Rule: Q[1, 81]

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)
468.54232243531142846 + 7.328255261040990272e-2268j 9.68e-1004, 9.68e-1004j
232.63882595413080284 + 2.8213217075002340157e-2244j 1.41e-987, 1.41e-987j
299.48182683402665299 + 7.8327607139228887229e-2262j 1.45e-994, 1.45e-994j
223.06025647177990727 - 2.623823590016190248e-2263j 1.08e-986, 1.08e-986j
254.25104211295814603 + 7.1800526551138885263e-2284j 1.13e-989, 1.13e-989j
150.7215898435225353 - 6.6584645896673408546e-2309j 1.32e-981, 1.32e-981j
37.94281664133630468 + 6.0472996705675270821e-2348j 3.61e-987, 3.61e-987j
134.14592030451421374 - 2.8396280547749367134e-2341j 5.41e-981, 5.41e-981j
114.46019607666464603 + 7.0418892982625618775e-2373j 1.16e-980, 1.16e-980j
281.3438410504514972 - 5.9644061888216279417e-2404j 1.51e-992, 1.51e-992j
53.04612832565084794 + 4.1625334111177491015e-2401j 3.16e-984, 3.16e-984j
128.98402522142425233 + 1.4204175459332517532e-2412j 7.47e-981, 7.47e-981j
119.1488755476909292 - 1.0168049060449836062e-2452j 1.12e-980, 1.12e-980j
205.65065584831982112 + 9.2690399124968683376e-2503j 3.57e-985, 3.57e-985j
42.653533588785646629 - 3.2859866757987413983e-2541j 4.05e-986, 4.05e-986j
13.17818696395735878 - 1.6609082414248835238e-2580j 2.68e-997, 2.68e-997j
9.6075827230436415904 - 8.9671634986508382032e-2581j 4.82e-1000, 4.82e-1000j
190.04679229009735244 + 9.6800221809635347719e-2564j 5.69e-984, 5.69e-984j
23.833847186026641429 - 3.3169160339488371155e-2605j 1.24e-991, 1.24e-991j
29.440445630829292874 - 6.0015795220306068309e-2604j 1.33e-989, 1.33e-989j
22.106694866335246938 - 1.4437009820484738271e-2606j 2.32e-992, 2.32e-992j
35.704100915352214255 - 3.9816655247565552441e-2601j 9.39e-988, 9.39e-988j
47.684076627879301382 + 5.3480075603866881163e-2595j 3.79e-985, 3.79e-985j
17.339208348805695358 + 4.3046940936595720285e-2630j 9.22e-995, 9.22e-995j
242.96763440878730981 + 9.642764679120516625e-2625j 1.44e-988, 1.44e-988j
20.449031857957969406 + 5.5310053842835801965e-2680j 3.77e-993, 3.77e-993j
5.7426361870093190699 + 1.1828878933958469069e-2689j 4.85e-1004, 4.85e-1004j
14.498860150271755507 + 1.4413984901048204182e-2687j 2e-996, 2e-996j
156.64875612584932293 + 2.0986238424279836405e-2671j 6.9e-982, 6.9e-982j
266.82678029053727622 - 5.0997957112780799224e-2701j 5.29e-991, 5.29e-991j
71.26202451684738018 - 7.0936750924248053063e-2692j 3.94e-982, 3.94e-982j
214.09621279289989799 - 1.0399963126463655182e-2713j 6.78e-986, 6.78e-986j
89.150476713246776698 - 1.5740059233375491223e-2761j 4.82e-981, 4.82e-981j
25.631285578133801398 + 7.1459677430204963776e-2823j 6.29e-991, 6.29e-991j
145.00385773059877947 + 3.303084296422131163e-2812j 2.23e-981, 2.23e-981j
175.84922075454761964 - 6.5755108199652017619e-2860j 5.29e-983, 5.29e-983j
4.9337132749983383403 + 4.5623678542423498215e-2933j 4.22e-1005, 4.22e-1005j
3.5023433399356300493 + 1.1453874947107771872e-2934j 2.72e-1007, 2.72e-1007j
31.454006689088993239 + 3.9678872696584174917e-2916j 5.91e-989, 5.91e-989j
109.91507490467377206 + 5.0496062855187778652e-2907j 1.16e-980, 1.16e-980j
182.79067868677120889 + 4.5173758877018217315e-2946j 1.87e-983, 1.87e-983j
85.357465496107266442 - 5.1114184728992525736e-2968j 3.17e-981, 3.17e-981j
