Rule: Q[1, 3, 63]

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)
218.61219660246657773 - 4.3239278986788628529e-2249j 2.7e-997, 2.7e-997j
235.23966256183020639 - 1.9057127909342447263e-2250j 3.85e-999, 3.85e-999j
157.65170511984630818 + 5.2671160811198379101e-2240j 1.36e-991, 1.36e-991j
205.35138125541157279 + 7.653194920868601762e-2250j 6.56e-996, 6.56e-996j
351.02684181779309665 + 1.790565784424269133e-2260j 7.3e-1006, 7.3e-1006j
38.941138840137644319 + 4.9373631556808590666e-2247j 6.24e-992, 6.24e-992j
174.32905441411154124 + 3.8518225351743958059e-2245j 5.97e-993, 5.97e-993j
165.6993091317363819 - 7.2578848542697238854e-2243j 3.35e-992, 3.35e-992j
183.66715916625544501 - 5.8364590938991564665e-2248j 8.45e-994, 8.45e-994j
150.09683745277072536 + 2.3217316559200383444e-2254j 5.12e-991, 5.12e-991j
17.525367025663470754 - 2.5704224587508080123e-2294j 5.58e-998, 5.58e-998j
117.84333101302554542 + 2.428999660495021108e-2284j 3.61e-989, 3.61e-989j
74.892657133390412839 - 2.5116055228760297774e-2312j 9.41e-989, 9.41e-989j
193.90347832907064673 - 1.8148469044721178398e-2326j 8.96e-995, 8.96e-995j
47.312970267436086615 - 9.2483545357098520333e-2329j 9.7e-991, 9.7e-991j
12.864894716739698937 + 6.1597600863881326429e-2348j 2.54e-1000, 2.54e-1000j
53.454546092201952642 + 3.5951099318464611619e-2337j 4.65e-990, 4.65e-990j
123.68249550778283308 + 1.2805822029086327594e-2361j 1.93e-989, 1.93e-989j
63.576024596694566431 - 1.0995938720657986854e-2403j 2.54e-989, 2.54e-989j
14.333167623469223106 - 3.9457106287433591514e-2447j 1.71e-999, 1.71e-999j
10.179294460959690867 - 1.6315837544750675026e-2449j 5.2e-1002, 5.2e-1002j
22.969787201156022718 - 1.5457543253584412964e-2443j 7.03e-996, 7.03e-996j
29.234092183524047479 - 1.413754046926932055e-2437j 5.48e-994, 5.48e-994j
60.075708734951176466 - 1.5579025301783157446e-2477j 1.5e-989, 1.5e-989j
87.556300718075638097 - 4.3468828435932292367e-2596j 1.5e-988, 1.5e-988j
56.703286572116846536 + 3.3972271021152773444e-2723j 7.91e-990, 7.91e-990j
3.369839231310923141 - 3.1792797844057181007e-2774j 1.85e-1008, 1.85e-1008j
5.79301309969411449 + 3.3810565032355819362e-2777j 1.23e-1005, 1.23e-1005j
4.9002792173040614578 + 3.4434246961741775252e-2838j 1.4e-1006, 1.4e-1006j
129.79759741752562598 + 4.6658825485147318299e-2935j 9.52e-990, 9.52e-990j
101.77436739106310102 - 1.6757391846439603857e-3035j 1.14e-988, 1.14e-988j
7.8232631436879996743 + 3.0636519564236085623e-3095j 8.75e-1004, 8.75e-1004j
1.8136106713131762864 + 6.3154627113358303909e-3103j 3.27e-1011, 3.27e-1011j
31.511867640613038144 + 9.6789658907270056899e-3082j 1.8e-993, 1.8e-993j
92.110575916723909577 + 8.739336871764772401e-3099j 1.53e-988, 1.53e-988j
112.25775059085455442 + 3.4845964809741631073e-3129j 5.81e-989, 5.81e-989j
4.0909943569360194869 + 4.438747305578602721e-3171j 1.62e-1007, 1.62e-1007j
24.96477170370796419 + 1.8660674582696562716e-3158j 3.12e-995, 3.12e-995j
36.363248000915004474 - 1.1543897751523938078e-3153j 1.98e-992, 1.98e-992j
6.7674996499124648337 - 3.5358030849477126202e-3168j 1.09e-1004, 1.09e-1004j
78.955340395019820214 - 1.3819338867839355933e-3150j 1.18e-988, 1.18e-988j
33.887565014725354907 + 1.4721099232688668717e-3173j 5.94e-993, 5.94e-993j
8.9603953382307350278 + 3.1880045706593121301e-3183j 7.57e-1003, 7.57e-1003j
19.251462986344136577 - 1.2954101544770566736e-3178j 2.99e-997, 2.99e-997j
11.480551099387945224 - 5.6038470336766265954e-3182j 3.69e-1001, 3.69e-1001j
96.846354266916793565 + 4.2691684065260225398e-3168j 1.36e-988, 1.36e-988j
50.325624346900193224 + 7.373934654801588096e-3178j 2.17e-990, 2.17e-990j
0.0018461781066932763373 + 7.1274282237332838387e-3210j 7.66e-1022, 7.66e-1022j
27.052321034006543832 + 3.0386739716712294425e-3182j 1.41e-994, 1.41e-994j
1.3939866678807454297 - 6.8120082609810159625e-3200j 1.9e-1012, 1.9e-1012j
142.9683848095586075 + 1.763716342196322912e-3175j 1.52e-990, 1.52e-990j
136.21538898953471393 + 1.3752362152420344073e-3185j 4.41e-990, 4.41e-990j
41.623632475271483182 + 4.2653282316807671473e-3200j 1.51e-991, 1.51e-991j
0.38768948046103022069 + 1.223284206703116935e-3235j 1.41e-1016, 1.41e-1016j
2.7486392249750858951 - 4.9113763970296970355e-3227j 2.28e-1009, 2.28e-1009j
83.174037125536479017 + 5.6038890738221780134e-3205j 1.39e-988, 1.39e-988j
106.90683014587312379 - 1.7804056636840717854e-3223j 8.44e-989, 8.44e-989j
21.065827635877466165 - 6.4174915453573935403e-3238j 1.49e-996, 1.49e-996j
0.18586281912263640809 - 3.288794979850373087e-3258j 3.48e-1018, 3.48e-1018j
2.2427376504443130743 - 9.8562249603180958825e-3251j 2.99e-1010, 2.99e-1010j
15.886312480329562674 + 5.1776499469051903537e-3239j 9.94e-999, 9.94e-999j
67.208838665371079627 + 1.8138198017578206595e-3228j 4.06e-989, 4.06e-989j
70.979198934399612133 + 1.0881440755840881305e-3230j 6.29e-989, 6.29e-989j
1 + 5.5982020590011661316e-3259j 7.65e-1014, 7.65e-1014j
0.66055886575144368336 + 1.5285616293617271929e-3259j 3.83e-1015, 3.83e-1015j
0.056897625001077184683 - 8.5400478256661658602e-3264j 1.06e-1019, 1.06e-1019j
44.413312651647190347 + 5.1759493309829950509e-3236j 4.12e-991, 4.12e-991j

