Rule: Q[1, 3, 79]

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)
300.98593598320988511 - 1.9978423026233442796e-2373j 3.36e-995, 3.36e-995j
244.06858576386106747 + 2.2792956185963096676e-2369j 5.33e-989, 5.33e-989j
268.08268361449188118 - 6.6202779467869089387e-2396j 1.58e-991, 1.58e-991j
224.04511780661751012 + 7.8851505174996539067e-2455j 4.71e-987, 4.71e-987j
24.050501010122352326 + 4.8525208148681642192e-2522j 2.33e-991, 2.33e-991j
151.35824252873207289 - 1.693150216560138179e-2523j 8.03e-982, 8.03e-982j
71.607717846501169868 - 9.5073647480954098068e-2553j 3.86e-982, 3.86e-982j
183.56954614423888401 - 1.4880880291342427578e-2571j 8.86e-984, 8.86e-984j
68.327747396018425376 - 1.9597063210506953741e-2596j 2.07e-982, 2.07e-982j
93.47581572810495634 + 9.9935088538605204514e-2628j 5.41e-981, 5.41e-981j
13.393158656997251698 + 1.269451257971027576e-2671j 9.89e-997, 9.89e-997j
53.336056628887191645 - 2.3009540755143859313e-2656j 3.87e-984, 3.87e-984j
47.958558880865080772 - 6.111860983882959953e-2662j 4.98e-985, 4.98e-985j
145.61684788839339842 - 4.6253470650580423895e-2676j 1.41e-981, 1.41e-981j
114.9543700740945452 + 7.8421030861097312535e-2708j 8.85e-981, 8.85e-981j
10.960085388618265361 + 5.4231925109761506217e-2751j 1.97e-998, 1.97e-998j
42.914048586096977329 + 4.3185133121823323265e-2738j 6.04e-986, 6.04e-986j
35.94641959862274489 + 3.0955948872632617353e-2740j 1.47e-987, 1.47e-987j
8.7990984501805991715 - 7.1247101871926510386e-2752j 3.49e-1000, 3.49e-1000j
157.3104494576360725 + 7.6879469030100085175e-2733j 4.02e-982, 4.02e-982j
27.723310151053843182 - 1.3814708739644979244e-2771j 5.27e-990, 5.27e-990j
282.70420764231224586 - 2.8089500210362194874e-2772j 3.94e-993, 3.94e-993j
176.59584461306901129 - 5.4266265637144185006e-2763j 2.84e-983, 2.84e-983j
129.53316437995065752 - 1.3558364845810163666e-2792j 5.26e-981, 5.26e-981j
255.42290910625274056 + 1.875447634783607132e-2821j 3.64e-990, 3.64e-990j
105.96911462078931511 - 4.3029401089927958667e-2817j 8.71e-981, 8.71e-981j
20.661037855159262913 + 3.0063131072633753462e-2838j 7.47e-993, 7.47e-993j
22.320726309950922301 - 2.1636478027289985155e-2837j 4.28e-992, 4.28e-992j
82.054803546582418408 + 1.1362990199519526358e-2825j 1.85e-981, 1.85e-981j
85.749203787188103917 + 1.1734118906813537476e-2848j 3.17e-981, 3.17e-981j
169.91025981884993324 + 2.1923857871418317588e-2895j 7.5e-983, 7.5e-983j
3.983791993269558821 - 1.6898775420533598234e-2963j 8.56e-1006, 8.56e-1006j
16.096154629775012833 - 8.2530153077719224528e-2954j 3.73e-995, 3.73e-995j
2.7956955457690225582 - 7.8151794992797587278e-2966j 4.6e-1008, 4.6e-1008j
74.987057485830043115 + 6.3476458331548890808e-2937j 7.24e-982, 7.24e-982j
140.07305463087203551 + 6.4024267361928617175e-2962j 2.18e-981, 2.18e-981j
233.67819836466736719 - 3.6088606966562011166e-2984j 5.58e-988, 5.58e-988j
1.3667165122533468031 + 1.6961221266175549113e-3007j 9.44e-1012, 9.44e-1012j
50.604896483469881034 + 1.6384503176392439949e-2981j 1.42e-984, 1.42e-984j
3.369839231310923141 + 8.4482474710583107448e-3003j 6.42e-1007, 6.42e-1007j
56.15374028729329344 + 1.228700312906605424e-2978j 9.47e-984, 9.47e-984j
89.555003606768990205 + 1.6482043976380443947e-2975j 4.18e-981, 4.18e-981j
