Rule: Q[2, 71]

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)
266.05711291178511251 + 6.3877431651864903445e-2404j 8.66e-998, 8.66e-998j
222.47951680586125036 + 1.2828530283825736616e-2398j 5.56e-993, 5.56e-993j
234.56076895006597966 - 2.1989349902520236574e-2400j 2.9e-994, 2.9e-994j
248.54081552819901875 + 5.8107142710099119407e-2402j 8.98e-996, 8.98e-996j
201.78429101749153944 + 8.342827263612400835e-2394j 6.08e-991, 6.08e-991j
154.42577332556827143 + 1.630605742227703241e-2392j 3.62e-987, 3.62e-987j
86.569925734616461439 - 4.2994853898988930413e-2394j 3.08e-985, 3.08e-985j
16.605187537067259299 - 2.2466940660351350553e-2414j 7.31e-997, 7.31e-997j
161.28238816085174819 - 1.3376184859382285679e-2402j 1.26e-987, 1.26e-987j
48.926852445987445438 + 1.2932036699623817269e-2416j 5.59e-988, 5.59e-988j
21.572105416302468758 + 8.4513110983460486159e-2423j 1.36e-994, 1.36e-994j
67.731868234640713818 + 5.9662449618546256447e-2414j 4.67e-986, 4.67e-986j
33.678789942367847857 - 4.8138348677523032865e-2438j 7.85e-991, 7.85e-991j
11.048522392884693459 - 4.9943421843699812117e-2455j 3.42e-1000, 3.42e-1000j
168.48395472527490978 + 4.9602635960452667585e-2440j 4.24e-988, 4.24e-988j
99.493926418470545433 + 1.4952197922704154641e-2495j 3.83e-985, 3.83e-985j
129.85043987149799684 + 3.5597493212306631523e-2545j 7.67e-986, 7.67e-986j
6.6648652014897038193 - 9.2786961580208517314e-2599j 5.69e-1004, 5.69e-1004j
71.25211487064252158 + 1.284281490376949224e-2579j 8.24e-986, 8.24e-986j
23.384931768528694598 + 1.2847660586807600354e-2610j 6.27e-994, 6.27e-994j
40.888075399620407791 - 1.5836208041205271833e-2602j 2.64e-989, 2.64e-989j
19.838545238548298507 + 2.5013784307621717569e-2631j 2.45e-995, 2.45e-995j
74.891784302508898325 - 8.1363469274389299208e-2640j 1.19e-985, 1.19e-985j
8.7127551176294391417 - 2.8138778449637640194e-2695j 5.05e-1002, 5.05e-1002j
135.61399263457719993 - 2.3581875363068148411e-2699j 4.25e-986, 4.25e-986j
51.800184497664904156 - 2.3543701882136492257e-2730j 1.35e-987, 1.35e-987j
113.8397162669359592 + 3.7285246990213405496e-2754j 2.65e-985, 2.65e-985j
211.6639082004350696 - 6.8427588706852292229e-2779j 6.54e-992, 6.54e-992j
13.67738230456447629 - 6.164086070758446088e-2799j 1.75e-998, 1.75e-998j
31.451793050897317616 + 1.0834637681727890356e-2790j 2.04e-991, 2.04e-991j
82.546050512084009575 + 5.4962209509492701096e-2784j 2.5e-985, 2.5e-985j
4.9001420211727392056 - 3.0598521567015729988e-2831j 5.26e-1006, 5.26e-1006j
1.2616013881677723175 + 5.1796152432554170016e-2839j 8.12e-1013, 8.12e-1013j
25.278114714230987612 + 1.1442244737772560079e-2817j 3.02e-993, 3.02e-993j
95.037738182723978025 - 4.3058177455374330904e-2808j 3.82e-985, 3.82e-985j
57.851560765400550528 - 8.00547084804116484e-2825j 7.01e-987, 7.01e-987j
184.10184223940908097 + 4.5468665071301368328e-2823j 2.16e-989, 2.16e-989j
