.02e-122, 5.54e-861j
2.3014711807213214747e-74 + 3.6214481621952367772e-2578j 1.42e-109, 3.88e-848j
3.8249869787613529176e-14 - 2.6029584547893977238e-2544j 2.14e-51, 5.86e-790j
5.6905195246840193998e-09 + 7.7001555689500898986e-2542j 1.73e-36, 4.73e-775j
9.4624406111541394271e-12 + 2.0279321875513925738e-2543j 1.92e-45, 5.26e-784j
8.3661956436059893687e-21 - 5.5478854675339349424e-2549j 2.59e-66, 7.09e-805j
4.6347172766918377535e-89 - 9.0826755475284153415e-2586j 5.16e-117, 1.41e-855j
2.1895070224992362531e-64 + 5.8149544934269014519e-2573j 4.48e-105, 1.22e-843j
8.2616886033743797528e-17 - 3.3306204412303715234e-2546j 3.67e-60, 1e-798j
9.0228374727312186669e-117 + 6.1834345225590552135e-2600j 6.43e-126, 1.76e-864j
3.3691877301282819661e-07 - 1.3997885377155001284e-2540j 1.42e-34, 3.9e-773j
1.6142028202178770732e-12 - 8.7875362992514333867e-2544j 2.3e-50, 6.28e-789j
1.2710219307790644068e-09 - 3.034639317397376788e-2542j 1.71e-42, 4.67e-781j
9.292663419490881129e-08 + 5.1848086011166318326e-2541j 4.88e-37, 1.33e-775j
4.4128646943363499508e-77 - 1.4065729035834821378e-2579j 2.39e-112, 6.54e-851j
4.2898002498249025914e-29 + 6.4491285112858272658e-2554j 3.66e-81, 1e-819j
2.188608994653809559e-92 + 1.7664906713765410699e-2587j 3.54e-119, 9.7e-858j
3.3757487838628701963e-33 - 3.1251311204859204899e-2556j 4.3e-86, 1.18e-824j
1.4289208692257742899e-53 - 2.9082367854184102861e-2567j 9.55e-102, 2.61e-840j
2.5719082019994738731e-13 + 4.1912279274174762561e-2544j 2.96e-57, 8.09e-796j
7.8707368135381797993e-83 - 1.4858323869237892787e-2582j 1.08e-115, 2.95e-854j
0.00010430979063658366997 - 8.4028254964318372514e-2539j 2.53e-34, 6.93e-773j
8.3946977486495419347e-28 - 3.5489417057405726123e-2553j 1.22e-81, 3.35e-820j
3.2569944315603746285e-06 - 1.197713567206781551e-2539j 1.4e-41, 3.83e-780j
9.3004396564109316103e-67 - 3.3359222422220573348e-2574j 2.46e-108, 6.72e-847j
7.3672024623118176977e-41 + 1.9086604494210314115e-2560j 2.81e-94, 7.68e-833j
9.3249217973100901739e-20 + 2.6253027387287328712e-2548j 1.82e-73, 4.99e-812j
0.0027308202164590356117 - 3.8401253651135444677e-2538j 1.13e-30, 3.1e-769j
1.3198395542622913753e-55 + 2.4316782295899846714e-2568j 1.93e-103, 5.29e-842j
1.5089524842047144349e-26 + 1.8910215450934579312e-2552j 1.26e-82, 3.44e-821j
1.0586070356006527093e-57 - 1.8995603220646994512e-2569j 8.59e-105, 2.35e-843j
7.3261210466560088565e-60 + 1.3817363844993690506e-2570j 7.05e-106, 1.93e-844j
2.3807752519777956095e-08 - 1.9794055777287539654e-2541j 2.04e-56, 5.59e-795j
6.9775042532710186127e-06 + 3.3344385679747388868e-2539j 1.51e-50, 4.14e-789j
2.4955985301199894044e-25 - 9.7797148238196673254e-2552j 2.8e-83, 7.66e-822j
1.9908077308320337764e-103 - 3.8703065631702412493e-2593j 1.47e-128, 4.02e-867j
7.1150223062094244628e-96 - 2.8563791553798585131e-2589j 1.24e-125, 3.4e-864j
1.1201645151135366455e-06 + 3.9685257848189498587e-2540j 4.75e-58, 1.3e-796j
0.10906610321474564212 - 5.2863374034695613061e-2537j 2.24e-31, 6.12e-770j
0.024406975466940473903 - 1.9852866568643456621e-2537j 8.62e-39, 2.36e-777j
1.5165312301101551026e-99 + 3.7482773001124143179e-2591j 2.84e-127, 7.78e-866j
