Rule: Q[6, 68]

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)
244.70651419931500937 - 2.9677653461964355678e-2843j 5.36e-996, 5.36e-996j
198.21608913123931762 - 3.2042505460977566495e-2832j 3.19e-991, 3.19e-991j
262.13335800845985233 + 2.4429553626470931003e-2849j 5.37e-998, 5.37e-998j
230.80154535870422482 + 4.3651295166371975718e-2841j 1.71e-994, 1.71e-994j
172.67217948140488771 - 1.0965530302011010536e-2841j 5.44e-989, 5.44e-989j
38.985668906427563824 - 4.3623243104359338968e-2858j 1.56e-989, 1.56e-989j
68.839607737975673296 + 1.4656098644496163496e-2870j 3.52e-986, 3.52e-986j
34.201069488476219692 - 1.558724876686594814e-2896j 1.59e-990, 1.59e-990j
218.78809263462201824 - 8.8501761839034902768e-2891j 3.06e-993, 3.06e-993j
15.982873980601701783 - 1.1370083505515389209e-2919j 4.57e-996, 4.57e-996j
6.6831825242569497156 - 3.8320326348772738682e-2927j 2.78e-1003, 2.78e-1003j
23.805416938875021031 - 4.9617027112944175179e-2915j 2.9e-993, 2.9e-993j
79.987274038727333656 - 1.30104504869734697e-2908j 1.11e-985, 1.11e-985j
65.368529143396647016 - 1.8887092248317106967e-2945j 2.15e-986, 2.15e-986j
126.80665537031266103 + 2.6886689569433820888e-2965j 3.97e-986, 3.97e-986j
20.283359844449530172 + 2.6552461942322040016e-2992j 2.18e-994, 2.18e-994j
157.9872620664984887 + 2.5115866233711410195e-2983j 6.81e-988, 6.81e-988j
132.52086584572442132 - 1.930083453299210729e-3009j 2.12e-986, 2.12e-986j
106.03764760814957745 + 3.4284002036090651565e-3044j 1.65e-985, 1.65e-985j
208.03569788312306858 - 8.8707186946150182054e-3065j 3.79e-992, 3.79e-992j
189.13054535349371357 + 1.4048635125242585651e-3065j 2.15e-990, 2.15e-990j
27.698341926245238771 + 1.4079991611678969587e-3088j 4.29e-992, 4.29e-992j
101.30702888926095113 + 1.0119263255397508421e-3081j 1.69e-985, 1.69e-985j
138.47442512777645871 - 3.5818456993770323316e-3111j 1.1e-986, 1.1e-986j
96.741708100341798797 + 4.0719955840699659722e-3131j 1.76e-985, 1.76e-985j
165.13664583163302604 - 9.3636050543745248631e-3160j 2e-988, 2e-988j
25.70742837300433328 - 3.1538923576018131393e-3189j 1.09e-992, 1.09e-992j
7.6644649305902576873 + 1.5645313740900327945e-3198j 2.81e-1002, 2.81e-1002j
13.53176806659035597 - 2.1893332166372292389e-3194j 1.52e-997, 1.52e-997j
44.142897781579996442 - 2.0489394563116554456e-3182j 1.19e-988, 1.19e-988j
151.1820322928766312 - 3.4544656566598974564e-3223j 1.84e-987, 1.84e-987j
3.540933177206991649 + 6.4551216664046940919e-3286j 5.65e-1007, 5.65e-1007j
29.777366843141835609 - 2.4991902427387063155e-3265j 1.48e-991, 1.48e-991j
8.7167571310436567737 + 7.7147373136320222383e-3301j 2.79e-1001, 2.79e-1001j
72.43033882725228795 + 2.104133462779363162e-3315j 5.53e-986, 5.53e-986j
17.245705136059815078 + 1.7516956596547451475e-3378j 1.7e-995, 1.7e-995j
121.31491652899614046 - 2.7661058004774670925e-3376j 6.3e-986, 6.3e-986j
2.0354008004343512531 + 1.3520747119237024436e-3440j 6.71e-1010, 6.71e-1010j