0.89082861214007298402 - 3.1865974600931529679e-2869j 5.03e-1014, 5.03e-1014j
78.654950921472250337 + 6.4947166426958547804e-2840j 1.75e-985, 1.75e-985j
38.395282843894476966 - 2.0002733186879503306e-2866j 8.37e-990, 8.37e-990j
54.774232892607508782 + 2.8695203521153887559e-2861j 3.32e-987, 3.32e-987j
176.07263722078982047 + 2.5783327103027234373e-2895j 9.42e-989, 9.42e-989j
9.8443416293862993347 + 1.2690532906753568571e-2961j 4.04e-1001, 4.04e-1001j
15.103522820557878229 + 4.8402929239876228049e-2958j 1.16e-997, 1.16e-997j
104.10755727815268678 + 1.8756899044744790842e-2945j 3.62e-985, 3.62e-985j
43.4729501283124933 - 4.9858816222688389566e-2972j 7.97e-989, 7.97e-989j
192.64111979270264774 + 2.5415870860358066237e-2979j 4.05e-990, 4.05e-990j
147.88006695659838693 + 1.1066869388953098324e-3047j 8.55e-987, 8.55e-987j
0.5857864376269049512 - 2.5717599986345933484e-3148j 2.48e-1015, 2.48e-1015j
4.1225940098927715664 - 1.0017624431561790495e-3119j 4.5e-1007, 4.5e-1007j
108.8865407741171075 + 9.0989706748191234818e-3144j 3.06e-985, 3.06e-985j
141.61726957866068242 + 2.8873503900485776087e-3236j 2.14e-986, 2.14e-986j
118.97701535989257869 - 7.712460753485537813e-3299j 1.79e-985, 1.79e-985j
12.325966326830096302 + 1.029594367301955231e-3357j 2.3e-999, 2.3e-999j
18.183226804887947517 + 4.3579396970954180309e-3354j 4.26e-996, 4.26e-996j
3.4142135623730950488 + 4.2409013261318227451e-3366j 3.9e-1008, 3.9e-1008j
0.058579193056520324448 + 4.2333607131729623803e-3378j 1.68e-1019, 1.68e-1019j
90.731879524722385091 - 8.6329934984109712418e-3342j 3.52e-985, 3.52e-985j
1.6987329741267562012 + 1.1234230279729489967e-3395j 1.38e-1011, 1.38e-1011j
0.34583859425308627752 - 5.9107164261901962104e-3401j 1.19e-1016, 1.19e-1016j
5.7473866963960173113 - 5.4434739503819316563e-3389j 5.96e-1005, 5.96e-1005j
35.992754970032634215 + 3.3726807804270564587e-3374j 2.64e-990, 2.64e-990j
124.30966448783731914 - 2.2066592538688094167e-3367j 1.23e-985, 1.23e-985j
46.15184967470772293 + 5.7551052147509604392e-3383j 2.14e-988, 2.14e-988j
2.7744714963570630254 + 2.8538220386023823081e-3404j 2.69e-1009, 2.69e-1009j
2.2028297835676012571 - 4.154534217104971257e-3405j 1.94e-1010, 1.94e-1010j
0.0079054448541765358068 - 2.3147647406465057386e-3415j 7.54e-1021, 7.54e-1021j
7.6531299961482681629 + 1.1765670348465377409e-3397j 5.76e-1003, 5.76e-1003j
0.17035090959224113206 - 2.0817820654729882932e-3413j 4.72e-1018, 4.72e-1018j
27.252815103899623517 - 7.7698165825955442607e-3388j 1.23e-992, 1.23e-992j
64.327292432121051109 - 8.5095839432341821519e-3383j 2.79e-986, 2.79e-986j
29.310269027725194456 + 6.3198707826707868626e-3388j 5.21e-992, 5.21e-992j
61.034924368604447707 + 4.3733371321028990007e-3382j 1.36e-986, 1.36e-986j

Weights

Weight (ball center) Error (ball radius)
5.8548183508523410314e-115 - 3.4013834920202643226e-2472j 5.37e-160, 2.4e-904j
