Rule: Q[3, 6, 43]

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)
171.98011435851273491 + 1.7462812619244957108e-2295j 2.14e-1004, 2.14e-1004j
134.88782368792684887 + 2.4087393236610043584e-2297j 1.65e-1000, 1.65e-1000j
117.65668861342030016 + 2.9340161554853596111e-2323j 5.4e-999, 5.4e-999j
156.95383060369821954 + 1.0347724505424718565e-2343j 9.16e-1003, 9.16e-1003j
125.84715890029944396 + 3.7186830696533965356e-2360j 1.04e-999, 1.04e-999j
30.084701751889232079 + 3.9504109997884904425e-2382j 3.76e-998, 3.76e-998j
145.07036994875330974 + 3.9966781302028517799e-2425j 1.69e-1001, 1.69e-1001j
65.007782391453765277 + 1.0905048956533348409e-2479j 2.13e-996, 2.13e-996j
12.802252846324662579 - 1.0983205298834971828e-2515j 8.47e-1003, 8.47e-1003j
18.21338567013583716 + 4.1824741018342194998e-2510j 1.9e-1000, 1.9e-1000j
5.5851793035623963442 - 3.3818650048263142866e-2529j 6.45e-1007, 6.45e-1007j
22.874547108557592398 + 1.2679101563480549684e-2530j 6.15e-999, 6.15e-999j
3.8343455071274751198 + 3.1025159198748012666e-2561j 4.07e-1009, 4.07e-1009j
90.610106812775586318 + 1.7375661719173325089e-2590j 3.36e-997, 3.36e-997j
96.6888594313743417 + 9.5674547560157816367e-2648j 1.54e-997, 1.54e-997j
3.0188972456229421288 + 2.8763208130006117016e-2699j 3.06e-1010, 3.06e-1010j
32.823234265053171035 - 5.6860532690262822806e-2693j 8.15e-998, 8.15e-998j
16.310510530938949131 + 3.8430015604083290427e-2720j 3.14e-1001, 3.14e-1001j
9.7500082014447782041 - 3.490091963304169007e-2743j 2.68e-1004, 2.68e-1004j
69.583437502413353 - 8.2134271612569996664e-2738j 1.94e-996, 1.94e-996j
25.069830484047890097 - 2.9732187214757018057e-2777j 9.14e-999, 9.14e-999j
1.656095027511132326 - 3.8616771498463233492e-2810j 3.05e-1012, 3.05e-1012j
103.17805301222012751 + 6.0204818067567002876e-2810j 6.07e-998, 6.07e-998j
27.497016059460416648 - 1.0301054915284917262e-2835j 1.78e-998, 1.78e-998j
79.503849284089274002 + 3.2698672975029308926e-2868j 1.01e-996, 1.01e-996j
21.386110825520344838 - 1.3391293179456735577e-2894j 3.87e-999, 3.87e-999j
1.2627083649697538623 - 2.1060244372388777921e-2930j 3.66e-1012, 3.66e-1012j
110.13953929576455404 + 1.3801207282786025769e-2918j 1.99e-998, 1.99e-998j
20.100257805743285241 - 5.7696932408314644769e-2960j 1.39e-999, 1.39e-999j
60.66401409191319811 + 1.3059951254985003443e-2985j 1.97e-996, 1.97e-996j
11.217580596169575199 + 1.0877873799562464513e-3032j 1.45e-1003, 1.45e-1003j
14.501292642300796639 + 3.5151472163355193507e-3027j 5.03e-1002, 5.03e-1002j
7.214526417044194217 + 2.6092961109907345307e-3036j 1.01e-1005, 1.01e-1005j
56.537139166049036992 + 2.5226525266820396413e-3053j 1.93e-996, 1.93e-996j
2.2942803602790417198 - 2.2414886404599990121e-3119j 2.35e-1011, 2.35e-1011j
52.614238490697834737 - 7.8929162599677562673e-3118j 1.4e-996, 1.4e-996j
74.40853490683410933 - 3.1228646089357677259e-3154j 1.38e-996, 1.38e-996j
0.19096887426093690763 + 2.6599793231158404444e-3191j 3.32e-1018, 3.32e-1018j
1.2340027043082441272 - 3.5994920849193460721e-3185j 3.36e-1012, 3.36e-1012j
41.964217990879297493 - 7.5460058854258528462e-3170j 4.44e-997, 4.44e-997j
48.884100521064765481 - 9.9716940198940706467e-3182j 1.07e-996, 1.07e-996j
4.7217020025043729408 - 2.0231444086202134719e-3212j 5.99e-1008, 5.99e-1008j
0.74417472753665332674 - 4.3719458252206065946e-3219j 3.91e-1015, 3.91e-1015j
0.013993151608491287585 - 1.124499318577302411e-3245j 6.91e-1021, 6.91e-1021j
38.758456826608755695 + 1.4046272588345665579e-3200j 2.94e-997, 2.94e-997j
45.336944814012373843 - 2.5218770225188176382e-3223j 7.47e-997, 7.47e-997j
35.713232334042475878 + 1.9143644227324005699e-3252j 1.46e-997, 1.46e-997j
0.066279617940602109847 + 1.5362852405025784664e-3299j 1.67e-1019, 1.67e-1019j
0.41577455678347908331 + 6.8473464073615585554e-3297j 1.03e-1016, 1.03e-1016j
6.2899450829374791969 - 5.4619878910723525625e-3278j 2.88e-1006, 2.88e-1006j
8.4063541772949054529 - 5.4817369992681005976e-3278j 4.71e-1005, 4.71e-1005j
84.894277114286279284 + 8.6628691475217103388e-3276j 6.21e-997, 6.21e-997j

