Rule: Q[2, 6, 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.

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)
308.75567208087344332 + 1.0804345122608473029e-2254j 1.25e-994, 1.25e-994j
275.55534304364974826 + 6.748119928234585148e-2244j 6.99e-991, 6.99e-991j
290.31222460270605455 + 2.9620740842154971117e-2249j 1.71e-992, 1.71e-992j
240.80807070851077179 + 8.9817906626392835896e-2240j 2.75e-987, 2.75e-987j
262.77363388434830984 + 8.4015338783042678796e-2244j 1.65e-989, 1.65e-989j
115.8416304130997227 + 1.3768597800688654378e-2253j 1.09e-979, 1.09e-979j
221.95964215484437957 - 1.0895381974379401471e-2273j 1.59e-985, 1.59e-985j
86.929950113554153065 - 4.8247448288589252203e-2289j 3.77e-980, 3.77e-980j
76.237032308356717429 - 7.3328273244939054119e-2307j 9.64e-981, 9.64e-981j
66.439092960729672309 - 6.0683346198403394412e-2327j 1.6e-981, 1.6e-981j
51.930980156555398178 - 1.0076825461727125961e-2344j 2.64e-983, 2.64e-983j
205.23989150977695167 + 2.1870424338482257363e-2398j 4.31e-984, 4.31e-984j
83.261697585405175177 - 2.0664282144726819259e-2505j 2.55e-980, 2.55e-980j
151.64855251276860944 - 1.4674110055867834089e-2605j 1.17e-980, 1.17e-980j
41.838790358992938821 + 2.2284982386692341874e-2657j 4.51e-985, 4.51e-985j
12.770820165595373722 - 8.1009923912675541092e-2690j 5.24e-996, 5.24e-996j
8.3224919094921121974 - 3.0602500541537110423e-2692j 1.48e-999, 1.48e-999j
23.799839032364896557 + 8.4511588157990160204e-2682j 5.82e-990, 5.82e-990j
146.02038481132799806 - 2.1105740409475115162e-2670j 2.12e-980, 2.12e-980j
120.48579187892331439 - 1.2327120884534756568e-2702j 9.72e-980, 9.72e-980j
39.515178151581337434 - 2.7457230281631344279e-2724j 1.46e-985, 1.46e-985j
15.325666411180559418 - 9.2785454841518942055e-2733j 2.96e-994, 2.96e-994j
46.723225007149992998 + 1.342610738022949665e-2722j 3.94e-984, 3.94e-984j
63.360642621352101051 + 7.2477870458229258568e-2721j 7.71e-982, 7.71e-982j
231.07205184179359583 - 3.154246803659655312e-2718j 2.39e-986, 2.39e-986j
251.30588732392820942 + 1.5214820219678790213e-2732j 2.69e-988, 2.69e-988j
19.408244165972686178 + 6.1863467044220227289e-2771j 7.5e-992, 7.5e-992j
4.0789588738931321308 - 3.7707368900699765646e-2783j 9.01e-1005, 9.01e-1005j
190.1229458854643621 - 9.8456923858342294101e-2758j 6.62e-983, 6.62e-983j
140.57869025340377204 + 1.0650401572715516932e-2781j 3.53e-980, 3.53e-980j
54.65931007312679267 + 2.7649100181492989911e-2798j 6.71e-983, 6.71e-983j
22.249212787852851883 + 7.6483207907121821929e-2806j 1.53e-990, 1.53e-990j
9.3459518428118469803 - 2.4260224811878104845e-2814j 1.15e-998, 1.15e-998j
27.21850409798041587 - 3.2662646725302257623e-2804j 8.43e-989, 8.43e-989j
98.596620069287001119 - 1.3775720338230656088e-2794j 8.34e-980, 8.34e-980j
16.666823210327960237 + 6.7992872781694504698e-2832j 2.07e-993, 2.07e-993j
35.101673646149132285 - 4.3029535259334815376e-2825j 1.34e-986, 1.34e-986j
3.4142135623730950488 - 4.5575914902021883696e-2844j 6.04e-1006, 6.04e-1006j
37.269613182752355686 - 1.3906701506136603798e-2824j 4.6e-986, 4.6e-986j
197.50448234535570964 + 1.2758416659987966396e-2817j 1.71e-983, 1.71e-983j
2.2533790708669879731 + 2.0560844626177177873e-2889j 4.09e-1008, 4.09e-1008j
213.37307231599055511 + 1.7283122111404935696e-2859j 9.23e-985, 9.23e-985j
60.37243873479510123 + 2.5421579065879896367e-2880j 3.77e-982, 3.77e-982j
11.571664377761134272 + 1.3829476234619019783e-2909j 7.38e-997, 7.38e-997j
