Rule: Q[3, 6, 44]

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)
179.49004112641252265 - 2.6105509128691973917e-2159j 3.11e-1004, 3.11e-1004j
151.4386892266670393 - 1.1569637959110069325e-2155j 3.12e-1001, 3.12e-1001j
163.77798916613745605 - 9.4226494603363585645e-2158j 1.56e-1002, 1.56e-1002j
131.56573815569170774 + 1.7315703155712155155e-2151j 2.21e-999, 2.21e-999j
123.11786680162866341 + 2.6747180449311258923e-2156j 1.15e-998, 1.15e-998j
16.317777875280653778 + 1.4948288882765525156e-2172j 4.38e-1001, 4.38e-1001j
95.253335431099332443 + 5.1937535916011211512e-2167j 7.74e-997, 7.74e-997j
20.249362409281220613 - 2.0006933363107701936e-2186j 3.37e-999, 3.37e-999j
27.323594806273701076 - 2.8078655606183119023e-2183j 3.05e-998, 3.05e-998j
11.216457343676777944 - 5.2109598208770700238e-2192j 1.83e-1003, 1.83e-1003j
24.886861090416336276 - 1.0141566118692913236e-2186j 1.61e-998, 1.61e-998j
108.19852013369276402 + 3.9243899986004530685e-2184j 1.33e-997, 1.33e-997j
3.8343455071274751198 - 2.3939580904195704493e-2215j 4.24e-1009, 4.24e-1009j
12.800686624585077831 - 6.2658994221798135831e-2209j 1.12e-1002, 1.12e-1002j
115.3703159959694064 + 5.4253964223017717894e-2202j 4.56e-998, 4.56e-998j
7.2167962098831444413 + 2.1833732447375489272e-2225j 1.26e-1005, 1.26e-1005j
140.90203015169048824 + 1.0999865139960827426e-2214j 3.19e-1000, 3.19e-1000j
8.4076286954266146317 - 8.0011751684544511192e-2240j 6.09e-1005, 6.09e-1005j
4.7205449648958142575 + 6.3554085017424761563e-2243j 6.47e-1008, 6.47e-1008j
3.0191673301420025746 - 1.3441213695988121376e-2244j 3.07e-1010, 3.07e-1010j
83.810485978056358161 + 4.4527277008818409041e-2230j 2.54e-996, 2.54e-996j
89.365071586571317913 + 1.3264792703191149804e-2247j 1.42e-996, 1.42e-996j
6.2899450829374791969 - 1.3489668745224652542e-2267j 3.28e-1006, 3.28e-1006j
0.065989249590369655405 - 2.6007867177487515341e-2281j 1.54e-1019, 1.54e-1019j
35.490206733977178814 + 3.4561250836814028075e-2257j 2.75e-997, 2.75e-997j
0.19065824475498282217 + 5.1121373744861846985e-2291j 3.39e-1018, 3.39e-1018j
101.51453977849414951 + 2.7280032159522187023e-2269j 3.64e-997, 3.64e-997j
1.6544655524259320062 + 3.7443791925303374269e-2297j 3.44e-1012, 3.44e-1012j
29.902839881782277929 + 2.4135092515340037597e-2279j 6.66e-998, 6.66e-998j
0.41577455678347908331 + 5.8357934724814111986e-2313j 7.46e-1017, 7.46e-1017j
5.5818282895833557182 + 1.8990515949288228674e-2303j 7.11e-1007, 7.11e-1007j
18.246772270957808884 - 5.0565417183880984058e-2293j 2.87e-1000, 2.87e-1000j
9.7500082014447782041 - 1.0652422874888127659e-2305j 3.25e-1004, 3.25e-1004j
1.240450626433030897 - 1.1764451252698936936e-2314j 4.59e-1012, 4.59e-1012j
38.506175509759077961 - 1.8239073951015614e-2297j 5.17e-997, 5.17e-997j
1.2627083649697538623 + 1.6575865364606932048e-2340j 5.25e-1012, 5.25e-1012j
32.623957615043232526 - 1.3977245954307450429e-2323j 1.32e-997, 1.32e-997j
22.625377909880118239 - 1.3411223188785376187e-2337j 1.28e-998, 1.28e-998j
21.386110825520344838 - 2.243688375383930524e-2353j 1.01e-998, 1.01e-998j
2.2942803602790417198 + 9.3888629829490693538e-2386j 2.35e-1011, 2.35e-1011j
14.501292642300796639 + 5.8339550041307013272e-2381j 6.79e-1002, 6.79e-1002j
0.013993151608491287585 + 4.1271217181361925904e-2402j 6.29e-1021, 6.29e-1021j
0.74475530457750882059 - 1.6236706493316522411e-2403j 3.76e-1015, 3.76e-1015j
60.108479380854460126 - 3.8047493554617872192e-2448j 4.94e-996, 4.94e-996j
52.187924745540839911 - 3.6793295816302891301e-2554j 3.37e-996, 3.37e-996j
68.859491569897985869 + 4.3972744954025341895e-2684j 5.42e-996, 5.42e-996j
41.677304534892144722 + 1.5701849262147356143e-2844j 8.96e-997, 8.96e-997j
64.373683275658997656 + 6.9575903752797364917e-2965j 5.92e-996, 5.92e-996j
56.050448853317753068 + 1.4388808096120640439e-3037j 4.44e-996, 4.44e-996j
73.581491764022659214 - 2.1553339827748467456e-3086j 4.79e-996, 4.79e-996j
48.510702534573329921 + 6.0624430247128482129e-3118j 2.26e-996, 2.26e-996j
78.55794575111294384 + 5.9090903014470972668e-3136j 3.57e-996, 3.57e-996j
45.009805886577704895 - 2.3805509690621827205e-3146j 1.49e-996, 1.49e-996j