Weights

Weight (ball center) Error (ball radius)
3.6314667825570449561e-74 - 7.2214617578452535386e-2365j 6.06e-196, 7.52e-947j
2.5055648113164449168e-58 - 3.2023379598926489036e-2355j 6.87e-191, 8.52e-942j
6.2536488985906728636e-51 - 3.0823291178329103202e-2352j 1.6e-188, 1.98e-939j
8.9529708845097949015e-68 + 2.7717064160312028227e-2361j 1.08e-194, 1.34e-945j
1.899853935113384873e-54 + 7.744518741707114169e-2354j 5.02e-190, 6.23e-941j
2.2899309110039862429e-13 + 1.8553273057801579881e-2331j 3.95e-165, 4.89e-916j
1.0821155662474077904e-62 - 2.885735618982933877e-2358j 5.6e-193, 6.94e-944j
2.6092951681635139278e-28 + 1.9480094413964117494e-2340j 4.9e-180, 6.08e-931j
4.5237189613736518733e-06 - 1.1447007902365874641e-2326j 1.42e-150, 1.76e-901j
2.37856952219963037e-08 + 7.032877066465885689e-2328j 4.99e-157, 6.18e-908j
0.0029070373682411251907 - 5.4465296422672287263e-2324j 3.62e-137, 4.49e-888j
2.3104411543452826946e-10 - 6.2024252693876695173e-2329j 3.17e-161, 3.93e-912j
0.018530656072934799443 - 9.122883759703270147e-2324j 1.21e-131, 1.5e-882j
2.6222208082387939082e-39 - 2.3235205693608304777e-2346j 1.2e-186, 1.49e-937j
6.3999751702128881544e-42 + 1.0112505177008973134e-2347j 9.89e-188, 1.23e-938j
0.037672446899318843272 + 1.5492487466600323261e-2323j 5.15e-132, 6.39e-883j
1.5643918647012675565e-14 - 2.9305093214637587697e-2332j 8.44e-170, 1.05e-920j
1.5353306637881391912e-07 - 1.5933658564960380774e-2327j 4.6e-158, 5.71e-909j
8.2049314674488212444e-05 - 1.0119215254665705772e-2325j 3.36e-151, 4.17e-902j
2.8322839913999160411e-30 - 1.6107945672215966934e-2341j 4.15e-183, 5.15e-934j
3.0252599805938645034e-11 + 8.0562231630068748044e-2330j 1.41e-165, 1.74e-916j
0.11737722914076842327 + 1.2559976867657321574e-2322j 1.34e-131, 1.66e-882j
1.0406213012128934389e-44 - 3.7383440166614767988e-2349j 1.89e-189, 2.35e-940j
2.8708026768069662165e-12 - 1.1857371539721316434e-2330j 1.13e-167, 1.41e-918j
1.5527773508461529765e-34 - 7.8958331923080303765e-2344j 7.26e-186, 9.01e-937j
5.2500030315581433057e-10 + 2.3515518540461231209e-2328j 1.5e-164, 1.86e-915j