139.48246996832116927 - 6.7253558347053390789e-2994j 3.68e-981, 3.68e-981j
74.630575685352541941 + 5.540152614555752846e-3011j 6.83e-982, 6.83e-982j
64.81918340610922729 + 5.1174375021313978964e-3016j 9.86e-983, 9.86e-983j
93.057939775446440816 - 1.2643563442020872099e-3023j 6.01e-981, 6.01e-981j
162.80036260343034302 + 1.1880634062541300779e-3058j 3.3e-982, 3.3e-982j
40.258874381942734324 + 1.4750339139535854783e-3094j 1.22e-986, 1.22e-986j
1 - 2.8300661768669290058e-3121j 2.49e-1013, 2.49e-1013j
169.19376206261356165 + 3.0533059195946642472e-3088j 1.33e-982, 1.33e-982j
15.885669669458637094 + 4.9037346303403438932e-3116j 1.39e-995, 1.39e-995j
6.6141287296190910684 + 2.4510983068368397011e-3124j 5.12e-1003, 5.12e-1003j
4.1870451588378480744 - 8.5461058482492642134e-3127j 3.34e-1006, 3.34e-1006j
61.740067642201605143 - 3.1878172006245122615e-3103j 4.28e-983, 4.28e-983j
81.675319981468693109 + 1.345995054776852002e-3101j 2.02e-981, 2.02e-981j
7.5485327736044042706 + 9.721163612663456193e-3137j 5.12e-1002, 5.12e-1002j
123.98771669117449398 + 7.8491103779387036074e-3115j 9.67e-981, 9.67e-981j
11.923092881692367998 + 1.4312068506646727383e-3144j 3.68e-998, 3.68e-998j
50.322878059559140595 + 2.4894176605672652368e-3130j 1.14e-984, 1.14e-984j
0.42551800066473786309 - 1.5314281015651118324e-3162j 5.49e-1016, 5.49e-1016j
78.100718036958508733 + 1.5358664799724037271e-3126j 1.2e-981, 1.2e-981j
18.860106153234473739 + 8.6492670872567752191e-3145j 6.16e-994, 6.16e-994j
97.083734560448918156 + 2.7015008700698635016e-3131j 8.38e-981, 8.38e-981j
27.499853895804673764 - 5.770775426494591057e-3157j 2.89e-990, 2.89e-990j
0.68243992585515612508 + 3.7773472816252582442e-3181j 1.16e-1014, 1.16e-1014j
2.317812539406949123 - 2.1227225358335521104e-3176j 1.22e-1009, 1.22e-1009j
197.65240134348485113 + 4.802625204879754023e-3148j 1.49e-984, 1.49e-984j
45.128129148217019311 + 4.0050796697400801317e-3164j 1.27e-985, 1.27e-985j
55.855522226966345744 - 7.69854717986135747e-3162j 7.92e-984, 7.92e-984j
1.3783170456683891688 - 5.4844077267647960474e-3190j 4.66e-1012, 4.66e-1012j
1.8175328439792666781 - 7.6850560176408928582e-3189j 6.67e-1011, 6.67e-1011j
8.5462179957038245001 + 8.5008683277961795042e-3179j 4.94e-1001, 4.94e-1001j
0.017691447250684226958 + 1.3181513428337030188e-3266j 1.34e-1020, 1.34e-1020j
67.992391874609039199 - 7.8753372938916250266e-3159j 1.99e-982, 1.99e-982j
105.50751902014322117 - 3.2900888616955243586e-3181j 1.1e-980, 1.1e-980j
0.093222378640379204333 + 7.0789644289666542644e-3297j 6.69e-1019, 6.69e-1019j
33.54153841839818837 + 2.172533116224274554e-3213j 2.34e-988, 2.34e-988j
58.752862321971835304 - 3.3046214245853785317e-3206j 1.91e-983, 1.91e-983j
101.23206901610093357 - 5.8402722703860427113e-3213j 9.97e-981, 9.97e-981j
10.733054856962993559 - 4.9178227503333739487e-3248j 4.97e-999, 4.97e-999j
2.8793450219998563995 + 1.5765524053991162764e-3257j 1.89e-1008, 1.89e-1008j
0.22913770060665575296 - 2.8267454135351496167e-3266j 1.9e-1017, 1.9e-1017j

Weights

Weight (ball center) Error (ball radius)
1.1418733646696300137e-176 + 1.9957246112216892188e-2383j 3.53e-149, 1.96e-890j