Weights

Weight (ball center) Error (ball radius)
2.0912419274508139476e-77 + 7.6288805962184403786e-2220j 7.63e-192, 1.34e-943j
1.9230137493242682326e-65 + 2.3275542778678961915e-2213j 2.1e-188, 3.7e-940j
1.0131775369928213435e-70 - 2.8599539314337098045e-2216j 4.85e-190, 8.54e-942j
6.4392058120311727242e-57 - 5.7420799865586534725e-2208j 3.32e-186, 5.85e-938j
2.7391676891190417725e-53 + 9.7430283806683659519e-2207j 3.44e-185, 6.06e-937j
1.5347289561484149466e-07 - 1.1559268398190588968e-2179j 7.28e-147, 1.28e-898j
2.6001998973493731026e-41 + 3.1540818212887624705e-2201j 2.22e-181, 3.92e-933j
3.1470581665098613769e-09 + 1.7916319080004334564e-2180j 1.39e-151, 2.45e-903j
3.4117046279337531498e-12 + 1.6522470112533319028e-2183j 4.61e-158, 8.11e-910j
2.0523263048046861731e-05 + 9.6183406678027597491e-2179j 3.23e-142, 5.69e-894j
3.6734628966561807215e-11 - 1.5697603870370906806e-2182j 4.02e-156, 7.08e-908j
7.0762191792887084758e-47 + 7.0771173384899657535e-2204j 1.72e-184, 3.03e-936j
0.018517522536552802942 - 1.105260916427914062e-2176j 3.93e-127, 6.92e-879j
4.5314408478881783934e-06 - 4.7782867400630615457e-2179j 4.46e-146, 7.85e-898j
5.8483200845814293553e-50 - 2.6464428940450681587e-2205j 1.7e-185, 2.99e-937j
0.00079970035564452737606 - 1.9348440831120366241e-2177j 2.18e-139, 3.84e-891j
6.3284732210976255874e-61 - 1.0339390187061312787e-2210j 9.3e-190, 1.64e-941j
0.00028450967953255771561 + 6.223073460535125438e-2178j 4.45e-142, 7.83e-894j
0.0080460734902940041687 + 8.5250288805129172482e-2177j 2.43e-134, 4.27e-886j
0.037662907038222396134 + 1.7646143906424595111e-2176j 7.85e-129, 1.38e-880j
2.1570836811220171943e-36 + 6.235724998386536072e-2199j 4.31e-182, 7.59e-934j
8.8369821807757831225e-39 - 4.993584278543996508e-2200j 1.11e-182, 1.96e-934j
0.0013860288670746736919 + 5.0966346544931463151e-2177j 2.92e-141, 5.14e-893j
0.074151953046051517216 + 7.003482394933427202e-2176j 7.35e-130, 1.29e-881j
1.1354966846812839066e-15 - 3.2066399969916063111e-2186j 1.68e-169, 2.97e-921j
0.14377919412758593442 - 7.7624746548363738957e-2176j 6.48e-130, 1.14e-881j
5.2874212076098072396e-44 - 1.6337341483004501146e-2202j 1.57e-184, 2.77e-936j
