Rule: Q[4, 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)
270.16295793211947103 - 6.5245599128426169372e-2976j 5.75e-989, 5.75e-989j
297.9555975089806219 - 1.4488228553904382354e-2978j 5.33e-992, 5.33e-992j
212.02270585843241286 + 3.6059794829363245271e-2965j 1.84e-983, 1.84e-983j
316.55873233361930875 - 5.3703183942671549922e-2982j 3.82e-994, 3.82e-994j
228.93104448533159772 - 3.9528188421017308336e-2969j 6.3e-985, 6.3e-985j
126.07564668944469597 + 1.3456489983632326449e-2965j 6.48e-979, 6.48e-979j
220.24904705557958808 - 7.2216428807413631163e-2978j 3.75e-984, 3.75e-984j
103.77740627947600984 - 4.70463075606989948e-2979j 6.39e-979, 6.39e-979j
22.870192395875844422 - 2.0604340352778108334e-3007j 6.45e-991, 6.45e-991j
247.97932085073126244 - 1.6267602411505281882e-2995j 1.12e-986, 1.12e-986j
12.75569615605243959 - 1.4705101430684815424e-3018j 2.2e-996, 2.2e-996j
61.652384927895969883 + 9.9317565027195844163e-3002j 1.19e-981, 1.19e-981j
32.086851913007245761 - 3.8220356972213078022e-3014j 1.46e-987, 1.46e-987j
19.654614642966705248 - 2.8324065028244401046e-3016j 2.31e-992, 2.31e-992j
50.551299071564345937 - 5.5063071623130258106e-3007j 3.18e-983, 3.18e-983j
40.723251412811859135 - 8.3659365371903523801e-3010j 2.95e-985, 2.95e-985j
130.94638321195297534 - 1.4040742755743860435e-3001j 5.11e-979, 5.11e-979j
34.138020352573710765 + 8.5625842385268625533e-3032j 5.89e-987, 5.89e-987j
157.73447088229648725 - 2.0360667802408310165e-3022j 6.28e-980, 6.28e-980j
189.57333855614804745 + 6.5998715700689770701e-3043j 8.55e-982, 8.55e-982j
24.57757855401704657 - 4.577293846675110651e-3085j 3.25e-990, 3.25e-990j
21.229400679424323631 + 8.4986543283499736222e-3087j 1.22e-991, 1.22e-991j
53.203616431343738065 - 2.4116241480484924342e-3074j 8.17e-983, 8.17e-983j
176.11723604626012667 + 9.4039823500207826263e-3081j 6.68e-981, 6.68e-981j
283.06506408803156715 + 1.5904548098753302185e-3109j 2.52e-990, 2.52e-990j
146.4979563234691494 - 9.6223735791071402474e-3120j 1.89e-979, 1.89e-979j
84.467881462359819975 + 6.6168661832790682979e-3145j 1.26e-979, 1.26e-979j
258.58321698159585775 + 3.2287483376813025226e-3155j 9.58e-988, 9.58e-988j
16.701047137323266997 - 1.9999284554354580074e-3178j 6.62e-994, 6.62e-994j
141.1496488222698267 - 3.6767227154746991319e-3163j 2.9e-979, 2.9e-979j
45.4836713987108259 - 5.980955348734692237e-3189j 3.32e-984, 3.32e-984j
5.9067735489285442761 + 9.4726828287804530402e-3209j 1.79e-1002, 1.79e-1002j
5.2053260913081381438 + 4.1162245640030522272e-3209j 2e-1003, 2e-1003j
95.723064194957878074 - 1.2043011484720723627e-3182j 3.92e-979, 3.92e-979j
14.006368441497519593 + 4.7679572562185862873e-3219j 1.59e-995, 1.59e-995j
238.14165142359592032 + 1.9066206554033211881e-3201j 9.29e-986, 9.29e-986j
9.3950709123011331292 + 2.3136845364036458888e-3250j 5.87e-999, 5.87e-999j
107.98089719126768197 + 1.180633119959052769e-3229j 6.79e-979, 6.79e-979j
152.02275790566016574 + 5.9926868273753843228e-3265j 1.16e-979, 1.16e-979j
135.96855951558211366 + 2.9601887780653767068e-3289j 4.13e-979, 4.13e-979j
204.19602040489318111 - 5.7621361775810476872e-3316j 8.17e-983, 8.17e-983j
70.874528686179854941 - 2.1541396435309907994e-3332j 1.16e-980, 1.16e-980j
2.2074290570406308951 + 1.6555296310941368884e-3375j 4.79e-1009, 4.79e-1009j
47.978443227867579756 + 1.4588398784308162662e-3348j 1.08e-983, 1.08e-983j
