Rule: Q[8, 54]

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)
211.80748257814393773 + 1.8100728418751014665e-2107j 1.23e-1001, 1.23e-1001j
171.70489816081899767 + 2.4582401159759013445e-2099j 2.78e-997, 2.78e-997j
182.77055484830851366 - 2.9888446682878965117e-2127j 1.96e-998, 1.96e-998j
161.83732206495555998 - 1.5861434850094551167e-2209j 2.4e-996, 2.4e-996j
152.85867187103955289 - 3.017947205589316e-2315j 1.52e-995, 1.52e-995j
17.283835708493610202 + 3.5279308400960848318e-2408j 4.15e-998, 4.15e-998j
79.449830526088481166 - 3.3162251371081092034e-2499j 1.23e-991, 1.23e-991j
9.4996167350771949103 - 3.1665207823686255259e-2550j 8.8e-1002, 8.8e-1002j
22.863131736889264106 + 1.4660280101992875858e-2552j 1.15e-996, 1.15e-996j
84.042076884368834844 + 8.7342697450732552357e-2572j 1.18e-991, 1.18e-991j
29.462627452716917318 + 1.0482104011995315682e-2595j 3.2e-995, 3.2e-995j
48.908763754814499775 - 4.3496336080926363353e-2592j 1.12e-992, 1.12e-992j
27.152912617380153889 + 2.7498393615401572167e-2619j 1.15e-995, 1.15e-995j
7.9013854683955204993 + 5.1741683068039010836e-2630j 1.17e-1002, 1.17e-1002j
24.953349691931163332 + 4.0494391683655979737e-2623j 3.58e-996, 3.58e-996j
52.194445581764792501 - 4.0618349898742470173e-2618j 1.86e-992, 1.86e-992j
5.1152694741800666288 + 1.4295719233081631718e-2653j 3.27e-1006, 3.27e-1006j
37.071606224136948737 - 1.5096803230701063494e-2638j 5.88e-994, 5.88e-994j
144.58164210921630237 - 8.714230361848483183e-2652j 7.28e-995, 7.28e-995j
195.62743432060161867 + 1.0394178482795215956e-2670j 8.61e-1000, 8.61e-1000j
15.740678641278004578 - 2.9245023755303070253e-2691j 1.63e-998, 1.63e-998j
2.8367386770481438235 + 6.179494732142411905e-2700j 1.54e-1009, 1.54e-1009j
14.515357418934913783 - 3.4631651108420310247e-2691j 6.47e-999, 6.47e-999j
88.839270545267297706 - 1.1390012251660068867e-2682j 9.51e-992, 9.51e-992j
110.38845804481330555 - 7.4501171907373433942e-2702j 1.58e-992, 1.58e-992j
13.388671045798874628 - 2.3475497305265352031e-2716j 1.83e-999, 1.83e-999j
7.0459054023934656973 - 2.8197153896264935699e-2720j 9.87e-1004, 9.87e-1004j
39.843075044110005662 - 3.8696403043277277484e-2710j 1.4e-993, 1.4e-993j
62.911268944197082414 - 3.5225090220997477063e-2707j 6.54e-992, 6.54e-992j
59.190041211250979057 - 4.9293769606868692934e-2709j 5.31e-992, 5.31e-992j
31.884134001489790387 + 1.1314443673338658451e-2718j 1.01e-994, 1.01e-994j
6.0481856386490510059 + 2.4887331691259627712e-2729j 5.28e-1005, 5.28e-1005j
1.7392379621587989343 - 1.6561876047085265084e-2737j 8.91e-1012, 8.91e-1012j
42.737280005055833105 + 1.971484319511758186e-2717j 2.91e-993, 2.91e-993j
34.41960218152030489 + 1.5138847042959438741e-2718j 2.61e-994, 2.61e-994j
122.88323874949286733 - 3.6478813604239644318e-2715j 3.01e-993, 3.01e-993j
12.086183977398051599 + 1.5770012596569443939e-2747j 2.85e-1000, 2.85e-1000j
0.90370177679937991219 + 4.6488484229261756391e-2762j 3.61e-1014, 3.61e-1014j
1.2907516423859763463 - 3.5329902406236110093e-2760j 5.71e-1013, 5.71e-1013j
99.105691541534308176 - 9.4152344715297888213e-2738j 4.57e-992, 4.57e-992j
3.5070346595129127503 - 6.5828825818733345303e-2790j 1.88e-1008, 1.88e-1008j
66.790037433986373856 + 2.2268140115469736234e-2772j 9.32e-992, 9.32e-992j
8.4277459928670801772 + 2.5464634886566814447e-2822j 2.94e-1002, 2.94e-1002j
20.883059871410511712 - 9.4519984011495379741e-2817j 3.69e-997, 3.69e-997j
75.050548122017719522 + 8.9423007723776663489e-2810j 1.21e-991, 1.21e-991j
55.619748610745158283 + 1.0838720721681373743e-2851j 3.29e-992, 3.29e-992j
104.60945538797822258 + 6.5062680358200992358e-2906j 2.87e-992, 2.87e-992j
93.855167433635232673 + 1.2280806840672190244e-2952j 6.88e-992, 6.88e-992j
4.2667001702876587936 + 1.0195703597661006756e-2993j 2.47e-1007, 2.47e-1007j
19.017805062892713293 + 3.2696184783462048941e-2984j 1.2e-997, 1.2e-997j
0.17027963230510099979 - 2.8946453511752895431e-3003j 5.2e-1018, 5.2e-1018j
45.757843851329816857 + 1.3871946187640955277e-2977j 6.25e-993, 6.25e-993j
0.017301665014485987071 + 7.9711438815335979835e-3017j 1.22e-1020, 1.22e-1020j
2.2510866298661306893 + 1.0396385542438148362e-3006j 1.09e-1010, 1.09e-1010j
0.077552300892043356563 - 5.9155635282290503491e-3016j 3.69e-1019, 3.69e-1019j
116.46904200869167073 - 6.2502782255952210492e-2987j 7.43e-993, 7.43e-993j
136.88171905783907437 + 1.6416540927966853008e-3021j 3.16e-994, 3.16e-994j
70.833713355340975758 - 7.0969486765878650054e-3058j 1.16e-991, 1.16e-991j
0.33614852614075702719 - 8.3065414273080954313e-3109j 8.25e-1017, 8.25e-1017j
0.58317690138887931733 + 7.628635468951922289e-3108j 1.61e-1015, 1.61e-1015j
10.758516010180995224 + 2.1002357373630861708e-3093j 4.57e-1001, 4.57e-1001j
129.6707185034191929 + 3.3289374011693379222e-3083j 1.01e-993, 1.01e-993j