-0.43760629275543206611 - 1.9238164699667905638e-2321j 3.66e-137, 4.54e-888j
1.0610380794666529548e-47 + 1.1638704896874795739e-2350j 7.08e-191, 8.78e-942j
3.2287223085158022852e-09 - 4.1754535202098088835e-2328j 3.46e-164, 4.29e-915j
1.9081067881153072065e-26 - 2.1325544541414403603e-2339j 1.87e-182, 2.32e-933j
2.0512492261513221511e-05 + 3.3208439804752729078e-2326j 1.27e-160, 1.57e-911j
8.8410577274647314896e-07 + 4.1311287872859833825e-2327j 1.6e-162, 1.99e-913j
0.00080179354547590994721 - 1.1876212392568294902e-2324j 3.07e-158, 3.81e-909j
1.1240103784323302978e-24 + 2.1294989737956959166e-2338j 3.23e-182, 4.01e-933j
0.068385227079329315232 - 3.284641382181803871e-2323j 3.21e-152, 3.98e-903j
5.4017288070709532645e-23 - 1.9535232628356389667e-2337j 7.97e-182, 9.89e-933j
2.3985750180820069364e-32 + 1.1957452635733372496e-2342j 2.01e-186, 2.49e-937j
0.14357656804865297164 - 8.2835811910156690317e-2323j 2.34e-154, 2.9e-905j
0.56770781204985320914 + 1.8835220476027283965e-2321j 1.21e-153, 1.51e-904j
1.9593631019616557428e-18 + 9.7086492219050534559e-2335j 4.96e-180, 6.15e-931j
2.14122883806874934e-21 + 1.6576561453465934907e-2336j 8.94e-182, 1.11e-932j
0.0080533592510025450589 + 6.5540768386985881329e-2324j 3.48e-164, 4.31e-915j
0.1817048868447488406 - 1.0569323404999780569e-2322j 7.86e-160, 9.75e-911j
0.032598159235065980094 - 3.2461942050608403798e-2323j 3.06e-160, 3.79e-911j
4.5940716253508075041e-17 - 6.8009432163433540368e-2334j 1.75e-179, 2.16e-930j
7.0683269234516401527e-20 - 1.3099491104007833229e-2335j 2.37e-181, 2.94e-932j
9.1671249186630382663e-16 + 4.5441722892724905869e-2333j 1.3e-178, 1.62e-929j
0.074394647039009838289 + 7.4875286201613743399e-2323j 2.32e-164, 2.87e-915j
0.18212730031275573445 + 8.3668036502574013131e-2323j 7.65e-165, 9.45e-916j
0.0013758667705532094479 + 3.4443932173272130105e-2324j 5.16e-169, 6.38e-920j
0.00028515212915386738222 + 3.3123698824628844615e-2325j 2.29e-170, 2.82e-921j
7.4986873115223595798e-37 + 4.5906842843042988289e-2345j 1.29e-191, 1.61e-942j

Download

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