Rule: Q[3, 59]

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)
191.9220493759390736 - 7.5805941540882120827e-2209j 8.7e-998, 8.7e-998j
180.66247933386977949 - 1.8113376494763396861e-2207j 1.29e-996, 1.29e-996j
130.84806547281892678 - 1.1314564858386387349e-2203j 1.92e-992, 1.92e-992j
204.99304025848474741 - 8.3807805172676642024e-2211j 3.47e-999, 3.47e-999j
221.42736720529083745 - 5.3988769054363525664e-2212j 5.15e-1001, 5.15e-1001j
42.10676661694971935 - 8.8652639845726189933e-2204j 5.57e-993, 5.57e-993j
137.7898399279002463 + 1.1579112595473232122e-2203j 6.5e-993, 6.5e-993j
13.902614378086987142 + 1.2477585467564574788e-2211j 1.3e-1000, 1.3e-1000j
48.071906696945073164 + 1.1709226053796345069e-2202j 3.03e-992, 3.03e-992j
161.46243324346387349 - 1.1913871389523500363e-2205j 8.48e-995, 8.48e-995j
26.949145227288153073 + 4.9201676826357927892e-2206j 7.22e-996, 7.22e-996j
29.20659036145276729 - 9.7613316671729125468e-2206j 2.56e-995, 2.56e-995j
39.302897555932833467 + 1.0041304489489140755e-2203j 2.09e-993, 2.09e-993j
5.3235370701534240777 + 2.3428652972786364312e-2217j 7.73e-1007, 7.73e-1007j
20.781363415720162098 - 6.0043949968800210501e-2209j 1.05e-997, 1.05e-997j
9.7021630777958836696 + 5.9256783839240876164e-2214j 4.21e-1003, 4.21e-1003j
145.15818889326677154 - 1.5364563293903071925e-2204j 1.85e-993, 1.85e-993j
170.61361823409917014 - 2.7283865452542540147e-2207j 1.21e-995, 1.21e-995j
4.4413731117322887588 - 1.9777340779348785951e-2218j 7.53e-1008, 7.53e-1008j
57.970376977591828583 - 7.2373159038993556878e-2201j 2.05e-991, 2.05e-991j
112.12428266693797068 - 5.7636924312488730872e-2203j 2.13e-991, 2.13e-991j
2.2942803602790417198 + 3.3215894086053558678e-2231j 5.13e-1011, 5.13e-1011j
6.2899450829374791969 - 3.1150609544218762659e-2225j 6.79e-1006, 6.79e-1006j
17.155076682315016774 + 1.1686328978385160391e-2219j 4.27e-999, 4.27e-999j
24.793767278516373754 - 8.4278980996208413547e-2216j 1.83e-996, 1.83e-996j
73.145407444500279173 + 1.7149678462895686082e-2208j 8.52e-991, 8.52e-991j
153.01930224306317239 + 4.9349313604816265269e-2218j 4.42e-994, 4.42e-994j
124.28202415065165579 - 6.1445963407108196673e-2215j 4.59e-992, 4.59e-992j
0.61028161460976250734 + 1.2771425448018674975e-2241j 3.42e-1015, 3.42e-1015j
3.6428014599347161911 - 2.8000092794687552603e-2235j 7.52e-1009, 7.52e-1009j
54.53844467326012471 + 2.7425714263279823731e-2216j 1.14e-991, 1.14e-991j
11.01341805082772522 + 3.5625569321590489051e-2237j 2.92e-1002, 2.92e-1002j
65.256562995827707492 + 2.4105333586359190835e-2225j 5.11e-991, 5.11e-991j
51.240469096676682521 + 4.01600767018843331e-2238j 6.08e-992, 6.08e-992j
18.920767290378199634 + 5.6053125764203145708e-2260j 2.16e-998, 2.16e-998j
2.9272516400149953531 + 1.677007841314821112e-2271j 6.25e-1010, 6.25e-1010j
101.07695977388724721 + 2.5830823818393193977e-2251j 5.55e-991, 5.55e-991j
106.47350259357850139 + 3.2987821320717028692e-2271j 3.49e-991, 3.49e-991j
1.7437183692748035641 - 2.5262857966648808265e-2311j 4.11e-1012, 4.11e-1012j
1.276166858746481592 + 1.5885636028503305566e-2314j 3.73e-1013, 3.73e-1013j
0.89483135566459241581 + 2.8063935684485845721e-2313j 3.24e-1014, 3.24e-1014j
0.24471173478963923572 + 2.1908609566913575339e-2316j 2.21e-1017, 2.21e-1017j
69.122372495477967083 - 1.1545262034164279599e-2289j 6.76e-991, 6.76e-991j
12.413206562827755349 - 2.5500446243842210179e-2313j 1.86e-1001, 1.86e-1001j
31.568260575873826652 + 3.3577650630051731531e-2306j 8.28e-995, 8.28e-995j
7.3413168597096041683 + 1.3299829984495607947e-2316j 6.2e-1005, 6.2e-1005j
45.028606461065201805 + 2.4910983216801568936e-2303j 1.38e-992, 1.38e-992j
8.4784381563394617766 - 6.939253119023203808e-2336j 5.38e-1004, 5.38e-1004j
22.738457557187155958 + 3.3249182255321540408e-2328j 4.52e-997, 4.52e-997j
0.41577455678347908331 + 1.3440459855219732238e-2347j 4.72e-1016, 4.72e-1016j
0.019770679224990936352 - 6.629091297499851104e-2372j 1.11e-1020, 1.11e-1020j
61.541252947447688729 - 3.6540767677588127025e-2322j 3.28e-991, 3.28e-991j
34.036486954297996409 + 2.2152074761054970455e-2340j 2.53e-994, 2.53e-994j
15.482815180053367014 - 2.0551174259807917426e-2364j 7.61e-1000, 7.61e-1000j
0.10303317298444065678 - 9.8515409737664178044e-2389j 7.3e-1019, 7.3e-1019j
36.613789913292414626 - 2.5433813860096867987e-2361j 7.71e-994, 7.71e-994j
118.05156908854099944 - 1.1158908762958822687e-2476j 1.05e-991, 1.05e-991j
86.237372246498805871 + 3.4101531165452052106e-2718j 1e-990, 1e-990j
77.333157948651515419 - 3.5653057196743415061e-2923j 1.04e-990, 1.04e-990j
81.694004323581637119 - 4.5208296944621860064e-3067j 9.84e-991, 9.84e-991j
95.91580967193136917 - 1.0452367867857991849e-3153j 7.15e-991, 7.15e-991j
90.973925688246327705 + 1.2391337783888234883e-3186j 9.01e-991, 9.01e-991j

