Rule: Q[5, 61]

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)
216.57140205004821746 - 8.6115466345845542399e-2060j 3.78e-998, 3.78e-998j
172.15866171064264139 + 2.635337774888711292e-2097j 1.06e-993, 1.06e-993j
191.76798539884783997 - 1.2691918037107803473e-2132j 1.53e-995, 1.53e-995j
233.30085678423100885 + 4.6330674971025488171e-2153j 4.97e-1000, 4.97e-1000j
21.913465396427325403 - 2.5181791665792807665e-2176j 7e-996, 7e-996j
147.92671258826839261 + 2.8341066953643784182e-2169j 1.07e-991, 1.07e-991j
42.911092453239662345 - 3.7133480117247193895e-2180j 1.87e-991, 1.87e-991j
73.045637793570213697 - 3.3054052303500916503e-2177j 3.24e-989, 3.24e-989j
94.846341253825790748 - 2.8415367252270249317e-2180j 4.06e-989, 4.06e-989j
20.073069813002744294 + 4.8480501771845162686e-2198j 1.75e-996, 1.75e-996j
9.2642060583824388872 - 3.731720153101181952e-2203j 5.34e-1002, 5.34e-1002j
40.164935668570767027 - 7.5136096792039692701e-2193j 8.06e-992, 8.06e-992j
13.804848658476683365 - 1.5214030915424890728e-2200j 6.82e-999, 6.82e-999j
51.828129118984079987 - 3.8689571451911998922e-2192j 2.01e-990, 2.01e-990j
85.613735542221758784 - 1.1304032186389262793e-2188j 4.43e-989, 4.43e-989j
61.834628108840129278 - 2.5177155915290645837e-2198j 1.18e-989, 1.18e-989j
155.47650205266420141 - 1.1286799843543929892e-2201j 2.71e-992, 2.71e-992j
37.527097426286510391 - 6.5712960942399949289e-2216j 2.92e-992, 2.92e-992j
203.25216645659254233 - 4.0254203608815729188e-2214j 1.09e-996, 1.09e-996j
8.1437663694352649283 - 9.9318134764516316396e-2227j 5.77e-1003, 5.77e-1003j
34.995066550353685728 - 1.0712444732897990574e-2216j 1.14e-992, 1.14e-992j
5.1876296284511003101 + 1.1714110033369195154e-2229j 4.94e-1006, 4.94e-1006j
55.037524529518165987 - 1.2292595212900551056e-2213j 3.8e-990, 3.8e-990j
81.262131289242629269 + 1.8314412324938936757e-2211j 5.02e-989, 5.02e-989j
23.850010193633799379 + 1.3308757970913554633e-2234j 2.69e-995, 2.69e-995j
6.0991938666682368173 - 4.2969994513510023996e-2245j 5.95e-1005, 5.95e-1005j
45.768308880094976017 + 7.9926986644732901666e-2230j 4.47e-991, 4.47e-991j
3.5964257710407220812 + 1.3994205836124293876e-2247j 3.74e-1008, 3.74e-1008j
18.330529106170367157 - 1.3883613741278506793e-2236j 4.32e-997, 4.32e-997j
181.50933304153317864 - 1.1758121141007542861e-2228j 1.54e-994, 1.54e-994j
99.747723758842990175 + 3.7418412596555766833e-2259j 3.21e-989, 3.21e-989j
10.42373258418873058 + 2.9422029307525362528e-2323j 5.34e-1001, 5.34e-1001j
16.691223897259447074 + 5.2279447843716422321e-2320j 1.01e-997, 1.01e-997j
4.3529429969391847843 - 1.7146675187835398416e-2329j 4.62e-1007, 4.62e-1007j
110.18254899881364166 - 6.7623149186026273773e-2311j 1.41e-989, 1.41e-989j
28.012033306978139246 - 4.1815017601179645732e-2356j 3.29e-994, 3.29e-994j
127.66358379177177902 - 2.7104641169372007668e-2359j 2.09e-990, 2.09e-990j
1.4134030591065167922 - 1.197410907774909147e-2408j 3.05e-1012, 3.05e-1012j
15.16998714827960692 - 6.3655595474496414836e-2395j 2.6e-998, 2.6e-998j