64.638063348397466992 + 3.4395845164853713049e-3344j 2.67e-981, 2.67e-981j
196.72479099984536156 + 5.9250160953296399126e-3369j 2.82e-982, 2.82e-982j
2.7222199069981752749 - 1.3065735729276032319e-3425j 7.36e-1008, 7.36e-1008j
0.015249888166187931047 + 5.1777606993153529397e-3475j 1.83e-1020, 1.83e-1020j
58.752563807364375997 + 4.6394981430209851643e-3396j 5.19e-982, 5.19e-982j
11.569691025035045591 - 4.5455874289126418413e-3429j 2.94e-997, 2.94e-997j
36.260483708266328487 - 1.1442451468658064181e-3415j 2.32e-986, 2.32e-986j
43.065683343422011668 + 2.1970438894442558861e-3410j 1.1e-984, 1.1e-984j
3.8943364863663828747 - 1.4531952126745455339e-3463j 1.66e-1005, 1.66e-1005j
15.321472669286790114 - 1.6220688259695917053e-3452j 1e-994, 1e-994j
4.5366202969211279833 - 2.4686722276379574907e-3462j 2.03e-1004, 2.03e-1004j
121.34959488008261763 + 1.8826110705414190118e-3435j 7.68e-979, 7.68e-979j
8.4103588820560599157 + 3.7176726593990810547e-3502j 8.05e-1000, 8.05e-1000j
28.194782166602502959 + 1.5271273013266803682e-3485j 7.42e-989, 7.42e-989j
74.129390384850941472 + 1.9155636175319535097e-3480j 2.21e-980, 2.21e-980j
0.07911433841584222263 + 5.1499760617496294682e-3550j 7.65e-1019, 7.65e-1019j
169.76733663520601085 - 1.9234970481157857612e-3509j 1.61e-980, 1.61e-980j
88.113893717961981434 - 1.4408402967320236767e-3519j 1.95e-979, 1.95e-979j
80.923590518463517239 + 1.6599534863952622073e-3523j 7.65e-980, 7.65e-980j
6.6651141562866062282 + 7.6427305811389863061e-3550j 1.54e-1001, 1.54e-1001j
77.478279907224959637 - 6.8766481387236261147e-3527j 4.14e-980, 4.14e-980j
55.936855272131158045 + 1.8559825753119524014e-3534j 2.04e-982, 2.04e-982j
0.99133562336015269888 - 8.05190695471361614e-3566j 1.18e-1012, 1.18e-1012j
30.10606034530551433 + 2.8148157023223340396e-3540j 3.35e-988, 3.35e-988j
18.145311743194324678 + 3.5536213541899712518e-3545j 3.89e-993, 3.89e-993j
1.7457611011583465757 + 9.6898811246251807772e-3562j 3.32e-1010, 3.32e-1010j
3.2865199401485028312 + 1.3433042600878298987e-3558j 1.15e-1006, 1.15e-1006j
10.449022389804406048 - 9.4134027219581698899e-3550j 4.39e-998, 4.39e-998j
99.692786111139253354 - 1.7953376146827518945e-3529j 5.24e-979, 5.24e-979j
67.711453559026961301 + 3.1935214986214967642e-3546j 5.68e-981, 5.68e-981j
0.18707836294588045574 + 2.4926680101127823412e-3612j 2.73e-1017, 2.73e-1017j
0.7043734052553487854 + 4.9832576403463790161e-3609j 9.32e-1014, 9.32e-1014j
26.352207279663373938 + 2.8865323706240059732e-3585j 1.62e-989, 1.62e-989j
91.864567835171207674 - 3.7110034254575625608e-3573j 2.94e-979, 2.94e-979j
38.455216374753538607 - 3.6034991939520880461e-3609j 8.78e-986, 8.78e-986j
7.4989206771266931508 + 2.2779245207047652436e-3646j 1.15e-1000, 1.15e-1000j
1.3396371188411656887 + 3.9853596732503430522e-3677j 1.82e-1011, 1.82e-1011j
0.48420356225542548362 - 8.4343436045468524344e-3681j 7.07e-1015, 7.07e-1015j
182.71232251338210933 - 2.4014110891009438171e-3670j 2.41e-981, 2.41e-981j
116.76209666482723168 - 1.6023209994965668873e-3798j 7.55e-979, 7.55e-979j
112.30756626947138503 + 7.2183531178317238844e-3895j 7.19e-979, 7.19e-979j
163.6448663727959637 - 7.4638385771554086e-3934j 3.12e-980, 3.12e-980j
0.3225476896193923118 - 3.2544441982824406517e-3986j 5.45e-1016, 5.45e-1016j

Weights

Weight (ball center) Error (ball radius)
5.6868125472520805321e-117 + 2.0130764625291461773e-3053j 5.98e-124, 9.03e-864j