2.7190108461594043923e-96 + 1.057486256518009808e-2462j 7.67e-155, 3.44e-899j
1.7440863965598958602e-101 - 2.396232475195080488e-2465j 1.68e-156, 7.5e-901j
1.7577946061391170544e-107 + 2.1360137748667905844e-2468j 1.9e-158, 8.49e-903j
2.2041119775939306409e-87 + 3.726887039391596323e-2458j 3.47e-153, 1.55e-897j
5.748536072699316796e-67 + 1.1656690199532887311e-2447j 4.6e-147, 2.06e-891j
1.0353649285923590002e-37 + 2.2506501610665433052e-2431j 1.29e-132, 5.77e-877j
9.460115656710933869e-08 + 1.3030776273864757659e-2417j 1.83e-87, 8.21e-832j
6.3454221202671846881e-70 - 3.4431565297213372189e-2449j 2.99e-148, 1.34e-892j
1.5928297382217389677e-21 - 1.9273159237099627919e-2424j 5.03e-118, 2.25e-862j
7.586939065584781429e-10 - 1.1212230890527578186e-2418j 3.39e-96, 1.52e-840j
1.3296175246317983852e-29 - 3.0139737518935228529e-2428j 9.24e-127, 4.14e-871j
5.3648307440499021025e-15 - 2.9966637467908443611e-2421j 1.01e-108, 4.5e-853j
1.974029570409501481e-05 + 2.0623016683361385689e-2416j 7.38e-81, 3.3e-825j
4.9754589701302971069e-73 + 8.6070650445559192557e-2451j 5.05e-150, 2.26e-894j
2.7976016425099617437e-43 + 5.2924335954149127971e-2435j 1.34e-137, 5.98e-882j
2.2839369173013371382e-56 + 3.9657004762741316103e-2442j 1.53e-144, 6.87e-889j
0.0012147237619945366555 + 1.8466892907877559577e-2415j 4.43e-74, 1.98e-818j
4.0681657795410222126e-31 + 6.3277744360345965157e-2429j 5.07e-129, 2.27e-873j
1.2938554104062454657e-10 + 4.5958227172325970154e-2419j 3.43e-103, 1.54e-847j
4.4372630540825335686e-18 + 9.1196629882562606712e-2423j 6.79e-117, 3.04e-861j
4.1040522665470352782e-09 + 2.635060339366077911e-2418j 1.2e-99, 5.38e-844j
1.1045780778042797767e-32 - 1.3352588671837132101e-2429j 1.27e-130, 5.71e-875j
0.00018018231252493203106 + 6.6241258484345523847e-2416j 6.6e-85, 2.96e-829j
7.4644236952433227323e-59 - 1.9586278321677471305e-2443j 1.6e-146, 7.18e-891j
9.3182823325477794561e-23 + 4.9124627729541952516e-2425j 2.75e-123, 1.23e-867j
1.831343655787778575e-49 - 1.9005789265124777513e-2438j 1.16e-142, 5.2e-887j
1.2264399749624344916e-91 - 2.500839569209950296e-2460j 1.02e-159, 4.55e-904j
1.594339586527474705e-06 + 5.5698059923436593623e-2417j 2.74e-98, 1.23e-842j
4.7853783332636219308e-14 + 8.8624147275359372301e-2421j 3.2e-114, 1.43e-858j
5.5979977738795763116e-36 - 8.32395119519234348e-2431j 2.81e-134, 1.26e-878j
0.0060480580881705050027 + 4.4645998244977306575e-2415j 1.01e-84, 4.52e-829j
0.1143700912120832771 + 2.5404171597577644512e-2414j 6.07e-64, 2.72e-808j
2.0335404558946345979e-11 - 1.8140511233934720516e-2419j 1.59e-110, 7.1e-855j
2.3286208876293866235e-41 - 7.5353133943909919517e-2434j 3.55e-138, 1.59e-882j
2.3491600056340796998e-25 + 2.8336007260552191972e-2426j 6.7e-128, 3e-872j
9.1863370203856362014e-80 + 2.9735929942367609237e-2454j 3.35e-157, 1.5e-901j
