Rule: Q[3, 7, 58]

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)
208.75337238450215973 - 7.7853139059268925954e-2385j 2.87e-997, 2.87e-997j
224.22849441023979682 - 6.4599327199536301741e-2389j 6.73e-999, 6.73e-999j
253.5615765914976368 - 1.26748793153256668e-2393j 1.22e-1001, 1.22e-1001j
196.14586133812673622 + 1.0872653343858451561e-2380j 5.61e-996, 5.61e-996j
185.15956438699421152 - 2.3733278754925440353e-2389j 6.27e-995, 6.27e-995j
13.267003866425797719 - 3.6450385903107997809e-2418j 4.14e-999, 4.14e-999j
135.78502156509386008 + 5.3105848505168521014e-2408j 6.52e-991, 6.52e-991j
105.89966077492171198 - 5.018274086189898386e-2440j 1.82e-989, 1.82e-989j
32.574987549804300702 - 5.9724025920209667589e-2470j 5.14e-993, 5.14e-993j
43.030969859873492269 + 2.6490061933469364491e-2466j 2.27e-991, 2.27e-991j
40.254031127211881503 - 8.1356041685363365488e-2469j 9.37e-992, 9.37e-992j
18.473060483615685957 - 2.6252091981295730616e-2488j 3.89e-996, 3.89e-996j
100.69501092994442242 - 3.0256871713542088426e-2497j 2.7e-989, 2.7e-989j
150.06278155043000101 + 2.8167292635863380728e-2566j 6.52e-992, 6.52e-992j
142.71877236519129518 + 4.0849479258778211297e-2618j 2.21e-991, 2.21e-991j
11.866242649035322842 - 6.6239545840050847942e-2661j 5.32e-1000, 5.32e-1000j
6.2899450829374791969 - 5.8356045626925801816e-2664j 4.79e-1004, 4.79e-1004j
35.028466536483169238 - 1.0447182704027215451e-2649j 1.51e-992, 1.51e-992j
25.829644150866535813 - 1.6507467330539651366e-2658j 1.8e-994, 1.8e-994j
175.28482751824048243 + 2.8985224559565330098e-2653j 4.96e-994, 4.96e-994j
5.5060198945244727485 + 1.3589221008611636298e-2704j 8.97e-1005, 8.97e-1005j
62.187249252067054375 - 1.6934972872971208984e-2694j 1.09e-989, 1.09e-989j
117.01659196750118015 - 6.2123826274440111277e-2746j 6.98e-990, 6.98e-990j
90.915520527022612456 - 4.083581015004331837e-2790j 3.76e-989, 3.76e-989j
166.24761605721041246 + 1.2791172789755093427e-2840j 3.21e-993, 3.21e-993j
27.976822998394519874 - 4.4730120874411923388e-2874j 5.91e-994, 5.91e-994j
86.315568575021779106 + 4.3710627770326172178e-2911j 4.1e-989, 4.1e-989j
3.9859351438217261538 + 3.0003006871643445117e-2979j 1.19e-1006, 1.19e-1006j
81.894605124432986518 - 2.5784989148750765994e-2968j 3.88e-989, 3.88e-989j
16.241947986781907748 + 5.6359593745623936981e-3021j 3.07e-997, 3.07e-997j
69.619230043923512264 + 8.6038362283409641695e-3012j 2.32e-989, 2.32e-989j
9.3222143615948634386 - 1.380416636304943226e-3052j 1.14e-1001, 1.14e-1001j
3.2649898203301768956 + 3.0251120986912592539e-3058j 1.34e-1007, 1.34e-1007j
37.587384230749320044 + 6.9134448950339266613e-3041j 4.22e-992, 4.22e-992j
65.832236315458140098 + 1.2418384561398906701e-3075j 1.69e-989, 1.69e-989j
2.5820248267264512401 + 1.7432094017666164748e-3139j 2.64e-1008, 2.64e-1008j
48.927302537814341673 + 4.5819455392731611012e-3149j 1.03e-990, 1.03e-990j
0.69597237981148797693 - 5.5740367279770395416e-3209j 3.56e-1014, 3.56e-1014j
2.2942803602790417198 + 3.3070711489783470023e-3205j 1.31e-1008, 1.31e-1008j
129.21404490794326738 + 4.4530217171687212462e-3210j 1.61e-990, 1.61e-990j
58.678916032589152337 + 1.0033116503226439365e-3250j 6.73e-990, 6.73e-990j
122.9681112363804148 - 3.0109458359492326948e-3282j 3.52e-990, 3.52e-990j
8.1928883636871282333 - 9.695816560408053918e-3315j 1.7e-1002, 1.7e-1002j
55.302371736454703532 + 2.7785847798406036787e-3300j 4e-990, 4e-990j
1.1294569298590887796 - 3.4105504476485916914e-3325j 5.17e-1012, 5.17e-1012j
17.487011118510389827 + 5.8300508846524706978e-3311j 1.61e-996, 1.61e-996j
73.554138265985320906 - 1.4040312208612326807e-3303j 3.02e-989, 3.02e-989j
7.1761870384892667136 - 1.5374107244423606485e-3324j 2.84e-1003, 2.84e-1003j
0.071930230287362735756 - 2.0666609127267163022e-3340j 2.34e-1019, 2.34e-1019j
52.05318327763317661 - 7.2680952820603559487e-3310j 2e-990, 2e-990j
10.549313797309160475 - 2.8834614369741550798e-3330j 7.49e-1001, 7.49e-1001j
111.33418160809962213 - 1.592304161064878563e-3317j 1.21e-989, 1.21e-989j
23.783892343800750961 - 2.6893960316476372959e-3341j 5.94e-995, 5.94e-995j
21.843925794791787693 + 5.283128525835255541e-3342j 1.99e-995, 1.99e-995j
0.97122857407045987065 + 2.9043539029286930114e-3359j 1.28e-1012, 1.28e-1012j
1.537975904934835722 + 4.1988184310872246066e-3358j 5.52e-1011, 5.52e-1011j
157.87840498605769348 - 6.9141493482066333611e-3336j 1.52e-992, 1.52e-992j
95.704764960537505141 + 2.755898556065507612e-3351j 3.46e-989, 3.46e-989j
4.7429036260756082131 + 4.4683326040026285329e-3384j 1.09e-1005, 1.09e-1005j
0.41577455678347908331 - 2.9278244420448176575e-3394j 5.78e-1016, 5.78e-1016j
2.0808132485172652658 + 7.658756098408585952e-3388j 3.23e-1009, 3.23e-1009j
20.030264379855966674 - 6.4278725761342849351e-3374j 7.46e-996, 7.46e-996j
0.20635794730174418872 + 3.5030754879052600644e-3396j 1.06e-1017, 1.06e-1017j
77.643504445083100291 - 1.9513672973412011787e-3366j 3.65e-989, 3.65e-989j
14.740701406169276261 - 6.1324810990438111383e-3382j 3.53e-998, 3.53e-998j
30.224965096445803412 + 2.2116177904224077929e-3377j 1.96e-993, 1.96e-993j
0.010179190465611048601 - 2.4961880649683842677e-3443j 7.15e-1021, 7.15e-1021j
45.921027395141509426 - 9.6436913524812280308e-3375j 4.88e-991, 4.88e-991j

