Rule: Q[1, 3, 5, 70]

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)
243.83786543473463073 - 9.0513896790668021967e-2124j 2.17e-993, 2.17e-993j
258.00143244745879046 + 1.7125705452466839982e-2127j 6.28e-995, 6.28e-995j
231.59101161624004703 + 4.7917766637001186644e-2120j 4.33e-992, 4.33e-992j
220.62111704816721699 + 5.1865583344274054334e-2117j 5.43e-991, 5.43e-991j
38.181564598190890396 + 1.5979183939270465505e-2122j 2.05e-988, 2.05e-988j
70.123137321691993809 - 2.7656456216410587973e-2117j 1.67e-984, 1.67e-984j
101.7576767934447046 + 3.8168213267401109554e-2146j 1.09e-983, 1.09e-983j
121.02395724039230558 - 5.5736577833981898571e-2212j 4.99e-984, 4.99e-984j
115.9541904717390841 - 3.5313952126274870132e-2276j 7.46e-984, 7.46e-984j
43.135558417006197598 - 2.2968210416658906341e-2317j 1.58e-987, 1.58e-987j
57.129955308321883968 + 1.6051341404677968301e-2313j 1.32e-985, 1.32e-985j
126.27834528828335093 + 9.566863044720420078e-2343j 3.89e-984, 3.89e-984j
60.22095541969675476 + 2.5842364832240066997e-2363j 2.72e-985, 2.72e-985j
29.310180237564545131 + 1.771458612209927277e-2392j 1.72e-990, 1.72e-990j
35.835831411162814219 + 1.9153660610076500859e-2390j 6.17e-989, 6.17e-989j
40.614331595042760978 + 1.7985409701173367716e-2386j 5.95e-988, 5.95e-988j
16.553990089047878309 + 3.0735414984232522531e-2408j 6.75e-995, 6.75e-995j
63.414931526886048047 + 1.5860725958835017677e-2396j 5.27e-985, 5.27e-985j
106.32950784293816405 - 2.3528685457759164318e-2468j 1.11e-983, 1.11e-983j
162.44741672235657793 + 1.9249900878001721038e-2535j 4.55e-986, 4.55e-986j
7.8232631436879996743 + 6.7205472876408010125e-2584j 2.7e-1001, 2.7e-1001j
11.18376057159834315 + 7.5145359438018350285e-2581j 1.44e-998, 1.44e-998j
15.136751134456485168 - 1.6538600786066929915e-2578j 7.61e-996, 7.61e-996j
21.84628785534164164 + 3.5915504927482233134e-2575j 1.55e-992, 1.55e-992j
155.77870516352035227 + 8.7569725432640555964e-2566j 1.21e-985, 1.21e-985j
275.73657319144297628 + 8.9778909336992239741e-2587j 5.62e-997, 5.62e-997j
23.558434911081373333 + 3.8695396070940572568e-2581j 4.93e-992, 4.93e-992j
54.139353457393558634 - 3.5332066086639773973e-2575j 5.95e-986, 5.95e-986j
31.400864349603232432 - 1.0212870870340223386e-2580j 5.93e-990, 5.93e-990j
8.875454637988796958 - 2.2999250767517879315e-2589j 2.34e-1000, 2.34e-1000j
97.336338624774179351 - 1.0089487957953934908e-2571j 1.1e-983, 1.1e-983j
66.714660628412464224 + 1.2835185831623841861e-2582j 9.06e-985, 9.06e-985j
9.995686969285035247 - 4.9089301052118793106e-2597j 1.93e-999, 1.93e-999j
77.27953178016585233 - 1.203934017009024428e-2579j 3.77e-984, 3.77e-984j
93.059003586086552905 - 6.280037231547518952e-2596j 1.01e-983, 1.01e-983j
19.12622188851013496 - 2.5835107498239480073e-2635j 2.2e-993, 2.2e-993j
25.384741218539713164 + 1.8085963411280194032e-2633j 1.64e-991, 1.64e-991j
1.3877459720128594285 + 2.7937548317170179977e-2653j 1.63e-1011, 1.63e-1011j
210.59514608335874896 - 1.0625451230267517404e-2624j 5.24e-990, 5.24e-990j
84.913328014304504582 - 3.6541844970874792266e-2668j 7.22e-984, 7.22e-984j
