Rule: Q[2, 5, 48]

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)
148.34699461667831341 + 1.2090332805727815186e-2935j 1.85e-999, 1.85e-999j
138.97876578362308449 + 1.655261062569031371e-2951j 1.29e-998, 1.29e-998j
186.63003221948121847 + 8.4096202578942250633e-2964j 1.73e-1003, 1.73e-1003j
171.14768871848626288 - 1.0029931387265741527e-2966j 9.61e-1002, 9.61e-1002j
75.301683050870667011 - 3.6348890241868205155e-2982j 6.37e-995, 6.37e-995j
32.058868825638281768 + 1.8184284715504815617e-2995j 2.39e-997, 2.39e-997j
47.17670740952691739 + 1.5661799025813141925e-2992j 1.26e-995, 1.26e-995j
130.47588764718794056 - 3.2213336952125962051e-2996j 6.85e-998, 6.85e-998j
70.690094657096687888 + 9.9725327544795881186e-3000j 6.1e-995, 6.1e-995j
7.3179127231309068604 - 2.7311852296632804683e-3020j 2.04e-1005, 2.04e-1005j
8.5160814711384053232 + 7.9685255933262335014e-3019j 2.56e-1004, 2.56e-1004j
122.6573767028601689 - 3.5520771991114847638e-3009j 2.92e-997, 2.92e-997j
58.108624473436217707 + 3.7986753648476523622e-3019j 4.02e-995, 4.02e-995j
50.652422304530551493 + 4.3855846498761191529e-3034j 1.92e-995, 1.92e-995j
40.694579676278169349 - 1.4725973390839178567e-3047j 3.6e-996, 3.6e-996j
16.402635230020449078 - 3.8222754018040659859e-3073j 7.69e-1001, 7.69e-1001j
10.257801186785141083 + 1.0108878058146368754e-3084j 6.43e-1003, 6.43e-1003j
14.638361334482629127 + 4.9925105629185035398e-3079j 1.76e-1001, 1.76e-1001j
158.87914378308788908 - 3.0239992439784143544e-3076j 1.68e-1000, 1.68e-1000j
11.476433715528536725 + 1.1979047133642145717e-3105j 1.52e-1002, 1.52e-1002j
102.2668394976910776 + 3.1595869857617462355e-3120j 6.44e-996, 6.44e-996j
1.2165851958674993057 - 1.4163321988623655632e-3175j 4.33e-1013, 4.33e-1013j
26.972326557680523299 - 5.1600029877971155366e-3167j 3.91e-998, 3.91e-998j
115.40287392184273761 - 4.7170880128997305115e-3220j 9.99e-997, 9.99e-997j
18.281587949390751729 + 2.6404392948168626525e-3250j 2.73e-1000, 2.73e-1000j
20.275986437879626552 - 1.1062894262194955881e-3263j 9.06e-1000, 9.06e-1000j
0.8564946200868494795 + 1.1821164988916140734e-3303j 4.43e-1014, 4.43e-1014j
12.990897884371396024 + 1.2770634600368610493e-3285j 4.67e-1002, 4.67e-1002j
96.273465136166618452 - 2.6800221458437665596e-3306j 1.28e-995, 1.28e-995j
6.196205771340291157 - 1.2957207091976511441e-3357j 1.78e-1006, 1.78e-1006j
34.799123068558727834 - 2.6534323898648560855e-3354j 6.44e-997, 6.44e-997j
9.6124726326687055278 + 1.8380800904926246837e-3393j 2.73e-1003, 2.73e-1003j
0.28109904433207587007 - 2.5917693601710728827e-3423j 4.17e-1017, 4.17e-1017j
22.387621278761020469 - 1.2405522725714887844e-3401j 3.42e-999, 3.42e-999j
5.1692184994818379292 - 7.8866115244597960244e-3432j 1.77e-1007, 1.77e-1007j
80.146096405028480831 + 3.7842430024689156688e-3463j 4.75e-995, 4.75e-995j
90.608618262072296968 - 5.6178392161149449796e-3510j 2.28e-995, 2.28e-995j
0.5857864376269049512 - 4.7132262786588168307e-3573j 1.08e-1014, 1.08e-1014j
1.6054525833172712334 - 1.9766090561829492621e-3570j 3e-1012, 3e-1012j
43.859536383970249894 - 4.5897668493884578128e-3553j 6.88e-996, 6.88e-996j
62.105981174123553377 + 1.4962603263590367307e-3603j 5.05e-995, 5.05e-995j
54.293751147390616116 + 5.0336676065557008674e-3655j 2.87e-995, 2.87e-995j
2.6926222759334657475 - 1.0910949655420599253e-3698j 1.82e-1010, 1.82e-1010j
0.11237331364323042761 + 8.0627950292517251178e-3734j 7.21e-1019, 7.21e-1019j
37.676150251907775554 + 9.1027688495937972573e-3718j 1.49e-996, 1.49e-996j
85.241319478359109794 + 1.8345295885080939019e-3792j 3.48e-995, 3.48e-995j
108.62711197312559328 - 4.5895786514349623409e-3855j 2.72e-996, 2.72e-996j
4.2410886883481072754 + 1.1338927411629382343e-3891j 1.91e-1008, 1.91e-1008j
0.51582574964901062495 + 4.2050997203640659618e-3911j 4.61e-1015, 4.61e-1015j
24.618825750930918779 + 7.5792813886425935955e-3891j 1.06e-998, 1.06e-998j
2.0857449385483801422 - 8.1467212132486188629e-3926j 2.09e-1011, 2.09e-1011j
66.295952646256143252 + 1.1990093864700223262e-3918j 5.82e-995, 5.82e-995j
29.451199796082864864 - 7.0583499837550275186e-3935j 9.51e-998, 9.51e-998j
0.020974822437409004193 - 1.5659454168702087447e-3960j 1.34e-1020, 1.34e-1020j
3.4142135623730950488 - 3.5415045809236488003e-3950j 1.74e-1009, 1.74e-1009j