Weights

Weight (ball center) Error (ball radius)
2.997029881550587137e-90 - 1.126655198284822444e-2468j 1.72e-167, 4.13e-915j
7.4357262143202149962e-97 + 2.2536378993540804026e-2472j 8.95e-170, 2.14e-917j
1.0497742657630771568e-108 - 1.9925666807431769232e-2478j 5.47e-174, 1.31e-921j
7.6272962394037451288e-85 - 4.2557934828755038842e-2465j 2.06e-166, 4.93e-914j
4.000225161384337306e-80 + 2.026040989068007191e-2463j 2.39e-165, 5.73e-913j
2.4922614795922934036e-06 + 1.1955857440560522906e-2422j 4.48e-98, 1.07e-845j
7.216392783394644709e-59 + 4.4400152614035607308e-2453j 7.09e-159, 1.7e-906j
5.4201724925355220439e-46 - 2.1009723596501830475e-2446j 5.18e-153, 1.24e-900j
1.7113391881602419608e-14 - 1.3426567921038373859e-2428j 9.48e-124, 2.27e-871j
5.8094436398023041684e-19 - 2.0230487213955178484e-2431j 3.62e-131, 8.68e-879j
8.9676739149879920991e-18 + 1.0812945116772496184e-2430j 2.05e-129, 4.91e-877j
1.2177349100660896807e-08 + 9.7930966824571939546e-2424j 1.49e-111, 3.58e-859j
9.4593516889502806313e-44 + 3.2047633430953896307e-2445j 7.78e-153, 1.86e-900j
5.0997886743772630805e-65 + 3.41427222214490625e-2456j 4.92e-163, 1.18e-910j
7.4321249281224581792e-62 - 1.3435075309282968422e-2454j 1.38e-161, 3.31e-909j
9.5515517313586439377e-06 - 2.8272308679270764591e-2422j 1.14e-105, 2.74e-853j
0.0015260573308555545514 + 3.4506677043026982875e-2420j 4.29e-93, 1.03e-840j
1.5356197223768095259e-15 + 2.7735154764245428662e-2429j 3.13e-129, 7.51e-877j
1.2701936868555583489e-11 + 1.3780979473079273524e-2426j 2.31e-123, 5.54e-871j
7.0612367249376331315e-76 - 1.6723695568487081203e-2461j 1.42e-167, 3.41e-915j
0.0030976122980443203171 - 7.0426334026231647419e-2420j 8.77e-94, 2.1e-841j
3.5139479540023170622e-27 - 3.3143137770644441808e-2436j 4.49e-145, 1.07e-892j
8.8054034863209743402e-51 - 6.5462677960605826286e-2449j 2.24e-158, 5.37e-906j
1.5392905077918095072e-39 + 5.5984555252957546841e-2443j 1.66e-153, 3.98e-901j
5.4717507439338473502e-72 + 1.2168804751212116686e-2459j 4.7e-167, 1.13e-914j
1.5551269657714481944e-12 - 2.963977370470096589e-2427j 1.4e-129, 3.34e-877j
1.4712626045573765512e-37 - 6.4869040986962868591e-2442j 6.51e-153, 1.56e-900j
0.013806606139878173966 - 2.3913668199053124912e-2419j 5.57e-100, 1.33e-847j
1.1764511108813452059e-35 + 6.9317838124779256179e-2441j 2.24e-152, 5.36e-900j
1.294125553052746059e-07 + 3.1934680132536223809e-2423j 1.68e-123, 4.04e-871j
2.2455898978613725198e-30 - 5.4323658687281844535e-2438j 3.55e-150, 8.51e-898j
0.00010550581740206189843 - 1.812684729297372653e-2421j 1.26e-116, 3.01e-864j
0.026605761287186422252 + 5.7434375617228501884e-2419j 2.84e-102, 6.8e-850j
1.2389173521551846797e-16 - 5.5681300602134765703e-2430j 1.04e-137, 2.5e-885j