0.13860523889925735332 - 2.9131890940655640845e-2414j 1.09e-72, 4.89e-817j
2.6507870658778643284e-34 + 2.9807010556131394682e-2430j 1.74e-133, 7.77e-878j
5.174157824401496088e-17 - 3.0408746886999975553e-2422j 1.73e-121, 7.75e-866j
4.927351240049447045e-24 - 1.2030161068257940192e-2425j 3.71e-127, 1.66e-871j
2.6586343955107310618e-76 - 1.7818893936457313243e-2452j 7.41e-156, 3.32e-900j
6.1946394519249004847e-05 - 3.7621201214409230358e-2416j 1.33e-104, 5.97e-849j
4.037335210735368082e-07 - 2.7432585923728171674e-2417j 1.51e-109, 6.76e-854j
2.8726995102792867452e-45 - 3.8660006949220990349e-2436j 4.31e-142, 1.93e-886j
3.4685636887511365491e-19 - 2.6262386883412032007e-2423j 3.95e-125, 1.77e-869j
1.9170818673748084068e-83 - 3.8626288354587358483e-2456j 3.08e-159, 1.38e-903j
3.8254588355161040534e-64 - 3.3995572727254854804e-2446j 9.93e-152, 4.45e-896j
0.15163031333638611135 + 3.1570522878872491133e-2414j 4.06e-94, 1.82e-838j
0.012036402106632435917 - 6.5751666468396628795e-2415j 4.23e-105, 1.89e-849j
2.5015909339151105625e-47 + 2.7738219487277209527e-2437j 3.24e-144, 1.45e-888j
1.9223125120865702532e-61 + 8.6696529125480507629e-2445j 5.63e-151, 2.52e-895j
1.1160614659199344256e-51 + 1.2218949838601553641e-2439j 3.76e-147, 1.68e-891j
5.8290541380137902873e-06 - 1.0910464656247847838e-2416j 3.4e-118, 1.52e-862j
2.0497784596939209738e-08 - 5.9675591937496443287e-2418j 2.02e-121, 9.05e-866j
0.022175230528063996502 + 9.3313693608567756666e-2415j 2.37e-112, 1.06e-856j
0.075763087267642091854 - 2.2271037717286502321e-2414j 2.43e-107, 1.09e-851j
1.6683308108394863864e-39 + 1.3271862651267849076e-2432j 2.81e-141, 1.26e-885j
0.08606437690985901645 - 2.1088830585841912317e-2414j 2.37e-110, 1.06e-854j
0.14691147735548737625 - 3.1915136734679583327e-2414j 4.2e-108, 1.88e-852j
0.0028154231868434106483 - 2.9233284949997355838e-2415j 1.29e-115, 5.77e-860j
5.509139546746824119e-16 + 9.7387972851437185374e-2422j 2.15e-129, 9.61e-874j
5.5995531688912910546e-54 - 7.2745682277549524202e-2441j 1.85e-148, 8.28e-893j
2.4667586046533018698e-20 + 7.2609673585811331973e-2424j 3.13e-132, 1.4e-876j
0.037778868747465938806 - 1.2748343432044355802e-2414j 9.07e-117, 4.06e-861j
0.059418770788300964754 + 1.6741483677474157347e-2414j 2.91e-116, 1.3e-860j
0.023408544896507400783 + 8.7450764699530620826e-2415j 7.52e-115, 3.37e-859j
0.00048587328558390774551 - 1.1257854570485289024e-2415j 3.99e-120, 1.79e-864j
0.12100370338493165065 + 2.9255109778564779304e-2414j 9.63e-115, 4.31e-859j
2.942484245646447982e-12 + 6.8926836619353469818e-2420j 3e-128, 1.34e-872j
3.8706738893464691075e-28 + 1.4117227653838049097e-2427j 1.3e-137, 5.83e-882j
3.9154227408035836374e-13 - 2.5200690259304115264e-2420j 1.19e-129, 5.34e-874j
1.0070687150670596721e-26 - 6.4319471008812537479e-2427j 6.54e-137, 2.93e-881j

Download

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