Weights

Weight (ball center) Error (ball radius)
1.6597681249496206927e-94 + 5.2350108484575580071e-2305j 1.75e-163, 9.45e-911j
1.3453319420065520251e-101 - 1.3534181859945036752e-2308j 8.88e-166, 4.81e-913j
2.6557858719419269693e-68 + 1.1569022659394935341e-2291j 1.56e-155, 8.42e-903j
8.0147720583748799901e-89 - 3.9915269596417771613e-2302j 2.87e-162, 1.55e-909j
5.6979302800171061141e-136 + 2.8805919860856888438e-2325j 1.22e-179, 6.61e-927j
3.2210491892824829035e-17 - 8.3572343260241262893e-2264j 1.38e-121, 7.45e-869j
1.7462401097321412412e-75 + 2.4565651925197697378e-2295j 1.18e-158, 6.41e-906j
9.0760310852921968339e-72 - 1.9449133486337896128e-2293j 1.73e-157, 9.34e-905j
1.6722035284386149247e-79 - 2.19124002282172839e-2297j 2.36e-160, 1.28e-907j
4.775280953167872327e-65 - 5.4029325503388808475e-2290j 2.88e-156, 1.56e-903j
4.1186376311496298455e-08 - 6.1173888259620431766e-2260j 3.9e-109, 2.11e-856j
3.7831068227900516219e-51 + 8.0456567815538350051e-2283j 8.22e-153, 4.45e-900j
1.188990110550487151e-32 - 4.5753732637113950384e-2273j 1.02e-143, 5.54e-891j
6.6249932137563744974e-84 + 1.2580277685523760986e-2299j 2.58e-162, 1.39e-909j
8.3731433548686818364e-21 - 2.5305453440736915296e-2266j 7.75e-134, 4.2e-881j
3.6899054387431194174e-06 + 6.7490835820115824417e-2259j 7.97e-107, 4.31e-854j
1.9432698913384177253e-23 - 6.2554850661881706437e-2268j 9.53e-137, 5.16e-884j
1.152319565682686623e-53 - 3.9857938109730826018e-2284j 2.14e-154, 1.16e-901j
8.7384768731469061298e-28 + 2.1007116312657279091e-2270j 5.84e-141, 3.16e-888j
9.0015583970193570508e-07 - 3.1185864590602939325e-2259j 2.44e-111, 1.32e-858j
4.7813182330133442036e-05 + 2.9135005241774675306e-2258j 1.26e-105, 6.84e-853j
2.0616269754576622476e-10 + 4.3310424917173402672e-2261j 1.13e-121, 6.12e-869j
4.4874104946459873782e-13 - 2.5839910511771120608e-2262j 1.14e-126, 6.16e-874j
2.7890630218292026996e-26 - 1.4579890657895304994e-2269j 2.76e-140, 1.5e-887j
4.214793954236514549e-38 + 5.5551461372053889925e-2276j 5.17e-150, 2.8e-897j
7.8323428022657975148e-25 + 9.7046051511847729279e-2269j 3.46e-139, 1.87e-886j
0.023183263810739131055 - 2.8188086495592989959e-2256j 5.01e-94, 2.71e-841j
0.0028468270473511133649 + 4.1518436573837328069e-2257j 6.19e-103, 3.35e-850j
0.0063386348863472891311 - 7.8190209376108367308e-2257j 2.61e-100, 1.41e-847j
2.6687158111560360119e-56 + 1.7265875344352670894e-2285j 4.27e-158, 2.31e-905j
3.172156967265284373e-44 - 3.2864849789963124937e-2279j 5.51e-154, 2.98e-901j
0.00043890414175301296019 + 1.1405375246674934926e-2257j 3.11e-111, 1.69e-858j
0.06857112673791142753 + 9.8336335430271845234e-2256j 3.52e-92, 1.91e-839j