5.3323287938656835101 - 1.6951987646469135414e-3000j 8.46e-1004, 8.46e-1004j
31.686082344265834929 + 5.8419175176957027616e-2986j 9.61e-989, 9.61e-989j
19.070765915553381645 + 2.4980530690350075436e-2991j 1.52e-993, 1.52e-993j
17.549311280791200814 + 2.4790480422495072799e-2991j 2.33e-994, 2.33e-994j
12.142870378689866708 + 1.8653287050329680183e-2994j 1.36e-997, 1.36e-997j
59.059757812521868547 - 6.9345601688279463242e-2980j 2.15e-983, 2.15e-983j
2.2673342538560685053 - 4.0611931973924207752e-3006j 2.83e-1009, 2.83e-1009j
97.515549403959910837 - 2.3751125563369149109e-2976j 6.72e-981, 6.72e-981j
1.7898713412551054741 + 3.6345465559350099064e-3030j 1.68e-1010, 1.68e-1010j
101.67844507627209016 - 1.7137286975393519243e-3000j 7.95e-981, 7.95e-981j
7.8232631436879996743 + 4.7050089956616980508e-3049j 4.3e-1001, 4.3e-1001j
45.395444472859900709 - 2.4240231359144252514e-3031j 1.75e-985, 1.75e-985j
38.190830446760543472 + 3.8980284371776073631e-3034j 5.27e-987, 5.27e-987j
134.71525172914691004 - 1.0906453645072656477e-3027j 3.37e-981, 3.37e-981j
190.8603079407132919 - 3.9305970871046772109e-3049j 2.81e-984, 2.81e-984j
33.778540817859529286 + 1.3181018154855570687e-3070j 4e-988, 4e-988j
6.9197777636806438028 + 8.7313130797483766538e-3085j 5.4e-1002, 5.4e-1002j
0.69109697472139995349 + 6.7455872218711145017e-3097j 2.5e-1014, 2.5e-1014j
40.51295500882803231 + 6.8453723660722957194e-3069j 1.89e-986, 1.89e-986j
29.667999110032000146 - 2.1029192067369672881e-3073j 2.37e-989, 2.37e-989j
206.54219203607667563 + 9.3452678474936456071e-3064j 1.51e-985, 1.51e-985j
215.03214191709184033 + 1.2166577061912474345e-3091j 2.92e-986, 2.92e-986j
14.710871838450362143 - 3.3042113073296776525e-3148j 6.19e-996, 6.19e-996j
163.4886157273449789 + 2.3140775642658975523e-3134j 1.76e-982, 1.76e-982j
124.51764453404122319 - 2.9443796834900829626e-3179j 6.21e-981, 6.21e-981j
4.6352893646943549759 + 7.3070557251120791375e-3240j 8.86e-1005, 8.86e-1005j
119.66050249384187071 + 2.9302976886934124293e-3215j 7.7e-981, 7.7e-981j
78.468456694002951758 + 9.6349828532282233634e-3242j 1.18e-981, 1.18e-981j
0.056897625001077184683 - 9.7783874418979874674e-3323j 3.98e-1019, 3.98e-1019j
25.851096690171419508 + 3.7563918005286374656e-3294j 1.16e-990, 1.16e-990j
0.25136117571394126274 - 4.7694710302504804649e-3320j 7.31e-1017, 7.31e-1017j
198.503324463144067 + 1.6031888384404044055e-3283j 6.66e-985, 6.66e-985j
110.39258832899844716 + 2.1143597809617839644e-3327j 9.14e-981, 9.14e-981j
0.44107859532708059835 + 1.3959562934335674528e-3383j 1.14e-1015, 1.14e-1015j
65.144635873489139123 + 1.4845099421987089447e-3348j 1.05e-982, 1.05e-982j
9.8452049391981589966 - 2.1180606741887959988e-3370j 2.61e-999, 2.61e-999j
62.056037616420059859 - 4.8294544860985098511e-3351j 5.11e-983, 5.11e-983j
0.012951032918652237451 - 4.584480351292090762e-3394j 1.42e-1020, 1.42e-1020j
6.090250972917348348 + 5.2854007632908683044e-3377j 6.44e-1003, 6.44e-1003j
1 + 3.0106722185029022861e-3387j 4.72e-1013, 4.72e-1013j
0.12513504453882085705 - 2.0859189267207432698e-3392j 4.97e-1018, 4.97e-1018j

Weights

Weight (ball center) Error (ball radius)
4.1325797952611444003e-130 + 1.95442806749620334e-2488j 4.49e-131, 1.33e-873j