0.11852440620429537345 + 1.327498302397318168e-2175j 4.08e-131, 7.18e-883j
2.7325957378446052939e-13 - 1.9979742164519181569e-2184j 3.32e-166, 5.84e-918j
0.18240514874195521596 + 7.924954011330214657e-2176j 4.56e-131, 8.03e-883j
0.0029131077699713877578 - 7.5881305273553770984e-2177j 3.72e-143, 6.54e-895j
2.3572050500565884626e-08 - 5.2290988452042132216e-2180j 1.18e-158, 2.08e-910j
8.1976278899969817179e-05 - 2.2859644334399509013e-2178j 1.75e-150, 3.08e-902j
0.73881136573159664026 + 2.4664790101989987715e-2174j 1.15e-134, 2.02e-886j
5.8519567246063757205e-17 + 3.9687977859641784271e-2187j 7.2e-172, 1.27e-923j
-0.61032246585503176431 - 2.5140555582129927377e-2174j 1.39e-135, 2.44e-887j
1.8952494985118988864e-14 + 2.5288282585089059391e-2185j 3.08e-168, 5.42e-920j
3.1439064024931902697e-10 + 2.2717884703718013864e-2181j 1.26e-162, 2.22e-914j
2.1028622625947484546e-10 - 9.7240289326348030808e-2181j 9.24e-162, 1.63e-913j
0.068442753111316984269 - 3.5580533430394787366e-2176j 2.77e-145, 4.88e-897j
8.8583891787427213329e-07 + 3.3097814137498584357e-2179j 2.47e-158, 4.35e-910j
0.032499013154947563813 - 3.0412193765669502361e-2176j 1.92e-141, 3.39e-893j
0.18199068442115551521 - 1.0199184928465507947e-2175j 1.91e-142, 3.35e-894j
3.267864868548447663e-26 + 3.2892218992372840759e-2193j 1.36e-182, 2.39e-934j
8.1510885613372735379e-23 + 5.2187460995504150823e-2191j 1.67e-180, 2.94e-932j
5.7222227878720057337e-30 + 7.6428138925731994318e-2196j 3.08e-185, 5.42e-937j
2.5808067026324789344e-18 - 4.7066233816524096903e-2188j 5.09e-177, 8.96e-929j
4.8267438929234464156e-28 - 1.9668583890490968642e-2194j 3.17e-184, 5.58e-936j
1.7993928844892250112e-24 - 4.4512164645005217566e-2192j 2.94e-182, 5.18e-934j
5.3621781393128700057e-32 + 9.8387648964525276124e-2198j 5.39e-187, 9.49e-939j
3.0681765953763272823e-21 - 5.4810337934015170388e-2190j 5.77e-181, 1.02e-932j
3.9010979300281105609e-34 - 5.3954795271748890234e-2198j 1.87e-188, 3.3e-940j
9.681406914337113523e-20 + 5.2669690573639918544e-2189j 4.85e-180, 8.53e-932j

Download

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