14.023914954138327016 - 4.4839514281301342227e-2908j 4.39e-995, 4.39e-995j
57.472583302740542594 - 9.2747657204678606274e-2893j 1.65e-982, 1.65e-982j
1.6155455140174800002 - 1.7096824969110705264e-2955j 2.49e-1008, 2.49e-1008j
29.067210545527864772 - 6.2073251571830033404e-2930j 3.03e-988, 3.03e-988j
2.8067455318520273664 - 2.0873559660648867801e-2954j 4.56e-1007, 4.56e-1007j
176.28603719974582965 + 5.4137669519777513966e-2926j 5.46e-982, 5.46e-982j
111.33593955783610005 + 2.0853655696166068988e-2961j 1.18e-979, 1.18e-979j
30.999306568931246448 + 1.0508387691686031106e-3000j 1.11e-987, 1.11e-987j
157.47488281263022933 - 9.9767796151482016774e-2992j 6.57e-981, 6.57e-981j
5.5557825472814642244 - 4.6750799978732676439e-3037j 5.69e-1002, 5.69e-1002j
1.0429703967621881842 - 3.0829630846863514091e-3047j 1.52e-1011, 1.52e-1011j
69.609826134802875983 - 3.7254940861574377743e-3015j 3.2e-981, 3.2e-981j
44.241162727448889549 + 9.7030902880271327654e-3021j 1.34e-984, 1.34e-984j
125.27450674357204141 + 1.6876868852773188813e-3014j 8.42e-980, 8.42e-980j
169.77718162206036343 - 6.417419743970575082e-3048j 1.38e-981, 1.38e-981j
0.39143729977705490718 + 2.6821156034870379303e-3119j 2.59e-1015, 2.59e-1015j
7.3609518832717663875 - 4.4409533100967033512e-3104j 2.58e-1000, 2.58e-1000j
163.51267596264374828 - 4.095516168963258396e-3083j 3.19e-981, 3.19e-981j
130.21447847280081519 - 6.8293543189285379267e-3101j 6.61e-980, 6.61e-980j
1.6682880962583043051 + 1.2543265039987234921e-3138j 2.75e-1008, 2.75e-1008j
18.032747866885902768 + 8.2292852611424986043e-3123j 1.35e-992, 1.35e-992j
10.429445331807150033 + 5.8828471829191999485e-3128j 8.79e-998, 8.79e-998j
5.9184086721992864573 - 2.2802179020505617216e-3133j 2.22e-1001, 2.22e-1001j
102.71828644636306449 + 1.1758273894217476082e-3108j 9.97e-980, 9.97e-980j
90.706234413782504105 - 4.4407764569921910382e-3114j 5.11e-980, 5.11e-980j
0.5857864376269049512 + 1.7722861115658047337e-3152j 9.17e-1014, 9.17e-1014j
1.4691704391763638497 - 1.5270867173293613201e-3147j 2.64e-1009, 2.64e-1009j
4.7997735404558826856 - 1.1557513282544508197e-3141j 1.8e-1003, 1.8e-1003j
106.96317921382052287 - 1.9168274925478427747e-3116j 1.1e-979, 1.1e-979j
72.875025565446644136 + 5.4069786422337980274e-3125j 5.43e-981, 5.43e-981j
33.011357208466170264 + 5.0316497871326548571e-3132j 3.99e-987, 3.99e-987j
0.77047820182520551578 + 2.6384902319171703382e-3157j 8.6e-1013, 8.6e-1013j
6.4710410025453870362 + 1.7263775870498357078e-3145j 5.97e-1001, 5.97e-1001j
0.08837702141245734094 - 2.5651773944368864484e-3163j 9.49e-1019, 9.49e-1019j
79.698357615099422674 - 1.3093399513792442033e-3123j 1.63e-980, 1.63e-980j
49.286080354754191968 + 1.9512966863059374789e-3139j 1.02e-983, 1.02e-983j
25.459441053667409052 + 1.3651368656287626369e-3144j 2.23e-989, 2.23e-989j
94.593913496820901077 - 5.5207884692925686293e-3134j 6.72e-980, 6.72e-980j
20.799370790425286883 + 2.5686384664372191779e-3181j 3.8e-991, 3.8e-991j
183.05984488475576106 + 2.3174444667579276275e-3170j 1.92e-982, 1.92e-982j
0.016826590312928975522 + 3.3999026336955501991e-3245j 1.78e-1020, 1.78e-1020j
135.31312470806414433 + 6.2953929962178800714e-3204j 4.93e-980, 4.93e-980j
0.21545615683958967567 - 9.7981369283582725542e-3262j 4.64e-1017, 4.64e-1017j

Weights

Weight (ball center) Error (ball radius)
1.7603553571083097369e-133 + 1.2240726061818772024e-2348j 6.64e-133, 1.6e-874j