Weights

Weight (ball center) Error (ball radius)
1.9694754465019040507e-91 - 2.1209855370999908327e-2183j 1.21e-178, 5.22e-928j
2.7960120346623272333e-74 - 3.5827676625757389295e-2173j 2.06e-173, 8.87e-923j
4.9714518276218466352e-79 - 2.0858043334932189721e-2176j 3.74e-175, 1.61e-924j
4.8680985690429679468e-70 + 1.1411018692327413116e-2171j 1.95e-172, 8.39e-922j
3.539772846158021258e-66 - 6.2803282668438154379e-2170j 1.58e-171, 6.8e-921j
5.1595769427820895266e-08 + 1.8154119022097838058e-2137j 7.35e-122, 3.16e-871j
1.4060483636539705028e-34 - 9.4105570624609449031e-2154j 3.28e-158, 1.41e-907j
9.0124597126688875854e-05 + 7.5357125870040687442e-2135j 5.19e-109, 2.23e-858j
2.3951644127500809008e-10 - 1.9021384834424086708e-2139j 1.91e-129, 8.23e-879j
1.4873119009946600206e-36 + 8.2071075175612799552e-2155j 1.31e-159, 5.63e-909j
3.7881515681120505657e-13 + 2.0867509145272222344e-2141j 3.93e-136, 1.69e-885j
1.8480616221057771644e-21 - 1.7707043974447169604e-2146j 1.6e-148, 6.91e-898j
3.6364261338267999775e-12 - 9.5513347669334136017e-2141j 2.18e-134, 9.39e-884j
0.0002008797000103592279 + 4.5453843741175706568e-2134j 1.18e-110, 5.08e-860j
3.1210094444875486223e-11 + 4.284992232809274055e-2140j 1.3e-132, 5.59e-882j
7.2091904764286692341e-23 + 2.7489622761394694445e-2147j 1.45e-150, 6.25e-900j
0.0053556801346599792912 - 4.3849454879840161485e-2134j 4.31e-105, 1.86e-854j
2.153628066109589084e-16 - 1.8084360685945918146e-2143j 5.88e-143, 2.53e-892j
1.2897996897090227969e-62 + 3.2322981599204821044e-2168j 1.55e-174, 6.65e-924j
1.5469217704440782008e-84 + 1.3292007758348118725e-2179j 2.27e-182, 9.79e-932j
2.0459359646687934936e-07 - 8.4555913519898512945e-2137j 1.02e-127, 4.38e-877j
0.036730151108874968148 + 1.331335373300609391e-2133j 2.56e-101, 1.1e-850j
5.3888592653370275661e-07 + 2.6703489029928349729e-2136j 1.17e-126, 5.06e-876j
1.282782966128761496e-38 - 6.5217142898761750762e-2156j 2.35e-164, 1.01e-913j
6.7856089020688996984e-48 - 8.9267384009682363267e-2161j 4.04e-170, 1.74e-919j
1.8820249258044774119e-06 - 5.4617824151893236532e-2136j 3.02e-127, 1.3e-876j
0.00087672901136642022942 - 3.6018228052376172425e-2134j 1.27e-118, 5.48e-868j
1.4076864712095428695e-17 + 3.4365163950137289766e-2144j 1.61e-147, 6.95e-897j
1.8098132351253958317e-27 - 7.1298233476991720208e-2150j 5.22e-158, 2.25e-907j
7.1739040391751043768e-26 + 5.5351529501350908869e-2149j 1.37e-156, 5.89e-906j
3.5238184879241943168e-14 - 4.4366776551493790801e-2142j 2.66e-144, 1.15e-893j