48.739570839410201068 - 9.3343294186405336884e-2386j 9.83e-991, 9.83e-991j
115.74647341181869637 + 1.0565122019816260316e-2403j 8.74e-990, 8.74e-990j
77.075299907843836344 + 6.7884620081755841713e-2423j 3.91e-989, 3.91e-989j
2.9197536881938593874 - 5.3439167073891491365e-2452j 3.41e-1009, 3.41e-1009j
7.0858100058588375569 - 4.6884002080871792925e-2447j 5.48e-1004, 5.48e-1004j
58.371618271010245045 - 1.0338022624776719861e-2431j 7.27e-990, 7.27e-990j
121.56596019963337031 + 1.0987585584588092137e-2454j 4.66e-990, 4.66e-990j
32.56655305574004641 + 2.7755676684924943484e-2492j 3.47e-993, 3.47e-993j
163.52365357748765823 - 8.2726392477506336877e-2535j 6.1e-993, 6.1e-993j
0.76012559199138320564 - 3.6431791029368973774e-2616j 1.76e-1014, 1.76e-1014j
11.564333137445839651 + 3.7900915824491395613e-2592j 4.04e-1000, 4.04e-1000j
90.138617683600944978 - 4.692450823132871426e-2666j 4.59e-989, 4.59e-989j
104.8550826510308551 - 6.087174083233028251e-2783j 2.37e-989, 2.37e-989j
2.3262286619987065143 - 1.5686562353963222038e-2860j 2.97e-1010, 2.97e-1010j
0.10783853920058164572 - 1.2200870234105460287e-2869j 7.05e-1019, 7.05e-1019j
0.2635603197181409102 - 6.6932758914405375859e-2868j 2.33e-1017, 2.33e-1017j
30.23948759523914047 - 6.9806107100060319992e-2840j 1.16e-993, 1.16e-993j
0.020519397040387319169 + 1.2933250376890130663e-2914j 1.42e-1020, 1.42e-1020j
140.80718189026735043 + 2.0202013427795992592e-2885j 3.27e-991, 3.27e-991j
69.166315130248539392 - 4.0729098500305390167e-2945j 2.36e-989, 2.36e-989j
0.48409953956323312395 - 7.6912660577103572405e-3012j 7.3e-1016, 7.3e-1016j
1.0724029293385499762 + 4.5387158065506730284e-3009j 3.13e-1013, 3.13e-1013j
65.431171247505500877 - 3.8860192008562245032e-2985j 1.78e-989, 1.78e-989j
134.06637091258454589 + 5.7640186201046028045e-3027j 9.04e-991, 9.04e-991j
12.640800844275782659 + 1.9451821462059250287e-3064j 1.92e-999, 1.92e-999j
1.8225039900310652022 - 8.3074993923968864942e-3076j 2.92e-1011, 2.92e-1011j
25.882618726382218868 + 5.935633749297959668e-3059j 9.91e-995, 9.91e-995j

Weights

Weight (ball center) Error (ball radius)
1.2840224509409208694e-93 + 5.6334413187828874278e-2153j 1.42e-174, 1.1e-919j
1.5314751634652936428e-74 + 1.3790005851338051884e-2144j 1.38e-168, 1.07e-913j
5.6203226076334668771e-83 + 1.1975182481745224653e-2148j 1.7e-171, 1.32e-916j
9.4181628322696897099e-101 + 1.5369007313795783398e-2157j 2.43e-177, 1.89e-922j
5.7443183777711119607e-10 - 7.427498529703748396e-2111j 9.74e-117, 7.54e-862j
4.178792229476638213e-64 - 2.0180130533419392939e-2139j 1.79e-165, 1.39e-910j
6.4758233640998803279e-19 + 4.6597725819846014704e-2116j 5.18e-135, 4.01e-880j
7.4757499336176825545e-32 - 5.7637188358974476725e-2123j 7.61e-149, 5.9e-894j
3.0919814780465343606e-41 + 7.8772674420568716148e-2128j 1.6e-155, 1.24e-900j
3.4332365780198799674e-09 + 2.4035727303297645582e-2110j 2.12e-117, 1.64e-862j
0.00010858703515148527702 + 1.8426961872047802607e-2107j 2.23e-100, 1.72e-845j
9.6960350157765932379e-18 - 2.0778757278324859294e-2115j 3.51e-134, 2.72e-879j