6.4747472747605612619e-129 + 1.5515584207018741374e-3059j 8.74e-128, 1.32e-867j
6.6648583123208975998e-92 + 1.6717802351532324331e-3040j 4.8e-116, 7.24e-856j
7.2515183305095879021e-137 - 1.3513978855970461264e-3063j 1.03e-130, 1.56e-870j
3.3688207724448536179e-99 + 2.7935092879474709038e-3044j 4.8e-119, 7.24e-859j
8.4535926370136299648e-55 - 5.8274178363478202042e-3020j 6.08e-101, 9.17e-841j
1.8775164816592961256e-95 - 2.4161789392285431024e-3042j 1.07e-117, 1.62e-857j
3.5269433897781570118e-45 + 4.4578933428915890381e-3016j 3.32e-95, 5.01e-835j
1.9559303440442294567e-10 - 2.7430401898636733938e-2998j 7.32e-46, 1.11e-785j
2.0523648910496154808e-107 + 1.6286350385514680031e-3048j 2.5e-122, 3.77e-862j
3.5161225329589962232e-06 + 1.0541460383782873796e-2995j 2.04e-27, 3.07e-767j
4.9364931482111994194e-27 + 4.1509911848731012465e-3007j 4.53e-79, 6.83e-819j
2.3405154912848657633e-14 + 1.817525777807514971e-3000j 4.47e-58, 6.75e-798j
4.4893490553422194313e-09 - 1.6851664296651828062e-2997j 2.14e-42, 3.22e-782j
2.9032282270126734944e-22 + 1.1827551352190494681e-3004j 3.8e-73, 5.73e-813j
4.7511220050721092179e-18 + 1.9092612855133662512e-3002j 2.92e-66, 4.41e-806j
6.6818807240010916643e-57 - 1.9581498379779690488e-3021j 7.13e-104, 1.08e-843j
3.1152827281733598597e-15 - 6.1004103508311268797e-3001j 3.56e-61, 5.38e-801j
1.8234279989300849295e-68 + 3.735324710524873717e-3028j 7.75e-111, 1.17e-850j
3.2700481042414894143e-82 - 1.8809462144729099994e-3035j 1.01e-116, 1.52e-856j
3.6886356580880097465e-11 + 1.0640784279489685697e-2998j 7.35e-54, 1.11e-793j
9.6915302552139687942e-10 + 6.886196114395969968e-2998j 1.13e-49, 1.7e-789j
2.1092260860063791131e-23 - 3.0410121003330398479e-3005j 2.13e-77, 3.22e-817j
2.1091815347396150183e-76 - 2.1457736135086101459e-3032j 8.87e-115, 1.34e-854j
1.6011054341441599812e-122 - 2.8878176533623778399e-3056j 1.03e-131, 1.55e-871j
1.2940143551916218793e-63 + 1.7284009752248776106e-3025j 1.75e-109, 2.64e-849j
7.4426101302924304849e-37 - 4.7898136966633559064e-3012j 1.43e-95, 2.15e-835j
5.5213609687644538563e-112 - 7.2911424567430473401e-3051j 3.08e-128, 4.65e-868j
7.8817447104129567784e-08 - 9.3905356011892978009e-2997j 5.53e-53, 8.35e-793j
2.6347501443402370369e-61 - 3.5384993020323258694e-3024j 1.44e-108, 2.17e-848j
4.3346178682678268832e-20 + 1.6093293626943102528e-3003j 3.19e-78, 4.81e-818j
0.0019737780482201477747 - 1.3970943671493783191e-2993j 2.45e-33, 3.7e-773j
0.0037428460950442089282 + 2.0955787552365261513e-2993j 1.31e-30, 1.97e-770j
1.0485014436066745276e-41 + 2.0255904874136287519e-3014j 1.11e-99, 1.68e-839j
1.0599967360675112692e-06 - 4.7977016270391688373e-2996j 2.35e-52, 3.55e-792j
3.583828036408073793e-103 - 2.4900573548715374606e-3046j 1.3e-125, 1.96e-865j
8.4784903197369572671e-05 - 1.021369156383597548e-2994j 1.33e-46, 2.01e-786j
5.4242941582329652794e-47 - 6.4042761692744801648e-3017j 7.83e-103, 1.18e-842j
5.3310701291088921468e-66 - 8.2478374890351111014e-3027j 2.09e-111, 3.15e-851j
4.5415332089737467827e-59 + 7.4992477061201965221e-3023j 4.35e-108, 6.56e-848j
1.5922974346691951674e-88 - 9.5220221517716863343e-3039j 1.7e-121, 2.56e-861j
5.3198550151346798342e-31 - 4.0270744483519305557e-3009j 2.34e-95, 3.54e-835j
0.053748340312938246445 - 6.5676937518232562444e-2993j 5.76e-31, 8.7e-771j
3.6894645234892574929e-21 - 4.4396305601837724977e-3004j 4.31e-85, 6.51e-825j