1.0888845506190085924e-105 - 1.2563948158845043418e-2474j 5.6e-124, 1.66e-866j
5.0477991336129205341e-116 + 6.10223629079636365e-2481j 2.65e-127, 7.84e-870j
4.6464246447408121936e-97 - 2.9162689751692686787e-2471j 1.83e-121, 5.42e-864j
6.3351803339238487726e-11 + 1.0627772127357115674e-2427j 1.93e-48, 5.71e-791j
1.0781871358008650948e-65 - 5.5199811466271422559e-2456j 1.1e-109, 3.26e-852j
2.6515880952470306279e-31 - 1.4817410633804639881e-2438j 1.03e-85, 3.06e-828j
1.3479149381817067134e-79 + 7.0423300855619563826e-2463j 4.23e-116, 1.26e-858j
6.8389856465995476382e-30 + 7.9488119207895219345e-2438j 2.39e-84, 7.09e-827j
1.008806598503528028e-40 - 2.1842559041683214734e-2443j 3.73e-95, 1.11e-837j
1.9587888067225645116e-06 - 5.1716298529311717025e-2425j 8.15e-36, 2.42e-778j
1.9035823105795904996e-23 - 1.8081067824657880182e-2434j 8.01e-78, 2.37e-820j
3.868846238880849199e-21 - 2.9712765092493376482e-2433j 7.33e-75, 2.17e-817j
3.2413565883889628749e-63 + 9.5628979552010346682e-2455j 1.07e-109, 3.17e-852j
5.5182893231109469463e-50 + 4.3272500746181071016e-2448j 6.13e-103, 1.82e-845j
1.9970553513077093343e-05 - 2.437241817411856702e-2424j 6.04e-35, 1.79e-777j
5.6264710675917923235e-19 - 4.1782648707559949829e-2432j 3.96e-73, 1.17e-815j
5.398396003587973202e-16 + 1.6696603023807277064e-2430j 9.64e-69, 2.86e-811j
0.00015257057637685504594 - 1.060943031221235581e-2423j 5.87e-31, 1.74e-773j
2.9079721396597021735e-68 + 2.8877492337861042924e-2457j 1.45e-112, 4.3e-855j
1.7400701538889451581e-12 + 1.4054821235920211909e-2428j 7.78e-63, 2.31e-805j
2.6733773361051275738e-122 - 2.5465741236156973717e-2484j 3.18e-134, 9.42e-877j
1.37885374068100742e-76 - 2.1425843943911238706e-2461j 4.17e-117, 1.24e-859j
2.8301347767591466528e-56 - 2.9068821946176402475e-2451j 5.78e-108, 1.71e-850j
1.4060488183357946507e-110 - 7.3305282276616437819e-2478j 3.17e-130, 9.4e-873j
4.1429115089915208973e-46 + 3.9746888341361643645e-2446j 1.51e-102, 4.49e-845j
1.7291991611142813005e-09 + 7.1271476691727981294e-2427j 1.9e-61, 5.64e-804j
3.4300671738081232941e-10 - 2.7925671517623936191e-2427j 6.21e-63, 1.84e-805j
8.4165383220460987195e-36 + 7.1819921963736599615e-2441j 2.04e-96, 6.05e-839j
2.1556078862403488685e-37 - 1.0982088752611642484e-2441j 1.27e-97, 3.77e-840j
1.0596147897079826651e-73 + 5.73221072625031251e-2460j 1.66e-117, 4.92e-860j
0.011772244216168187041 - 2.8751919787409773007e-2422j 2.07e-33, 6.15e-776j
1.4506398861420001022e-07 - 1.0048512667476892873e-2425j 6.86e-61, 2.03e-803j
0.033727075646204252647 - 4.6385472548656441977e-2422j 6.96e-27, 2.06e-769j
9.3071525706349907043e-33 + 2.6341928225498606596e-2439j 1.46e-94, 4.33e-837j
8.0049880264980957868e-61 - 1.5099540844599349097e-2453j 1.63e-111, 4.83e-854j
3.2671623989427078137e-101 + 4.4203775863243358148e-2473j 1.29e-129, 3.82e-872j
0.1007564390998701899 + 8.4116856566414295029e-2422j 3.45e-20, 1.02e-762j
2.8319041870876323576e-22 + 7.4771232744951736991e-2434j 8.33e-87, 2.47e-829j
0.020464110991077493396 + 3.723544289970793844e-2422j 1.26e-37, 3.74e-780j
1.1731138843526651008e-24 + 4.1976573143159872513e-2435j 1.68e-89, 4.98e-832j
4.9390663614189800051e-39 + 1.5920526894045942996e-2442j 8e-100, 2.37e-842j