0.071436621800237366475 + 4.1348335687749201344e-2537j 2.23e-31, 6.12e-770j
6.8609047729244725039e-16 + 2.3234646556220894194e-2545j 5.28e-76, 1.44e-814j
0.052993124288657992543 - 3.3490110673244955215e-2537j 2.67e-35, 7.31e-774j
0.015467024885858791791 + 1.4010780874718596431e-2537j 3.53e-43, 9.66e-782j
3.8035185337356626408e-24 + 4.9225607022272902548e-2551j 2.63e-86, 7.2e-825j
3.8782726177185901904e-05 + 7.0526849018895584158e-2539j 1.59e-57, 4.36e-796j
5.5820582405876735988e-112 - 1.6827978285425135146e-2597j 5.96e-133, 1.63e-871j
8.6192377356484301367e-32 + 1.9173660042394784317e-2555j 2.97e-93, 8.13e-832j
0.088370325467114440026 - 4.9941681250118463222e-2537j 9.85e-39, 2.7e-777j
1.2049482768303065649e-34 + 4.8944897718874771122e-2557j 2.22e-96, 6.07e-835j
1.1219159984840293801e-49 - 3.4331084953008428365e-2565j 2.04e-106, 5.58e-845j
6.6906629094904742328e-80 + 4.8666912325055650862e-2581j 1.23e-120, 3.38e-859j
0.0052154671867759771643 + 6.0247577203453531559e-2538j 6.15e-59, 1.68e-797j
1.3525311861816415276e-05 - 5.7689100107926454637e-2539j 2.01e-65, 5.51e-804j
0.12188048053498735047 + 3.991169543816205409e-2537j 1.21e-47, 3.3e-786j
6.9546468833771105192e-22 + 1.1665057878339262618e-2549j 6.36e-88, 1.74e-826j
9.6475247230880481133e-72 - 8.3744635579958492134e-2577j 2.13e-117, 5.84e-856j
7.0257716204418505486e-86 + 3.9585726596550807468e-2584j 1.34e-123, 3.67e-862j
0.036843175148357719823 + 2.6421349377047920566e-2537j 7.19e-59, 1.97e-797j
0.12629865864104274565 - 2.5288762087746255556e-2537j 7.48e-54, 2.05e-792j
0.00026019184056050542132 + 1.1234813447285171561e-2538j 1.86e-68, 5.09e-807j
5.1834058899762123676e-11 - 4.8946776679138016039e-2543j 3.57e-78, 9.76e-817j
1.3512009095541471237e-51 + 3.259490105195451409e-2566j 1.73e-108, 4.73e-847j
0.00060851148868572018034 - 1.626706372714229144e-2538j 4.3e-69, 1.18e-807j
0.0013333499763018471446 + 2.4677971438868377984e-2538j 1.61e-68, 4.4e-807j
9.6411850398518645123e-19 - 1.2530402347633050163e-2547j 3.64e-88, 9.96e-827j
3.2969712821276739013e-69 + 1.7518293164276973459e-2575j 1.57e-116, 4.3e-855j
5.3369726619389280491e-46 - 3.193487352186262041e-2563j 3.2e-107, 8.75e-846j
5.3499619845029605726e-23 - 2.4196599759422708804e-2550j 1.01e-92, 2.76e-831j
0.099561060244256070899 + 5.6054416835611965471e-2537j 2.06e-70, 5.63e-809j
0.038183154453861603274 + 1.8103585612707661411e-2538j 6.92e-72, 1.89e-810j
1.5919874331706228838e-42 - 2.3852794475870821481e-2561j 4.58e-106, 1.25e-844j
1.151319586074553282e-37 + 1.0577999290186545574e-2558j 9.24e-104, 2.53e-842j
0.11333138524881142414 + 1.4187362285164699235e-2537j 2.07e-76, 5.66e-815j
9.2567167514078238231e-18 + 6.1833182398077164683e-2547j 1.71e-91, 4.69e-830j
0.082562518608887805193 - 6.6399749932268916811e-2538j 2.81e-77, 7.69e-816j
0.0092826178522286332316 - 9.3479469680015931816e-2538j 1.14e-79, 3.11e-818j
3.9108027504741172584e-36 - 7.353086200049463694e-2558j 5.84e-103, 1.6e-841j
3.0839853052474775794e-44 + 2.8336364400801445287e-2562j 2.54e-107, 6.94e-846j

Download

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