2.8963648761066974471e-119 + 2.8575395359893547808e-2341j 4.93e-129, 1.19e-870j
1.3392475851106951506e-125 - 1.473655435542263029e-2344j 6.33e-131, 1.53e-872j
2.6439259174117356154e-104 - 1.7969603478377763255e-2333j 1.99e-125, 4.81e-867j
9.1172372130772231134e-114 - 2.0689152857290959602e-2338j 6.02e-128, 1.45e-869j
2.2434246909931830336e-50 - 1.645379569554844021e-2303j 1.05e-102, 2.55e-844j
3.5513335294655522147e-96 - 3.2975856331719772846e-2329j 2.53e-123, 6.1e-865j
6.569723680682364942e-38 + 5.5063509188243571425e-2298j 1.95e-93, 4.71e-835j
2.6520938333759559469e-33 - 1.3540039335656955183e-2295j 1.67e-89, 4.04e-831j
4.3713239495410118196e-29 + 2.4221193332159889766e-2293j 1.54e-85, 3.71e-827j
7.513256528397593214e-23 - 6.8636605181820603598e-2290j 1.94e-78, 4.69e-820j
5.8144558075673355714e-89 - 2.107034895501848746e-2325j 6.61e-123, 1.6e-864j
2.5006216552836003554e-36 - 3.5686538564172926795e-2297j 1.37e-92, 3.32e-834j
7.9005864628353684678e-66 - 5.9028967583670819432e-2313j 4.82e-114, 1.16e-855j
1.5961769066332860706e-18 - 2.257662268537891137e-2287j 2.25e-74, 5.43e-816j
3.4871163420889638923e-06 + 2.1593500792771269481e-2279j 4.91e-40, 1.18e-781j
0.0002412804645285722339 + 6.9420821808840365152e-2278j 1.98e-27, 4.79e-769j
7.4068323834219265709e-11 + 2.6069383228400882149e-2282j 8.87e-59, 2.14e-800j
2.1238379278732316157e-63 + 1.3215215321289817125e-2311j 5.89e-113, 1.42e-854j
2.2243428070453550346e-52 - 5.7085460295611259986e-2305j 1.44e-106, 3.48e-848j
1.5760340771139906747e-17 + 8.9821332762300249059e-2287j 5.41e-74, 1.31e-815j
2.9231282884084007126e-07 + 4.6372165324302344146e-2280j 5.94e-49, 1.43e-790j
1.28869872013611199e-20 - 1.3182435433852730128e-2288j 1.21e-78, 2.92e-820j
9.2192348644082402849e-28 - 1.2710016678524303789e-2292j 3.48e-87, 8.39e-829j
4.1691892047017154816e-100 + 2.8426501999929881886e-2331j 7.52e-129, 1.82e-870j
7.9114340429884197915e-109 + 7.7687522596871994561e-2336j 6.24e-132, 1.51e-873j
5.1364357032755495797e-09 - 4.9544041333691967537e-2281j 1.73e-60, 4.18e-802j
0.011735042440567277615 + 1.9859901324686530544e-2276j 3.25e-23, 7.85e-765j
1.9454056844583934162e-82 - 6.1360314660142670676e-2322j 6.18e-124, 1.49e-865j
4.742061788463795053e-61 - 2.7750686076018836282e-2310j 8.69e-114, 2.1e-855j
5.0620625054403619092e-24 + 1.4956111712564574171e-2290j 2.24e-86, 5.4e-828j
3.2526177616820026184e-10 - 7.933439072788865344e-2282j 1.18e-65, 2.85e-807j
9.2006301056301722069e-05 - 2.6780557569621878222e-2278j 4.86e-47, 1.17e-788j
2.7269976896333000316e-12 + 2.2875022877854924901e-2283j 3.61e-71, 8.71e-813j
6.1477883233560681292e-43 - 1.7339959324085659285e-2300j 1.29e-104, 3.11e-846j
7.8357440967398269739e-08 - 2.212060571113636578e-2280j 3.41e-60, 8.22e-802j
1.2126835891312654369e-15 + 1.325187472192949219e-2285j 1.61e-77, 3.87e-819j
0.020925978067638842212 - 2.8804534368726918913e-2276j 8.08e-32, 1.95e-773j
1.4379977066888019452e-16 - 3.4885956558174970252e-2286j 1.71e-78, 4.13e-820j
1.2675122258440628244e-85 + 1.2392582638708189547e-2323j 1.24e-126, 2.99e-868j
0.055705560994957837088 - 1.1447869342601429552e-2275j 1.68e-28, 4.07e-770j
1.7984905178764464849e-92 + 2.9477651661212116626e-2327j 7.43e-129, 1.79e-870j
1.776152124090295754e-26 + 6.4418320891371075052e-2292j 4.21e-92, 1.02e-833j
1.1042535430082441783e-05 - 4.8257402184101663584e-2279j 1.26e-59, 3.05e-801j