Weights

Weight (ball center) Error (ball radius)
5.3629723165050775271e-83 - 6.7872710249285795945e-2256j 5.34e-180, 1.19e-925j
3.6647186511287905146e-78 + 2.0190676651976588387e-2253j 1.38e-178, 3.08e-924j
1.0057319384129287234e-56 + 2.1334107348563605837e-2242j 1.84e-171, 4.1e-917j
1.3459364800675540404e-88 + 9.3455173808185400032e-2259j 2.4e-182, 5.36e-928j
1.3275600741279635592e-95 - 2.4926983364109086092e-2262j 5.05e-185, 1.13e-930j
1.4790345934390467151e-18 - 5.1531817964553264435e-2222j 5.37e-147, 1.2e-892j
1.0295930407139838686e-59 - 6.0903602579045814251e-2244j 1.73e-173, 3.87e-919j
1.4065876131022437033e-06 + 2.3044741198417616878e-2215j 1.42e-122, 3.17e-868j
4.1184665491898479636e-21 - 3.5329921065153726031e-2223j 1.16e-150, 2.6e-896j
6.6200096371942005552e-70 + 3.4562974533583899964e-2249j 2.78e-177, 6.2e-923j
4.3626799612494023798e-12 - 1.6976282225887973681e-2217j 1.63e-138, 3.64e-884j
4.7774651618104797072e-13 - 8.9716805125748552673e-2219j 2.73e-140, 6.11e-886j
2.3424218233419068501e-17 - 1.8916523981441550457e-2220j 1.27e-146, 2.84e-892j
0.0045057781828213884567 - 1.9573089500207900045e-2213j 1.42e-107, 3.18e-853j
1.8008458795885417195e-09 + 1.2366200451248399002e-2216j 3.31e-134, 7.39e-880j
7.749855131308477871e-05 - 1.8086261017492156698e-2214j 7.92e-120, 1.77e-865j
6.910881390411221042e-63 + 1.4075778057702171051e-2245j 6.28e-176, 1.4e-921j
7.6551080571176746373e-74 - 3.2998135501946764806e-2251j 1.26e-179, 2.82e-925j
0.0098981160941498613707 + 3.3266080045936093118e-2213j 3.58e-109, 7.99e-855j
2.3330248558800621623e-25 + 3.3110379368057731031e-2226j 1.53e-158, 3.42e-904j
1.167738533039459053e-48 - 3.2478652526757979842e-2238j 1.68e-172, 3.76e-918j
0.0596710618122559854 - 1.4459466372282814025e-2212j 2.1e-101, 4.7e-847j
0.0018711186943293733808 + 1.1232166907003438033e-2213j 2.03e-117, 4.53e-863j
6.0933321631700240939e-08 + 5.361960686200512954e-2216j 4.77e-135, 1.07e-880j
3.5930278643202176672e-11 + 3.8233045722894959665e-2217j 4.41e-141, 9.84e-887j
7.0237402234111447847e-32 - 2.2739537191304012594e-2229j 8.35e-165, 1.87e-910j
2.8504102136527502259e-66 - 2.5481354553411300593e-2247j 7.92e-178, 1.77e-923j
6.7710886461602080544e-54 - 6.2060533429014557279e-2241j 3.82e-174, 8.53e-920j
0.12602170158599956428 - 9.3345768436640080295e-2212j 2.78e-111, 6.22e-857j
0.019816743463366745263 - 5.5260694899323552477e-2213j 5.64e-117, 1.26e-862j
6.9363543607178422117e-24 + 7.2447680228556841275e-2226j 9.23e-159, 2.06e-904j