137.3878917968220312 - 1.7844620466950435523e-2718j 1.29e-984, 1.29e-984j
45.746842875706028511 + 8.9636079003351241741e-2757j 4.61e-987, 4.61e-987j
3.369839231310923141 - 3.959218252805457797e-2782j 1.17e-1004, 1.17e-1004j
3.4849364779110753601 - 1.120797002843879634e-2782j 2.3e-1004, 2.3e-1004j
20.324889578972396265 + 2.7732002278170924681e-2777j 5.9e-993, 5.9e-993j
201.31153313631206487 + 7.3127599481588117863e-2788j 3.79e-989, 3.79e-989j
184.47499657324015568 + 4.0220820977926508903e-2884j 1.14e-987, 1.14e-987j
27.304142150422560117 - 1.2993785072453759291e-2937j 5.23e-991, 5.23e-991j
0.41546649377722713336 + 8.4594174347365681396e-2979j 6.91e-1016, 6.91e-1016j
131.72869020987779939 + 5.6306465083700767266e-2951j 2.23e-984, 2.23e-984j
143.27074230878081429 - 5.5331409327947326411e-2988j 6.84e-985, 6.84e-985j
48.449939638202026218 - 2.0630125118520552718e-3013j 1.13e-986, 1.13e-986j
1.8405898770806362133 - 1.1478809809909665995e-3037j 5.41e-1010, 5.41e-1010j
13.758594583719250753 + 3.2224266939925019555e-3024j 9.62e-997, 9.62e-997j
3.7068293223182415456 - 9.7551517246842126912e-3033j 2.06e-1004, 2.06e-1004j
6.8389936471389864143 + 3.1217960408277790809e-3029j 3.87e-1002, 3.87e-1002j
111.05901618042736196 - 2.0280639766118287806e-3009j 9.12e-984, 9.12e-984j
12.438835636362665227 + 4.6927348273789399327e-3044j 1.28e-997, 1.28e-997j
192.63639996621838736 + 3.603355027602597824e-3030j 2.34e-988, 2.34e-988j
2.3605011286819221 - 1.4542266009303049841e-3069j 2.27e-1008, 2.27e-1008j
17.939573837640229516 + 7.7680714783520641619e-3055j 5.2e-994, 5.2e-994j
73.643595212205970686 - 1.4679943760839229026e-3044j 2.62e-984, 2.62e-984j
149.39435136309915771 + 1.1843226090380765007e-3062j 3.12e-985, 3.12e-985j
81.034737231061384399 + 7.9050085287522039946e-3070j 5.39e-984, 5.39e-984j
1 + 2.2300477081636325494e-3109j 6.03e-1013, 6.03e-1013j
0.67625958927143935662 - 2.8002124796760762719e-3112j 1.95e-1014, 1.95e-1014j
0.21603014196028690674 + 2.4444451083582479256e-3114j 2.12e-1017, 2.12e-1017j
169.4287546476297547 - 3.6022822976705527224e-3080j 1.48e-986, 1.48e-986j
5.922329542134522503 - 2.7397223507648854421e-3108j 5.19e-1003, 5.19e-1003j
4.2898472831159051468 - 1.240362162260870065e-3109j 2.1e-1004, 2.1e-1004j
0.056897625001077184683 - 2.5143126698212035544e-3122j 9.15e-1018, 9.15e-1018j
5.0727651973022576645 + 6.4554856966265176133e-3109j 8.29e-1004, 8.29e-1004j
176.75709042005779736 - 2.781187268827024452e-3088j 4.29e-987, 4.29e-987j
51.246755890486686772 + 3.6938855052268309854e-3097j 2.64e-986, 2.64e-986j
0.029976192234391554262 + 5.60398590805377919e-3188j 2.6e-1019, 2.6e-1019j
2.9602267567533973598 - 2.3720239205757981894e-3117j 2.12e-1006, 2.12e-1006j
0.052485028214125533477 - 4.4138941985288636244e-3130j 7.84e-1018, 7.84e-1018j
33.575911958336609349 - 3.7721769368363534509e-3100j 1.96e-989, 1.96e-989j
88.919785881340227113 - 2.1884246600260028277e-3093j 8.95e-984, 8.95e-984j

Weights

Weight (ball center) Error (ball radius)
1.6533686400114575547e-105 - 1.0646014150908600545e-2188j 1.22e-148, 3.05e-892j