2.5667050203471616568e-28 - 9.2025034601085471843e-3008j 5.4e-93, 8.16e-833j
2.6741601078929452823e-85 + 4.5680226900939132698e-3037j 2.55e-121, 3.85e-861j
0.035513409381712151428 + 5.3014675532112403866e-2993j 5.51e-40, 8.32e-780j
0.038420094870840223485 + 1.4441386723707700333e-2993j 9.71e-37, 1.47e-776j
8.711027052032429145e-26 - 1.8026558581729646459e-3006j 1.35e-90, 2.04e-830j
1.0898409415184352084e-05 - 2.2788518436888107628e-2995j 5.61e-63, 8.46e-803j
3.8584257356872898729e-16 + 1.984895864350522327e-3001j 1.26e-81, 1.9e-821j
4.7140085785562348019e-19 - 5.6371613975937684329e-3003j 3.33e-84, 5.03e-824j
0.01275894105184242126 + 3.5086052073213448004e-2993j 1.62e-50, 2.45e-790j
2.9883970082636989517e-07 + 2.1440352751685788489e-2996j 4.07e-68, 6.15e-808j
0.0070275926621797705881 - 2.7991406689036712669e-2993j 1.16e-52, 1.75e-792j
9.2583793473778544119e-53 + 2.6724882718710917217e-3019j 4.96e-109, 7.48e-849j
0.00021117104174877103171 + 2.1151494718314388624e-2994j 3.44e-62, 5.19e-802j
1.0680184115640159233e-12 + 1.4736696995030349925e-2999j 6.3e-79, 9.52e-819j
2.1121500798879324331e-32 + 7.9412130320758682623e-3010j 3.08e-98, 4.65e-838j
0.081091834680901130823 - 5.5507492949201671924e-2993j 3.58e-50, 5.4e-790j
1.1633500897759046911e-73 + 6.1063762118158788453e-3031j 2.5e-119, 3.77e-859j
1.9978816873112343149e-38 + 8.0490008446621430907e-3013j 6.42e-103, 9.69e-843j
2.5043716790069736328e-35 + 2.7390750504877963096e-3011j 4.34e-101, 6.55e-841j
0.0010127425462000369296 + 8.1326237260700895312e-2994j 2.66e-68, 4.02e-808j
7.6324893477799752766e-34 - 1.5047286836366278267e-3010j 3.77e-100, 5.69e-840j
1.4127699157478214608e-24 + 7.5413104766580014268e-3006j 1.35e-93, 2.04e-833j
0.11815801676533746907 + 1.3558825889090187377e-2992j 8.5e-63, 1.28e-802j
1.6376595406367860819e-13 - 5.2528343639310038575e-3000j 2.05e-85, 3.1e-825j
1.944860585248886227e-08 + 4.0243873255192892626e-2997j 1.12e-79, 1.69e-819j
0.075782232706486011084 + 8.2232147807846846099e-2993j 5.27e-65, 7.96e-805j
0.021956136834097305173 - 4.3115149866055163182e-2993j 1.09e-67, 1.64e-807j
3.1515473121002958459e-05 + 4.8565225348428187312e-2995j 2.05e-75, 3.09e-815j
2.0365946007571908953e-43 - 3.0480872847085278821e-3015j 3.08e-107, 4.66e-847j
1.2222234939285614457e-29 + 1.9630368884851006761e-3008j 3.58e-98, 5.4e-838j
0.10378394119737144121 + 1.2464191080053775629e-2992j 1.46e-68, 2.21e-808j
0.12580256545648364926 - 1.7862927704914829131e-2992j 2.09e-69, 3.15e-809j
6.4967403878980251603e-12 - 4.0162016561710145736e-2999j 8.84e-86, 1.33e-825j
4.8302552069420963983e-40 - 1.3008922027357445191e-3013j 3.45e-105, 5.21e-845j
4.4427464098928314252e-17 - 6.2565182921071092288e-3002j 1.74e-90, 2.63e-830j
0.00048346126325020816243 - 4.2655852649670177983e-2994j 1.63e-79, 2.46e-819j
0.098918641927050770252 - 1.0449960708257354479e-2992j 3.35e-76, 5.06e-816j
0.11487443473679766963 + 2.1805945527541863001e-2992j 6.39e-76, 9.64e-816j
2.9970522576278280654e-79 + 6.7550805037669537797e-3034j 1.46e-126, 2.2e-866j
8.8311283524717169945e-51 - 1.4060129911619921094e-3018j 1.24e-112, 1.87e-852j
7.3771227064765348025e-49 + 9.2340848551977635117e-3018j 1.25e-111, 1.89e-851j
5.1180507358444498402e-71 - 1.5759546298023217315e-3029j 4.01e-123, 6.05e-863j
0.10460764071200504851 - 1.9991976370504751677e-2992j 2.07e-83, 3.13e-823j

Download

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