Weights

Weight (ball center) Error (ball radius)
3.704495441888254829e-64 - 2.3325332271849283134e-2999j 1.2e-187, 2.76e-939j
3.9047911072315018146e-60 + 6.00333021999872284e-2998j 2.84e-186, 6.55e-938j
1.6227378464542161951e-80 - 3.8229425430160377985e-3009j 4.74e-194, 1.09e-945j
6.3255884058432347466e-74 + 1.6531119427699523331e-3005j 9.76e-192, 2.25e-943j
9.3609176798035388393e-33 + 2.5626658719281126079e-2984j 1.63e-175, 3.75e-927j
3.1919609456879586636e-14 + 5.0032126244069392895e-2974j 2.16e-158, 4.99e-910j
1.1022961186887554555e-20 - 9.1064271174520771647e-2978j 2.22e-166, 5.12e-918j
1.7599196317890796416e-56 - 2.5683065176361372214e-2996j 2.03e-186, 4.69e-938j
8.9730882934378272486e-31 - 2.8857151166423626502e-2983j 9.32e-175, 2.15e-926j
0.00077357988614084564945 + 1.2702808797985599822e-2966j 1.17e-132, 2.69e-884j
0.00024327753132327052106 - 9.1301204373758128136e-2967j 1.29e-135, 2.97e-887j
4.0438287627478866546e-53 + 1.0372068370323488629e-2994j 9.64e-186, 2.22e-937j
2.2662827866827453125e-25 + 2.3421450663661975144e-2980j 9.33e-172, 2.15e-923j
3.5731404604100064605e-22 + 1.3436310403082282263e-2978j 3.68e-169, 8.48e-921j
6.5559967879262776768e-18 - 3.4166841489949249181e-2976j 5.69e-166, 1.31e-917j
1.3705143895803490464e-07 - 1.2573772739433475249e-2969j 3.81e-152, 8.78e-904j
2.9914655952394878002e-05 - 5.5590397959592981362e-2967j 2.21e-144, 5.1e-896j
7.4953545451052927407e-07 + 5.0648429882995128386e-2969j 2.32e-150, 5.36e-902j
1.1258205809757964879e-68 - 1.8977962531858824264e-3002j 1.67e-193, 3.85e-945j
1.481287285458219637e-05 + 1.0839178224497766295e-2967j 2.45e-147, 5.66e-899j
2.3786983451911435202e-44 - 2.4701029660827236926e-2990j 2.43e-185, 5.6e-937j
0.10984475235616629783 + 4.011975578667726236e-2964j 5.58e-121, 1.29e-872j
4.6676755414006047053e-12 + 1.074646785378295632e-2972j 6.6e-163, 1.52e-914j
5.3266850161345049595e-50 - 3.5474577084292524681e-2993j 4.24e-187, 9.78e-939j
2.2254125321611088634e-08 + 3.1732639792377456615e-2970j 5.7e-157, 1.31e-908j
3.2104735030160047168e-09 - 7.9577361397559187418e-2971j 6.28e-159, 1.45e-910j
0.14568450132255698737 - 7.4569352597653124936e-2964j 1.28e-128, 2.95e-880j