1.3861590335071413337e-111 + 7.2032703615806980751e-2192j 8.14e-151, 2.04e-894j
3.0435065421739785254e-100 + 6.0277852764478653384e-2186j 2.32e-147, 5.82e-891j
1.6026952461737798585e-95 - 1.7983525542984947073e-2183j 3.36e-146, 8.41e-890j
6.2542959027583205686e-17 - 6.4883965517558136103e-2139j 1.18e-92, 2.94e-836j
1.2175159611837673501e-30 + 1.6550549940303704268e-2147j 4.03e-112, 1.01e-855j
2.8838687745403146466e-44 - 6.9031670630177516049e-2156j 4.17e-124, 1.04e-867j
1.4211454631409419867e-52 - 1.6175003795978100935e-2160j 6.3e-130, 1.58e-873j
2.1829434479946948781e-50 + 2.6061298098679471187e-2159j 1.5e-128, 3.74e-872j
4.739337023600600586e-19 + 8.7181832960494167108e-2141j 3.52e-100, 8.8e-844j
4.6957454411434863667e-25 - 2.3729368181521925706e-2145j 1.06e-108, 2.64e-852j
7.6982883869541140469e-55 + 9.2111981008542172731e-2162j 3.34e-132, 8.36e-876j
2.2058877742250306681e-26 + 3.3034571877007932978e-2147j 2.73e-110, 6.82e-854j
3.8210908016150126338e-13 - 4.1977774226288822084e-2137j 2.66e-92, 6.65e-836j
6.293942082135612954e-16 + 1.9416867287414582792e-2138j 7.76e-97, 1.94e-840j
5.6924739916297977742e-18 - 8.712468119245728075e-2140j 9.05e-100, 2.26e-843j
9.1938712315535666761e-08 - 2.1630170174924367832e-2133j 3.78e-80, 9.45e-824j
9.3463812277312684005e-28 + 8.4598249271194924589e-2147j 1.05e-112, 2.63e-856j
3.0837506828114536403e-46 + 5.3528664838540447072e-2157j 1.38e-128, 3.45e-872j
1.9220243576701482803e-70 + 3.3769841953724758323e-2170j 2.71e-144, 6.78e-888j
0.00040759589242809978349 + 4.9757562643322021392e-2131j 1.52e-65, 3.81e-809j
1.6980597539579046063e-05 - 3.6204984391952952057e-2132j 4.83e-74, 1.21e-817j
3.7432259014479389774e-07 + 3.8864094982480387392e-2133j 7.98e-81, 2e-824j
5.329576240899437517e-10 - 8.0728191939684853463e-2135j 7.83e-90, 1.96e-833j
1.4473225872504892245e-67 - 1.175208683205448968e-2168j 3.64e-143, 9.12e-887j
3.7070523937524065811e-119 - 8.264214749899934816e-2196j 1.12e-163, 2.79e-907j
1.0421117379411345342e-10 + 1.9964523533353490659e-2135j 1.4e-92, 3.51e-836j
9.0386664968593620339e-24 + 2.4474182332041746929e-2144j 1.56e-111, 3.91e-855j
4.9173836046971716809e-14 + 1.2884579950334252304e-2137j 7.86e-99, 1.97e-842j
0.00015182865861375495848 - 1.9863067595521776639e-2131j 4.72e-75, 1.18e-818j
2.3210556366052088843e-42 + 8.3641505792022602133e-2155j 1.55e-128, 3.87e-872j
3.5620523675893632228e-29 - 4.8405628282646025764e-2147j 1.29e-117, 3.23e-861j
5.2628179570498312367e-05 + 8.3186273511078190765e-2132j 5.13e-80, 1.28e-823j
1.0128147999052968467e-33 - 1.2535812776321970244e-2149j 4e-123, 1e-866j
1.6180652809121103345e-40 - 9.5872752476837377813e-2154j 3.99e-128, 9.99e-872j
5.4039405722783987767e-09 - 8.0818959341555668854e-2134j 6.35e-94, 1.59e-837j
1.7719432646445289489e-11 - 5.2422548359751918401e-2136j 1.1e-98, 2.75e-842j
0.10486978355950934249 - 7.6320062210484475581e-2129j 6.87e-55, 1.72e-798j
3.3360506513490893406e-91 + 3.3406747262875858956e-2181j 7.11e-157, 1.78e-900j
5.2275561048051960733e-37 - 1.1085263338771239267e-2151j 1.28e-126, 3.22e-870j