9.1842839399384537599e-101 - 1.2845714933241364653e-2344j 6.79e-125, 3.78e-866j
1.8442596477246534564e-129 - 2.3247184304477325479e-2360j 3.51e-134, 1.95e-875j
1.2371641149336274394e-96 + 3.0142540070181789385e-2343j 8.15e-124, 4.53e-865j
4.5095891281161258637e-110 + 2.9129538478276572505e-2350j 2.1e-128, 1.17e-869j
2.0294445719523373699e-65 + 1.0321343421583614396e-2328j 8.77e-113, 4.88e-854j
7.5690611178320929357e-17 + 3.6177566021601853765e-2305j 5.04e-70, 2.8e-811j
2.8915437699890014488e-58 - 2.9806082664541294021e-2325j 1.87e-109, 1.04e-850j
9.011984881609237408e-50 - 3.9372981419561134893e-2321j 2.26e-105, 1.26e-846j
1.034226574379247887e-121 + 2.2017851790806055137e-2356j 4.95e-134, 2.75e-875j
2.5363910448159311407e-23 + 2.732607208749597587e-2308j 6.55e-84, 3.64e-825j
4.8821874671438733389e-56 + 3.5812391846562989028e-2324j 8.59e-109, 4.78e-850j
8.5535293315918381726e-52 + 4.1024177880787668208e-2322j 1.12e-106, 6.25e-848j
3.9947000969550693102e-89 + 5.6417754607626057205e-2340j 1.64e-124, 9.14e-866j
7.2811063721032363916e-19 + 3.8765506602158158895e-2306j 4.62e-80, 2.57e-821j
2.4357482633669454054e-06 + 3.299929029664553847e-2300j 1.16e-48, 6.46e-790j
7.3491464756170879816e-05 - 1.5170071453876375043e-2299j 4.51e-40, 2.51e-781j
2.1596875446333075727e-82 + 7.7650032283076493765e-2337j 1.87e-122, 1.04e-863j
7.8548285093868916354e-11 - 2.6801739005992441304e-2302j 1.46e-65, 8.12e-807j
3.2371643237595986645e-13 + 1.9775003808100685237e-2303j 2.29e-71, 1.27e-812j
4.2428364199414216927e-10 + 5.9384312489162741972e-2302j 6.6e-64, 3.67e-805j
6.8614647067010340696e-16 - 1.0419201005595857043e-2304j 2.84e-76, 1.58e-817j
5.0764497838863905884e-21 + 3.5363866244626966594e-2307j 8.54e-85, 4.75e-826j
4.3855150777784461016e-08 - 5.2009700588079043436e-2301j 1.79e-59, 9.95e-801j
3.2544160326073028986e-105 - 1.5604192078987231291e-2347j 7.33e-132, 4.07e-873j
2.1353202455821551959e-09 - 1.2689423561816896013e-2301j 2.18e-63, 1.21e-804j
0.0026937866017191655691 - 6.9506255483281537829e-2299j 3.35e-37, 1.86e-778j
6.8348660428782271874e-07 - 1.8473198895209324928e-2300j 3.67e-56, 2.04e-797j
5.6118964705469951079e-68 - 6.020898033230792727e-2330j 5.08e-119, 2.83e-860j
1.7601261156745216349e-115 - 3.8403090518564520574e-2353j 4.01e-136, 2.23e-877j
3.7347280904033790679e-31 + 4.3736134548919584467e-2312j 1.32e-100, 7.34e-842j
9.0839947234650630424e-93 - 1.2840901054122797547e-2341j 5.73e-128, 3.19e-869j
7.3766184219404985056e-39 - 7.9114310652390137563e-2316j 5.81e-107, 3.23e-848j
1.35395143314444543e-11 + 1.1663123129002760341e-2302j 1.46e-74, 8.09e-816j
5.9589447733426075451e-63 - 1.6072447470838221161e-2327j 2.94e-117, 1.64e-858j
2.8959211090994803671e-76 + 6.328629314134716013e-2334j 9.36e-124, 5.2e-865j
0.0055995473512467762164 + 9.2475509700932880012e-2299j 3.26e-49, 1.81e-790j
0.019697091271600044055 + 1.4499581169800695147e-2298j 9.75e-44, 5.42e-785j
4.4826176848682757602e-14 - 7.699895707997861714e-2304j 5.57e-82, 3.1e-823j
8.2284879604349113303e-48 + 3.5278012904293313484e-2320j 3.74e-112, 2.08e-853j
2.9233490313549119015e-79 - 2.3635393603329928781e-2335j 7.98e-125, 4.44e-866j
3.1786833111579862019e-37 + 4.9263786222500348863e-2315j 6.17e-108, 3.43e-849j