3.6185333297705796194e-06 - 2.1667012607163071815e-2968j 1.88e-152, 4.34e-904j
8.9979268365264141352e-42 + 5.1355616796912752457e-2989j 5.77e-185, 1.33e-936j
0.0021908260283496508492 - 2.1935004383300572143e-2966j 2.84e-147, 6.56e-899j
2.1642911597167935376e-15 - 1.0031624585060398157e-2974j 5.78e-168, 1.33e-919j
5.3822834764819686475e-05 + 8.8619783081954438059e-2967j 1.67e-150, 3.85e-902j
0.15672401132160165566 + 3.6848733736483792791e-2964j 8.6e-136, 1.98e-887j
4.1099688920682093457e-10 + 1.9559194088604788214e-2971j 1.83e-161, 4.23e-913j
0.0055636490434228980578 + 4.1997497122653528376e-2966j 3.98e-148, 9.17e-900j
7.7454995782832710834e-35 - 2.0489587779773123871e-2985j 3.11e-182, 7.18e-934j
2.4572003079388809395e-39 - 9.2584625386593003272e-2988j 1.45e-184, 3.35e-936j
0.045339408008533493114 + 2.3998694092111230448e-2963j 4.97e-142, 1.15e-893j
0.084598114356886482137 - 2.2847118887342662397e-2964j 1.85e-145, 4.28e-897j
2.9013435068697991377e-19 + 5.762046614775551356e-2977j 1.01e-172, 2.34e-924j
4.3615055630101472038e-27 - 2.7427569108764045502e-2981j 1.17e-178, 2.71e-930j
9.8140439222705477132e-24 - 1.8435234571061524587e-2979j 2.48e-176, 5.73e-928j
0.045123202025526719096 - 4.3366448586242858764e-2965j 5.84e-155, 1.35e-906j
0.11580550659929754228 - 1.3117938899226920481e-2964j 2.28e-150, 5.26e-902j
1.2788623879218005594e-16 + 1.9055300696849930123e-2975j 7.47e-172, 1.72e-923j
4.9940308846375579014e-37 + 1.4635819200357083104e-2986j 2.4e-184, 5.55e-936j
4.3719423773573325811e-47 + 1.0176727960497805229e-2991j 1.42e-189, 3.29e-941j
0.01263523928278925583 - 8.6016315197123927815e-2966j 7.79e-161, 1.8e-912j
0.12928114019523642052 - 2.1721100147236850186e-2963j 1.4e-155, 3.23e-907j
4.6598241389320864076e-11 - 4.6683811736564533601e-2972j 2.03e-169, 4.69e-921j
0.067626552729976942213 + 1.0468769408190001978e-2964j 4.17e-160, 9.62e-912j
6.9261315930141099368e-29 + 2.9457663119395020461e-2982j 2.26e-180, 5.22e-932j
4.1190456401770006807e-13 - 2.3729603812360609769e-2973j 5.01e-171, 1.16e-922j
0.052957304037066781519 + 3.3683764637163632713e-2965j 1.64e-161, 4.25e-913j
0.025505853864021967473 + 1.8711837794683793807e-2965j 2.47e-162, 5.6e-914j

Download

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