12.261138340267688682 - 2.02333370472612756e-3428j 1.86e-998, 1.86e-998j
110.94236218257696079 - 1.9443510583749272662e-3414j 1.22e-985, 1.22e-985j
21.995042375079335177 - 4.4816510865926226772e-3463j 7.99e-994, 7.99e-994j
92.333814005221071926 - 1.6708126090152065667e-3452j 1.74e-985, 1.74e-985j
88.076270314362594394 - 2.3684230028240880868e-3500j 1.62e-985, 1.62e-985j
2.5088464594793843486 + 5.1587746552521947561e-3548j 7.68e-1009, 7.68e-1009j
0.22284660417926068946 + 6.5649240038858369524e-3556j 3.34e-1017, 3.34e-1017j
14.784373782960315006 + 1.0130937481020898348e-3534j 1.09e-996, 1.09e-996j
46.865777157644118939 - 1.4619467674917032329e-3523j 2.81e-988, 2.81e-988j
4.1945530938283806692 + 5.7835532642353860841e-3556j 4.02e-1006, 4.02e-1006j
1.1889321016726230307 - 4.4396512522711848016e-3561j 2.36e-1012, 2.36e-1012j
83.962687627264106807 + 1.1463272608127995682e-3533j 1.35e-985, 1.35e-985j
180.64705587786647896 + 4.6116139146055894127e-3555j 1.15e-989, 1.15e-989j
144.68704912515873393 + 1.3381201677340626885e-3585j 4.61e-987, 4.61e-987j
36.547604711424621543 + 8.8621911912673672565e-3609j 5.26e-990, 5.26e-990j
5.7751435691045105018 - 1.4612879051191575551e-3651j 3.31e-1004, 3.31e-1004j
0.59691770256722293719 + 5.4353448227670310687e-3662j 1.05e-1014, 1.05e-1014j
62.013389370330164739 - 9.3500840868315981068e-3632j 1.22e-986, 1.22e-986j
2.9927363260593140777 - 9.4696323017904788593e-3687j 7.36e-1008, 7.36e-1008j
31.944693112808295099 - 4.8569843574016230107e-3664j 5.16e-991, 5.16e-991j
52.610681362958574403 + 9.3206217192850778848e-3695j 1.62e-987, 1.62e-987j
0.017961328517581336628 + 5.3784745606100086834e-3784j 1.61e-1020, 1.61e-1020j
0.09339533820209298647 - 1.5012174431053634922e-3782j 8.34e-1019, 8.34e-1019j
76.144760613375000341 - 5.3361549864156052206e-3748j 7.93e-986, 7.93e-986j
4.9435180735107523559 - 4.2112581415534613225e-3791j 3.64e-1005, 3.64e-1005j
41.516843683515998834 + 3.4459504192248421011e-3771j 4.38e-989, 4.38e-989j
11.022118363439274326 + 2.4114491878489483432e-3797j 2.09e-999, 2.09e-999j
0.85713202981591944904 - 5.6890306787859524118e-3810j 1.52e-1013, 1.52e-1013j
49.687603941641300733 + 1.7342018638372954362e-3781j 7.17e-988, 7.17e-988j
116.03105938241494739 - 2.2453105538873653915e-3804j 9.39e-986, 9.39e-986j
9.8374674183825899177 - 4.8419445296446151779e-3828j 2.31e-1000, 2.31e-1000j
18.68772883882461834 - 1.756013018670410334e-3822j 6.18e-995, 6.18e-995j
0.39291634704120916978 + 2.4666643812621348018e-3843j 6.96e-1016, 6.96e-1016j
1.5866209809572019869 - 1.0195145994603492601e-3838j 3.78e-1011, 3.78e-1011j
55.637503145333231344 + 1.3247784260304403049e-3812j 3.38e-987, 3.38e-987j
58.770766633440145384 - 3.1855012488588763479e-3817j 6.7e-987, 6.7e-987j

Weights

Weight (ball center) Error (ball radius)
8.0890694060097405379e-106 + 1.9552914343582580231e-2923j 2.32e-156, 7.68e-901j