1.4391508220824495214e-60 + 2.2852366072969237065e-2326j 5.67e-117, 3.15e-858j
1.3250655728815738746e-32 - 8.6469093041533669494e-2313j 1.29e-105, 7.18e-847j
2.2097626191886788981e-28 + 9.678923907250433099e-2311j 2.55e-103, 1.42e-844j
1.5268563100129664934e-40 + 1.2016234955524540842e-2316j 4.02e-110, 2.23e-851j
1.2414411399114591879e-70 + 3.1724622694768968593e-2331j 1.07e-122, 5.93e-864j
7.7234295218219674691e-18 - 1.2079610299481484439e-2305j 8.69e-95, 4.83e-836j
0.1279914592124842461 - 1.9484425313380493784e-2298j 1.07e-64, 5.96e-806j
2.1596428953673928323e-73 - 1.5005395428932124433e-2332j 5.56e-124, 3.09e-865j
1.7916441798252667798e-07 + 9.9786147529771978213e-2301j 3.58e-82, 1.99e-823j
0.0012110296156905293119 + 5.0255009539694890886e-2299j 3e-73, 1.67e-814j
0.010871348557958754613 - 1.1821946578028387449e-2298j 4.75e-68, 2.64e-809j
4.6609486523950572954e-27 - 4.2440894969864152583e-2310j 4.04e-104, 2.25e-845j
1.2260478836155949994e-35 - 2.905971542541906476e-2314j 6.29e-109, 3.5e-850j
0.00050895841862057000409 - 3.4984461670212125281e-2299j 4.61e-78, 2.56e-819j
6.9896691466844671549e-54 - 3.979017161946534669e-2323j 5.97e-117, 3.32e-858j
8.1116444602783991063e-06 - 5.6877106982703120568e-2300j 1.48e-83, 8.2e-825j
3.7437632504032533737e-22 - 1.0039930828723302622e-2307j 1.76e-101, 9.79e-843j
0.1480915780778907638 - 1.3629498535691427959e-2298j 4.18e-70, 2.33e-811j
4.2468144455344402859e-34 + 1.6262966984333792293e-2313j 2.3e-108, 1.28e-849j
1.0019214051220428896e-08 + 2.6155158842298502931e-2301j 2.57e-89, 1.43e-830j
2.8080424313514254155e-42 - 1.7230873294662913149e-2317j 2.54e-113, 1.41e-854j
2.1713483019580571804e-12 - 4.8922694557971481551e-2303j 4.25e-94, 2.36e-835j
0.14515748958467562069 + 1.7112252997484795308e-2298j 9.21e-76, 5.12e-817j
0.052285001127732008648 + 1.9094714504917211583e-2298j 4.61e-80, 2.56e-821j
1.1282574387812114807e-85 - 2.2339494872621069001e-2338j 1.29e-132, 7.15e-874j
6.3335245514372570585e-20 - 1.1950047835167648607e-2306j 9.15e-101, 5.09e-842j
1.576033292875620416e-24 - 7.1247935975814079872e-2309j 1.58e-104, 8.81e-846j
0.10300363810127575009 + 2.0562832230819230288e-2298j 2.28e-83, 1.27e-824j
0.076294451637903189553 - 2.0370363189567183215e-2298j 2.12e-84, 1.18e-825j
0.00020000117064035852885 + 2.3464099169842378161e-2299j 9.1e-90, 5.06e-831j
0.044606610241330356878 + 1.521901633695814783e-2299j 4.98e-85, 2.77e-826j
9.5339455835460921424e-30 - 2.1070036350488847212e-2311j 2.66e-107, 1.48e-848j
6.5496767804710849391e-46 - 2.9587203167722062569e-2319j 3.52e-116, 1.96e-857j
0.096296628672226089303 - 5.1350755095636315187e-2299j 3.62e-89, 2.01e-830j
5.7600515052442031343e-15 + 2.8870269597064317311e-2304j 4.45e-100, 2.47e-841j
8.9658260069638438128e-26 + 1.7781407763910794185e-2309j 3.96e-106, 2.2e-847j
4.5694744256954194971e-44 + 2.328355913776961491e-2318j 2.4e-115, 1.33e-856j
2.5251114741944727545e-05 + 9.457846398556289253e-2300j 7.43e-96, 4.13e-837j
0.033266351888448638938 - 1.7027688819738748656e-2298j 3.21e-94, 1.79e-835j
0.13211481931671016907 + 9.4367385123742169746e-2299j 5.13e-94, 2.81e-835j

Download

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