1.2423696936238044487e-59 + 2.2465846658092093776e-2164j 4.14e-142, 1.04e-885j
3.6038889756635171452e-20 - 1.1093249691269645638e-2141j 3.32e-112, 8.3e-856j
-0.017869857992748540618 - 3.1505988076089899001e-2127j 9.92e-76, 2.48e-819j
0.030942602415160863009 + 3.819849537316780472e-2127j 3.19e-76, 7.98e-820j
2.040473707583078913e-09 + 3.185745038917127038e-2134j 1.34e-98, 3.34e-842j
3.3409241143018885278e-87 - 4.2765023109554333239e-2179j 3.34e-156, 8.37e-900j
6.0641994090046754343e-80 - 2.9469320115594025033e-2175j 9.36e-154, 2.34e-897j
2.7223459543933001288e-12 + 1.4492211064265332523e-2136j 4.49e-106, 1.12e-849j
0.15163897136648584051 + 9.5061221526278139894e-2129j 3.31e-74, 8.29e-818j
3.4311805668475317805e-57 - 4.7816703471392828692e-2163j 2.49e-141, 6.24e-885j
3.6013888356700615885e-62 - 9.4768532905586698112e-2166j 9.73e-145, 2.43e-888j
2.4988039177062229851e-21 + 1.4976595327358436248e-2142j 2.74e-118, 6.85e-862j
0.077119930827647669849 + 8.8910339042095776414e-2129j 1.54e-83, 3.85e-827j
1.4296805448366500725e-06 - 7.7235014224480700705e-2133j 3.06e-102, 7.66e-846j
0.0029145761322509341135 - 1.1400368809119863833e-2127j 3.08e-90, 7.7e-834j
0.0010180497985232690133 - 1.3354384717043096841e-2130j 8.55e-97, 2.14e-840j
2.8178102415519812267e-48 - 3.8761796945165803657e-2158j 1.39e-136, 3.48e-880j
5.1026868346245193768e-06 + 1.6355098017800472142e-2132j 3.12e-102, 7.82e-846j
1.8348704634917465634e-83 + 4.0363614046266488012e-2177j 3.85e-156, 9.63e-900j
0.052375765396438358311 - 1.3482157985810187665e-2128j 8.87e-93, 2.22e-836j
2.1257203980482501768e-08 + 1.3694034178730305698e-2133j 3.93e-106, 9.84e-850j
3.7203487735117797797e-32 + 1.6520049547997455352e-2148j 3.96e-128, 9.91e-872j
8.217955619563310646e-65 + 3.5567086266090197475e-2167j 7.6e-147, 1.9e-890j
2.4473155579881691314e-35 + 1.1575620916313914979e-2150j 6.82e-131, 1.71e-874j
0.13080932262404973616 + 7.509745576425400175e-2129j 1.39e-98, 3.48e-842j
0.14852457138605141796 - 8.0958475291165451108e-2129j 2.73e-98, 6.84e-842j
0.13684700442591492725 - 1.2924165279452904741e-2128j 1.26e-98, 3.16e-842j
1.8717258026390690946e-73 - 8.3166881629831743517e-2172j 3.67e-152, 9.17e-896j
0.0023655461931706572119 + 4.0096791868505069555e-2130j 2.48e-106, 6.19e-850j
0.010263913990570274862 + 9.3964964490837397203e-2129j 6.6e-105, 1.65e-848j
1.1343436663843182935 + 4.7403637679524374411e-2127j 2.58e-102, 6.46e-846j
0.0051137855999848101037 - 1.4881748514762263988e-2129j 5.46e-106, 1.37e-849j
1.2921471210092377617e-76 + 1.7247033063284557161e-2173j 6.24e-154, 1.56e-897j
1.5768840323709051473e-22 - 1.9942368705605025904e-2143j 1.26e-124, 3.15e-868j
0.17371064463361759403 + 5.9667914223352436901e-2128j 3.01e-105, 7.52e-849j
0.034648237809871709867 + 4.7400296640570312588e-2128j 1.41e-106, 3.53e-850j
-1.1802725758673176368 - 5.2601015243947342552e-2127j 1.93e-104, 4.83e-848j
5.8076712113901721744e-15 - 4.3805406286333860949e-2138j 8.63e-120, 2.16e-863j
9.8272925932443186883e-39 + 1.0486782187465265581e-2152j 4.19e-134, 1.05e-877j

Download

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