4.8001531877922203222e-14 + 1.0225476482251556659e-2262j 6.05e-133, 3.27e-880j
4.6101648153543444373e-40 - 5.0874646078247747823e-2277j 5.43e-152, 2.94e-899j
9.6537449123165348952e-49 - 1.4362896558593559536e-2281j 8.67e-156, 4.7e-903j
0.012816328091585604239 + 1.4771060293630176865e-2256j 1.94e-106, 1.05e-853j
2.9361657990239527785e-11 - 1.7105736897183376509e-2261j 9.39e-131, 5.08e-878j
4.0751595541230537073e-16 + 2.349442321076551679e-2263j 1.83e-136, 9.91e-884j
0.001167992622008159586 - 2.1907811569560834652e-2257j 6.39e-115, 3.46e-862j
2.1236311841425973338e-34 + 5.2421673531407734623e-2274j 6.8e-150, 3.68e-897j
4.6514565389828057399e-15 - 4.34668770556694311e-2263j 2.01e-135, 1.09e-882j
0.0001512409962992130212 - 5.8286212826520725736e-2258j 9.23e-120, 5e-867j
7.712114240349790967e-09 + 2.5976289477166933908e-2260j 3.34e-129, 1.81e-876j
1.3868478900227261431e-05 - 1.4208963963110868396e-2258j 7.68e-123, 4.16e-870j
4.2083244511321545322e-42 + 4.2792506696527639423e-2278j 5.79e-154, 3.13e-901j
4.2759104172411672721e-22 + 3.9625081451985185496e-2267j 2.1e-142, 1.14e-889j
0.016905935994517739783 - 1.4241392063783654223e-2256j 4.64e-114, 2.51e-861j
3.8071216757747801146e-12 + 6.6584853661729402076e-2262j 7.41e-134, 4.01e-881j
0.10252759491589220477 - 9.0066327142143803821e-2256j 1.06e-114, 5.76e-862j
5.6306154087816549147e-62 + 2.0470238434091271929e-2288j 6.88e-164, 3.73e-911j
4.5771492398653705804e-59 - 6.4527328729761934983e-2287j 1.33e-162, 7.2e-910j
2.2916326029503335121e-18 - 1.4805580859316090895e-2264j 5.92e-142, 3.2e-889j
0.16136798576383208943 + 5.7145714781398868342e-2256j 1.61e-121, 8.7e-869j
0.036153418664815534223 + 5.2878073267958423494e-2256j 5.84e-124, 3.16e-871j
3.2460664152785481973e-36 - 5.6014452844419829734e-2275j 1.68e-152, 9.08e-900j
1.9508221395336504632e-46 + 2.2895681381996179184e-2280j 3.21e-157, 1.74e-904j
1.3197477959071484756e-09 - 1.0738475310682912383e-2260j 9.37e-137, 5.07e-884j
0.13750069664903644137 - 4.7413937482967317142e-2256j 3.37e-127, 1.83e-874j
0.048082451661278387297 - 8.4083460907905027133e-2256j 3.03e-128, 1.64e-875j
2.0122084921463503945e-07 + 1.4009401184338218773e-2259j 4.4e-135, 2.38e-882j
2.3980422000874334729e-29 - 2.8818622945368773276e-2271j 5.12e-150, 2.77e-897j
5.7353897711740843108e-31 + 3.7420672147553039266e-2272j 7.25e-151, 3.93e-898j
0.13604257720328838443 + 7.704357601797599426e-2256j 9.32e-133, 5.02e-880j
0.15872706823108532487 - 6.6435013557327122909e-2256j 7.42e-133, 3.99e-880j
0.087111429180829261364 + 3.535844967017403635e-2256j 6.43e-133, 3.46e-880j
1.4638659454196995309e-19 + 1.721350802072564757e-2265j 7.56e-145, 4.09e-892j

Download

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