9.5364825911780988534e-29 + 4.376297885690712592e-2437j 3.36e-149, 8.05e-897j
0.054232364023001157507 - 3.3253660457266932453e-2418j 7.64e-103, 1.83e-850j
1.7283914943283465128e-21 - 6.2470210861982763346e-2433j 1.76e-144, 4.23e-892j
0.154254077929437736 - 2.5467666750100567987e-2418j 3e-103, 7.19e-851j
-0.027218080575958709717 + 8.1265916990065071495e-2418j 3.17e-103, 7.6e-851j
4.8913105600244214036e-56 - 1.2525118117741943016e-2451j 2.64e-164, 6.34e-912j
1.1293777764404116383e-25 + 2.3670435724446606441e-2435j 3.83e-148, 9.17e-896j
2.4018086440256069404e-53 + 3.0588598115239737167e-2450j 2.61e-163, 6.27e-911j
0.00029771381020686521823 + 4.977554620167408236e-2421j 3.14e-123, 7.53e-871j
3.1812409356034427287e-24 - 1.5989956942784929821e-2434j 1.27e-147, 3.05e-895j
0.095777898056002854935 - 6.8233619963382265867e-2418j 1.04e-108, 2.5e-856j
2.389787707443654881e-08 - 2.1776318877148592671e-2423j 6.49e-133, 1.56e-880j
4.5613680013671837779e-32 + 6.318427303137684953e-2439j 5.12e-153, 1.23e-900j
0.00072889024184607777521 - 1.3780272105137081418e-2420j 9.51e-125, 2.28e-872j
0.090280636463190186351 + 3.8298127492132668761e-2419j 5.58e-113, 1.34e-860j
7.8878165220239782365e-23 + 1.024671499158001915e-2433j 5.77e-147, 1.38e-894j
3.3367530364451083029e-05 + 6.9116000832835576167e-2422j 3.12e-129, 7.47e-877j
2.4710446820199276493e-48 + 1.2406039926451518497e-2447j 6.66e-162, 1.6e-909j
9.3443975547366826557e-11 - 6.5036549054230079436e-2426j 7.03e-139, 1.68e-886j
6.1402400214529563807e-10 + 3.214853210697859772e-2425j 3.38e-138, 8.09e-886j
0.059613846583945173284 + 6.7769794223570900849e-2418j 7.06e-121, 1.69e-868j
0.10236562896908452807 + 3.3914032389695792126e-2418j 1.27e-122, 3.03e-870j
2.1953647274320727353e-68 - 7.1574891335983143673e-2458j 1.59e-172, 3.81e-920j
1.3336748913797671978e-41 - 4.4338931996814190402e-2444j 5.69e-159, 1.36e-906j
0.0066628158840907551215 + 1.2644342719771236633e-2419j 1.28e-129, 3.06e-877j
0.16254248923852618263 + 1.1238545019765329427e-2418j 2.5e-126, 5.99e-874j
0.086011887303324551321 - 6.7364436280960812486e-2418j 1.84e-126, 4.41e-874j
3.4590893374294871462e-09 - 1.7586856491012925831e-2424j 1.33e-138, 3.19e-886j
0.13996085586450638434 - 6.5156381083454985357e-2419j 5.47e-128, 1.31e-875j
7.9411165942449789526e-34 - 6.8618542599771422083e-2440j 4.32e-155, 1.03e-902j
5.9543353932559111176e-07 - 5.1828988518763174521e-2423j 4.08e-137, 9.79e-885j
1.717818684462180378e-13 + 6.354705617112207382e-2428j 3.33e-143, 7.98e-891j
0.02930125688952857288 - 1.3391805047718999679e-2419j 2.52e-133, 6.04e-881j
3.3591055406884593425e-20 + 3.6339420508659205441e-2432j 1.14e-147, 2.74e-895j

Download

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