7.7658236575806198809e-86 + 4.2740432497242389065e-2913j 2.63e-150, 8.7e-895j
2.9472330374208329266e-113 - 2.8813059592674209606e-2927j 4.39e-159, 1.45e-903j
7.443625833177272432e-100 - 2.3400470345808965954e-2920j 6.28e-155, 2.08e-899j
7.915129454282856075e-75 - 2.3299871356975386856e-2907j 1.74e-147, 5.76e-892j
2.9103827844786583993e-17 + 7.4091556424688573673e-2875j 1.38e-105, 4.56e-850j
4.4786272496882042161e-30 - 3.0005989794834322172e-2883j 2.37e-122, 7.84e-867j
3.2257260222451323005e-15 + 4.3286835386142903329e-2874j 2.67e-102, 8.82e-847j
1.0841261981194142676e-94 + 1.0941891805443331754e-2917j 7.51e-154, 2.48e-898j
1.3718757424114297864e-07 + 1.8956717053473587991e-2869j 1.3e-82, 4.29e-827j
0.0011830171753176298829 + 1.4483751073771612059e-2867j 1.64e-59, 5.43e-804j
8.5157985681300228709e-11 - 8.965289740441910668e-2872j 2.48e-93, 8.2e-838j
7.1439232200750157238e-35 + 5.7189531214029148e-2886j 2.22e-127, 7.36e-872j
1.3927819953155205184e-28 + 2.1950489674661218053e-2882j 2.71e-121, 8.96e-866j
4.7510093964772529767e-55 + 6.2130204467767483182e-2897j 3.25e-141, 1.08e-885j
2.5740077740203650241e-09 - 8.7831738416967927177e-2871j 1.17e-92, 3.88e-837j
1.6994287062475852802e-68 - 4.8435258735157952928e-2904j 2.6e-147, 8.6e-892j
1.6317423265105736967e-57 - 3.0399217375662478186e-2898j 1.32e-142, 4.36e-887j
4.2769253528128075583e-46 + 3.9476926118612088811e-2892j 1.28e-137, 4.25e-882j
4.5894569875714172201e-90 - 2.729059946643268088e-2915j 5.16e-155, 1.71e-899j
6.3748078757608641776e-82 - 4.640686901855824297e-2911j 1.76e-152, 5.81e-897j
1.9025114137976328052e-12 - 9.6119504281914672206e-2873j 2.9e-107, 9.59e-852j
4.6778932638630226411e-44 - 5.0271302131734101107e-2891j 1.91e-137, 6.32e-882j
4.4176541348319039132e-60 + 1.3232399204743739099e-2899j 6.2e-145, 2.05e-889j
4.339182002989047505e-42 + 5.9233684180120650586e-2890j 5.93e-137, 1.96e-881j
1.4042534544113217071e-71 + 1.1691431870473705113e-2905j 1.31e-149, 4.32e-894j
1.3326220040564105132e-11 + 2.9163431961714126301e-2872j 1.69e-109, 5.58e-854j
0.00047725452770518695368 - 7.8719435685818667362e-2868j 1.26e-88, 4.16e-833j
1.6899881664151869707e-06 + 5.3422505695349455207e-2869j 4.46e-99, 1.47e-843j
1.8037038762191126e-19 - 1.3038140602903228304e-2876j 2.21e-122, 7.32e-867j
1.4620877989519597272e-65 + 1.6922265473042417685e-2902j 1.04e-147, 3.45e-892j
0.017402820783330081888 + 1.9812642223662543917e-2866j 2.55e-79, 8.42e-824j
2.4821152936525766114e-13 + 3.2330079600865134955e-2873j 1.07e-113, 3.54e-858j
0.00017807384731208656226 + 4.3536462897022183102e-2868j 4.5e-94, 1.49e-838j
1.2776719936550993874e-31 + 3.9167851389211847195e-2884j 2.56e-132, 8.48e-877j
4.3690452714452621358e-08 - 8.1330071183572405686e-2870j 2.18e-105, 7.22e-850j
1.1087406382063439499e-52 - 1.1396032451066056088e-2895j 4.84e-143, 1.6e-887j
0.060941845980220083174 - 4.5048042388407656688e-2866j 3.79e-78, 1.25e-822j