0.0035035334941601063272 - 1.3382356191332089897e-2422j 8.71e-49, 2.58e-791j
3.5624000354215967444e-14 + 1.6373448297808280017e-2429j 2.86e-79, 8.48e-822j
8.1211382094247849805e-09 - 1.7684635319717300195e-2426j 1.2e-69, 3.56e-812j
3.5547415600086513382e-08 + 4.270658492175513873e-2426j 1.71e-68, 5.06e-811j
6.4797225585547448672e-06 + 1.1343382441934350459e-2424j 1.87e-63, 5.56e-806j
6.6163024533615668972e-26 - 9.3467494564553178176e-2436j 9.24e-92, 2.74e-834j
0.052168500708881028444 + 5.6830201593136327356e-2422j 1.68e-42, 4.98e-785j
1.8297009623609135017e-42 + 2.8307893460901147525e-2444j 6.6e-104, 1.96e-846j
0.07526721642845376334 - 6.9196496435208264205e-2422j 3.3e-42, 9.79e-785j
2.9345390492830647695e-44 - 3.4585226821370140026e-2445j 2.58e-105, 7.65e-848j
0.00037630756485423567516 + 2.1433728001566987732e-2423j 8.93e-63, 2.65e-805j
4.8613411529550881355e-20 + 1.1356343366082058078e-2432j 4.05e-88, 1.2e-830j
5.9217669046339263211e-17 - 5.0622171873477824931e-2431j 5.2e-86, 1.54e-828j
1.6427926274013434489e-58 + 2.1840014715559528188e-2452j 1.48e-114, 4.38e-857j
9.6201998484114326121e-83 - 2.0157907205199176148e-2464j 7.96e-128, 2.36e-870j
4.5555778666263806329e-15 - 5.3184104803258728934e-2430j 3.27e-85, 9.68e-828j
0.00085625618139820977673 - 4.1962569751495464477e-2423j 2.54e-68, 7.52e-811j
0.14010579654048711626 + 1.2561601307501354518e-2421j 1.67e-55, 4.94e-798j
6.0064180897581612788e-18 + 1.4810809829999079362e-2431j 9.21e-88, 2.73e-830j
2.58396197669635987e-13 - 4.8757455841321879457e-2429j 7.66e-84, 2.27e-826j
1.6463846230505964495e-89 - 1.0483428142137631792e-2467j 5.35e-132, 1.58e-874j
3.5820053466113617808e-93 + 1.8795741470328572567e-2469j 1.8e-133, 5.32e-876j
5.5201691920352251999e-07 + 2.3064930526560601131e-2425j 2.76e-80, 8.19e-823j
6.2648922939542165045e-71 - 1.3605455243076237727e-2458j 1.11e-122, 3.3e-865j
4.1301386360928581339e-54 + 3.5749032078828777178e-2450j 1.8e-115, 5.33e-858j
0.0065202093798907798872 + 2.0644480109263501746e-2422j 2.01e-77, 5.95e-820j
5.1472447085922525183e-52 - 4.0772941846734184441e-2449j 1.14e-114, 3.39e-857j
2.9496595641595042639e-34 - 4.4601061548852239965e-2440j 9.91e-106, 2.94e-848j
0.049171426857346762015 + 1.9692997267618437897e-2421j 2.37e-78, 7.04e-821j
1.0887974876557828222e-11 - 3.9250033367473986345e-2428j 5.22e-91, 1.55e-833j
0.12345073934066093754 + 2.0141731855829940657e-2421j 3.9e-80, 1.16e-822j
4.8419541828587796657e-86 + 4.9741133676909705349e-2466j 6.01e-132, 1.78e-874j
5.1228976814836488882e-48 - 4.2866322653773767429e-2447j 7.01e-113, 2.08e-855j
0.1416562057749565323 - 1.5669664426635442851e-2421j 9.27e-83, 2.75e-825j
1.6008392602683031193e-28 - 4.0717968549942568804e-2437j 7.52e-104, 2.23e-846j
5.7277143793351366416e-05 + 5.1351392579718955451e-2424j 4.59e-90, 1.36e-832j
3.4086048895247232329e-27 + 1.9940777930438368795e-2436j 3.77e-103, 1.12e-845j
0.031469287653990928635 - 6.2697766990340515558e-2422j 3.28e-87, 9.71e-830j
0.0017954098398968044169 + 7.8050868802588296507e-2423j 7.04e-89, 2.09e-831j
0.12434277344737426171 - 1.0243254628916606247e-2421j 1.49e-87, 4.41e-830j
0.082357467151333314324 - 2.4828587942455599643e-2421j 4.74e-87, 1.4e-829j

Download

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