1.03804194782756965e-06 - 9.8996655785064391935e-2280j 1.51e-62, 3.65e-804j
3.131663512616452035e-25 - 3.1557972361180513982e-2291j 6.1e-91, 1.47e-832j
-0.47054703944848754076 - 5.3722518930603762559e-2274j 1.57e-31, 3.8e-773j
4.4978074039817318307e-13 - 6.4788123914677852766e-2284j 1.83e-77, 4.43e-819j
0.034991196003446091293 + 5.013363811884732476e-2276j 2.26e-40, 5.45e-782j
1.8279273956945276993e-76 - 9.6459584967815970757e-2319j 2.97e-125, 7.16e-867j
1.9707737714523512915e-48 + 7.4685971360691960629e-2303j 1.08e-111, 2.59e-853j
6.7948951074873559936e-14 + 1.8029864789859699541e-2284j 1.13e-80, 2.73e-822j
2.4130133956110997249e-68 + 2.4398724782391202617e-2314j 6.99e-122, 1.69e-863j
0.0028019592065228847969 + 2.737344047661245565e-2276j 8.79e-59, 2.12e-800j
0.11619846443253963775 - 3.6009374106345337995e-2275j 2.85e-40, 6.87e-782j
1.8895886837107551135e-30 - 4.4554830381027566845e-2294j 6.96e-99, 1.68e-840j
1.4930045924582506971e-19 + 5.530360055245669322e-2288j 2.56e-88, 6.17e-830j
1.9093803319409115534e-54 + 2.2484044933150151168e-2306j 1.3e-115, 3.14e-857j
1.1796870709353024805e-73 + 3.1541509640789097312e-2317j 5.04e-125, 1.22e-866j
0.13129130777472322028 + 1.186390225814568394e-2275j 4.97e-50, 1.2e-791j
0.00059057728234791723837 - 2.0798794991564692006e-2277j 4.99e-69, 1.2e-810j
5.971879232852389656e-71 - 9.2238740944333009982e-2316j 9.83e-124, 2.37e-865j
1.4096194297296006823e-56 - 1.0964952026802663079e-2307j 1.38e-117, 3.32e-859j
0.42244452424621488905 + 3.9398792095994471251e-2274j 7.06e-58, 1.7e-799j
2.0230062966827263797e-08 + 1.0616749588237407021e-2280j 8.53e-81, 2.06e-822j
3.2891257929455303735e-05 + 1.1119387183229202655e-2278j 4.42e-75, 1.07e-816j
0.00043545513875145890082 - 2.6250186210014530528e-2276j 1.59e-70, 3.83e-812j
1.0267269803249130494e-44 + 2.5164799369211563347e-2301j 1.36e-112, 3.28e-854j
1.5493173132710191793e-39 - 8.2428200828650933267e-2299j 4.21e-110, 1.02e-851j
0.10179547180712955678 - 2.5832521235630832284e-2275j 7.98e-66, 1.92e-807j
0.20744866212468694466 + 1.7036034051662048544e-2274j 3.15e-66, 7.59e-808j
0.0061468679110963588122 - 1.7309888031984496072e-2276j 2.2e-73, 5.31e-815j
1.5162093441320535055e-46 - 3.8721750410498850319e-2302j 1.28e-113, 3.1e-855j
7.4306374764134137157e-32 + 7.9078905710960678264e-2295j 1.71e-105, 4.13e-847j
9.449127623052215404e-15 - 4.9330384554330532304e-2285j 1.26e-93, 3.05e-835j
0.098829831948562156598 + 3.4470835477335581881e-2275j 7.38e-73, 1.78e-814j
0.0012969048628146115423 + 9.1631188977621415844e-2277j 1.71e-79, 4.14e-821j
0.091323724932104168355 + 1.9020581102603524627e-2276j 7.28e-76, 1.76e-817j
8.5700062917306871579e-35 + 2.2369631865545206103e-2296j 1.52e-107, 3.68e-849j
1.0254420462604467186e-21 + 3.0533757177586724532e-2289j 3.03e-99, 7.3e-841j
1.5011149705810176233e-11 - 7.8880765961663409685e-2283j 3.91e-92, 9.44e-834j
3.268769494029205794e-41 + 1.2039192766883607333e-2299j 1.3e-111, 3.14e-853j
1.3079220018554276967e-09 + 2.1208817374862168644e-2281j 4.1e-91, 9.89e-833j
2.1769643410247625475e-79 + 2.6061202765825229434e-2320j 1.1e-132, 2.66e-874j
0.042433710018308403747 - 4.7695034844808395419e-2277j 9.28e-87, 2.24e-828j
8.884672021078266754e-59 + 5.5649927322776625529e-2309j 8.99e-122, 2.17e-863j
0.12376965677655367539 - 4.8521317594381852556e-2276j 6.29e-86, 1.52e-827j

Download

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