0.0022950261824390812163 + 3.4857529189053827338e-2134j 7.8e-123, 3.35e-872j
0.084138861424357715333 + 2.4173870259433249798e-2133j 9.05e-111, 3.89e-860j
8.1329814754055600178e-19 - 6.2400647528131265689e-2145j 2.76e-150, 1.19e-899j
2.9214977273915936664e-15 + 9.1275519003663064559e-2143j 6.7e-146, 2.88e-895j
2.8287931177275660485e-53 - 1.5344826128098716925e-2163j 1.25e-175, 5.38e-925j
7.5493504190195163624e-06 + 1.0471943707616007615e-2135j 3.65e-134, 1.57e-883j
0.1437618652916726267 + 3.4134971892360134858e-2133j 3.7e-116, 1.59e-865j
0.11504156938830059818 - 2.9253558036003226432e-2133j 3.69e-116, 1.59e-865j
4.8890609338149550869e-43 - 3.0351926394103327318e-2158j 2.53e-170, 1.09e-919j
0.02143137511475060233 - 9.0758626913487833803e-2134j 2.07e-125, 8.92e-875j
3.9006976126598386421e-29 + 8.5682147762788052217e-2151j 2.31e-161, 9.92e-911j
0.00017939118269580620686 - 3.1402704376127430263e-2134j 1.03e-132, 4.44e-882j
1.6398488177993107653e-09 + 8.4647918304023558204e-2139j 1.03e-142, 4.44e-892j
1.0966725893240662688e-32 + 9.8876878570885264702e-2153j 5.13e-164, 2.21e-913j
2.4452767932509296905e-24 - 4.0239398064408423361e-2148j 9.78e-158, 4.21e-907j
2.0881851616091381332e-45 + 1.75094787311458125e-2159j 2.15e-172, 9.24e-922j
8.8995054874456091342e-41 + 4.6923216193892472281e-2157j 1.55e-169, 6.65e-919j
0.011285536048183162271 + 6.1683992938067815626e-2134j 2.05e-137, 8.8e-887j
9.9300791842844800057e-09 - 3.8450529184103964556e-2138j 5.6e-146, 2.41e-895j
0.10436880312104751095 - 5.5592275590924422391e-2133j 1.41e-135, 6.07e-885j
4.1388732303249423033e-20 + 1.0789780282244424819e-2145j 4.5e-156, 1.93e-905j
0.042042539149947610659 - 1.2862879234706148141e-2133j 3.89e-136, 1.67e-885j
0.057550390452290804339 - 1.862786874183094768e-2133j 7.52e-138, 3.24e-887j
0.067106451054144471496 + 4.1792069069897569001e-2133j 6.29e-136, 2.71e-885j
1.6346554816942309856e-50 + 3.9806017027907836932e-2162j 6.91e-176, 2.97e-925j
2.6593284228886262668e-59 - 1.3987389447389353466e-2166j 3.2e-181, 1.38e-930j
7.1307125501813574145e-31 - 9.5685644180698190319e-2152j 1.17e-165, 5.03e-915j
0.14845608231276640271 + 4.8327922779172083312e-2133j 1.08e-143, 4.64e-893j
0.15905060203812676089 - 3.9980813913572223811e-2133j 4.13e-144, 1.77e-893j
2.7704391893009482548e-05 - 2.4484818570188460832e-2135j 2.73e-148, 1.16e-897j
3.3821032688721979881e-56 + 5.0481422220882135707e-2165j 1.28e-179, 5.51e-929j

Download

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