2.2334903217670558027e-05 + 9.3196463733925094352e-2215j 6.37e-134, 1.42e-879j
1.7298814622858230249e-28 - 1.6942472267386719183e-2227j 3.1e-163, 6.93e-909j
1.803398627666887855e-22 - 2.0893467655936826207e-2224j 1.08e-157, 2.41e-903j
1.0994769386147799816e-08 - 2.5974415056717791345e-2216j 8.78e-143, 1.96e-888j
0.036099452666919518822 + 9.0024171860261678087e-2213j 1.11e-121, 2.47e-867j
6.6855167746891049299e-44 - 9.8550181362157339547e-2236j 6.36e-173, 1.42e-918j
3.1703344891858518737e-46 + 6.0203719225106214925e-2237j 1.7e-173, 3.79e-919j
0.089055838887353162754 + 2.3100080474954662141e-2212j 4.79e-122, 1.07e-867j
0.11872774525638230684 - 3.7226144068947908684e-2212j 3.32e-120, 7.42e-866j
0.13712565835118399529 + 6.1219369020550495558e-2212j 1.8e-119, 4.01e-865j
0.12810598904933983561 - 6.1649085739987784321e-2212j 8.08e-120, 1.8e-865j
3.7704085096915035476e-30 + 1.9909979665752382597e-2228j 3.38e-165, 7.55e-911j
5.8708825893294801114e-06 - 4.6778090851761780773e-2215j 1.51e-141, 3.38e-887j
4.7088391585583372333e-14 + 1.168475016193137506e-2218j 3.87e-153, 8.65e-899j
0.00070919813330264911851 - 6.2783767184896203928e-2214j 6.38e-138, 1.43e-883j
8.2952030158241249388e-20 + 2.1940088852060594421e-2222j 8.15e-158, 1.82e-903j
0.00024538287899483863302 + 3.4161096312755904568e-2214j 8.53e-140, 1.9e-885j
2.673767661457020838e-10 - 5.8677718917493725947e-2217j 3.17e-149, 7.08e-895j
0.1147476053355983736 + 9.6587998472409602575e-2212j 8.52e-130, 1.9e-875j
0.049640999769870315737 - 7.2691539654908395414e-2213j 1.02e-130, 2.29e-876j
6.8285609716165615033e-27 + 1.5699811324815696653e-2226j 1.55e-163, 3.46e-909j
4.1681475439143403365e-15 - 2.2533958001584870631e-2219j 5.65e-155, 1.26e-900j
3.0691807898658254596e-07 - 1.1229787730031911775e-2215j 2.01e-147, 4.48e-893j
0.10365011795818393101 + 2.7478535320095258559e-2212j 5.64e-135, 1.26e-880j
3.3055199480250004273e-16 + 6.4967031798212758448e-2220j 6.04e-156, 1.35e-901j
3.2683595495642711676e-51 + 1.5297561211337761357e-2239j 2.44e-178, 5.45e-924j
1.6365237197167939348e-37 + 2.2490309737760492418e-2232j 1.27e-173, 2.83e-919j
1.1100712801107780965e-33 + 2.4467379302823555642e-2230j 3.16e-171, 7.05e-917j
1.4762084429290020233e-35 - 2.445255985025000687e-2231j 1.15e-172, 2.57e-918j
1.1155802744675483824e-41 + 1.4386724343140764334e-2234j 1.35e-176, 3.01e-922j
1.4966052962858359646e-39 - 1.8892057818591256322e-2233j 1.73e-175, 3.87e-921j

Download

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