5.9643888212134665977e-06 - 8.5142659138543400574e-2869j 3.74e-102, 1.24e-846j
3.2875785528150329233e-48 - 2.8544401341087311658e-2893j 3.31e-141, 1.1e-885j
4.9416326554464572615e-10 + 2.7891506425878466105e-2871j 3.93e-111, 1.3e-855j
3.4401900127206916916e-40 - 6.4868485883155361652e-2889j 4.21e-138, 1.39e-882j
2.3475273416365289058e-38 + 6.6301421058386941164e-2888j 1e-137, 3.32e-882j
0.038731499020801010062 + 4.1825005563090946823e-2866j 2.97e-90, 9.84e-835j
0.12204791403533537266 - 2.9214819335188104587e-2866j 3.69e-87, 1.22e-831j
4.6395943890998749141e-07 - 3.386877017292810656e-2869j 5.68e-109, 1.88e-853j
1.2281244995137676795e-20 + 1.8493410482785054975e-2877j 7.1e-129, 2.35e-873j
0.010615441937422792658 - 1.0269900011580198667e-2866j 4.26e-98, 1.41e-842j
0.11162905219946481106 - 5.2517831385418071409e-2866j 3.26e-87, 1.08e-831j
1.3875031393836995467e-36 - 6.3495027096835489319e-2887j 3.87e-137, 1.28e-881j
2.8882791908964128223e-78 + 3.7322359174848392675e-2909j 4.01e-157, 1.33e-901j
9.246083623150272217e-63 - 5.0725764096607456542e-2901j 8.74e-150, 2.89e-894j
3.2088371171589938525e-16 - 2.1396381579359745062e-2874j 8.57e-126, 2.83e-870j
0.0027018778508385583465 - 2.7176543772359299785e-2867j 2.17e-107, 7.19e-852j
0.12507832071187220802 - 6.07442550391884302e-2866j 8.15e-97, 2.7e-841j
3.8567527645005603493e-27 - 1.5403273965065196726e-2881j 7.62e-135, 2.52e-879j
0.025236623125255361357 - 3.2671886364239149063e-2866j 4.46e-104, 1.47e-848j
2.960197727103301812e-14 - 1.1313653638135299317e-2873j 3.92e-124, 1.3e-868j
4.2158769306162091783e-23 + 4.4136927248498157105e-2879j 2.57e-133, 8.5e-878j
0.04514555082610265846 - 3.5067039167822363686e-2867j 5.07e-103, 1.68e-847j
0.094742272011708511999 + 1.3273369766470492742e-2866j 8.65e-103, 2.86e-847j
3.2209079183923829206e-33 - 4.8623688097825829323e-2885j 1e-137, 3.31e-882j
0.0056448130729992397049 + 5.2232459250682350045e-2867j 2.98e-112, 9.85e-857j
2.403245438190314746e-18 + 1.1768783142945958074e-2875j 2.28e-129, 7.53e-874j
1.9834465552313894402e-05 + 1.4194197734955578769e-2868j 1.17e-118, 3.88e-863j
0.12554172121620644688 + 5.9207087667390278268e-2866j 3.73e-110, 1.23e-854j
7.5707725552029554524e-22 - 2.8282854821067247488e-2878j 1.8e-132, 5.96e-877j
2.1039765358162944972e-50 + 1.8902619054906430615e-2894j 1.97e-147, 6.51e-892j
6.1621659394206277421e-05 - 2.4543753691746487664e-2868j 1.22e-119, 4.02e-864j
1.1691497992355782054e-08 + 2.767370205128649491e-2870j 7.87e-123, 2.6e-867j
0.12534378533847435756 + 4.8854840148154460675e-2866j 1.75e-115, 5.78e-860j
0.087268346139896447493 + 4.7554516646229060633e-2866j 1.53e-116, 5.06e-861j
2.1155837867423070187e-24 - 6.8509187855753981232e-2880j 6.73e-135, 2.23e-879j
9.5416183217436555568e-26 + 1.0424522686633524105e-2880j 1.15e-135, 3.81e-880j

Download

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