1.2803136924414442073e-06 + 2.3222793988665484079e-2108j 3.79e-110, 2.93e-855j
9.7591963540943485419e-23 - 3.8919659184935658299e-2118j 5.4e-141, 4.19e-886j
2.9207297863556418975e-37 + 8.8583054145633158308e-2126j 1.09e-153, 8.43e-899j
4.93412724188791195e-27 + 1.9811255040551826099e-2120j 8.36e-146, 6.47e-891j
2.337271022881318994e-67 + 4.8359326024365484398e-2141j 4.9e-169, 3.79e-914j
1.301880202388892496e-16 + 8.8435869113330606902e-2115j 1e-134, 7.77e-880j
6.5641837826960216401e-88 - 6.7619769139130525436e-2151j 1.99e-176, 1.54e-921j
0.00031709625599569738027 - 2.7418786007975665607e-2107j 7.97e-107, 6.17e-852j
1.5713444867156290557e-15 - 3.6000509686532259514e-2114j 5.99e-134, 4.64e-879j
0.0048778808542901549196 + 1.0088501578631335792e-2106j 2.26e-100, 1.75e-845j
4.0944633456317713539e-24 + 7.0946322245408136141e-2119j 1.15e-143, 8.92e-889j
2.1803037707414544648e-35 - 8.2872610191503705618e-2125j 3e-153, 2.32e-898j
8.704114777310984908e-11 + 2.2502669677660481718e-2111j 1.65e-128, 1.28e-873j
0.0021312986520340864651 - 6.4936037916051544797e-2107j 2.35e-106, 1.82e-851j
3.8683330267940360727e-20 - 9.9533301598568801148e-2117j 1.16e-139, 8.97e-885j
0.01966005467142694273 + 2.4273555603042805588e-2106j 5.34e-100, 4.13e-845j
1.8519643794353296314e-08 - 7.6841492754947934369e-2110j 2.01e-124, 1.55e-869j
1.4493558507014385639e-78 - 1.5235519854731795512e-2146j 2.12e-174, 1.64e-919j
2.3948216141405350651e-43 - 6.4896184250663265644e-2129j 9.56e-160, 7.4e-905j
3.4579034657813561287e-05 - 1.2910315882409227355e-2107j 1.37e-118, 1.06e-863j
8.9302919274855853053e-08 + 2.4474395762181033581e-2109j 3.27e-125, 2.54e-870j
0.010241290302876409938 - 1.5659168787318364626e-2106j 6.76e-108, 5.24e-853j
7.6585446071755093075e-48 - 3.2649753734454250819e-2131j 3.27e-163, 2.53e-908j
1.4880781149997308327e-12 + 1.9029858000419737706e-2112j 2.46e-135, 1.91e-880j
2.2488535754071128506e-55 + 4.9139080453320706836e-2135j 9.87e-168, 7.64e-913j
0.089203351275738790992 + 1.1394256714804033622e-2105j 9.74e-104, 7.55e-849j
3.7482742327674191894e-07 - 7.7677894149033002629e-2109j 5.4e-127, 4.19e-872j
2.0607346855898873701e-21 + 2.0208690536291798554e-2117j 1.27e-144, 9.82e-890j
3.0684901437384438755e-50 + 1.9658117956870461304e-2132j 3.95e-165, 3.06e-910j
1.3808684780211082458e-33 + 7.1722035074101946861e-2124j 2.41e-155, 1.87e-900j
0.034303429235481373783 - 3.7650565539723466607e-2106j 5.98e-117, 4.63e-862j
0.00085628692518200393666 + 4.193425426009222537e-2107j 1.92e-123, 1.49e-868j
1.5161015157817163777e-25 - 1.2213806500330238742e-2119j 1.18e-149, 9.13e-895j
9.5371074935955399974e-53 - 1.0492215219105299575e-2133j 9.3e-167, 7.21e-912j
1.7085965876914728547e-14 + 1.4048277297798666773e-2113j 2.93e-142, 2.27e-887j
7.9962337394026107567e-71 - 9.2790541948357472053e-2143j 2.02e-175, 1.56e-920j
0.13937222358559568471 + 8.7172380072831005866e-2106j 9.35e-122, 7.24e-867j
1.0487801020382706176e-05 + 9.0659894500439817768e-2108j 6.11e-133, 4.73e-878j
3.2917807075459370365e-39 - 8.7231340964737244568e-2127j 1.41e-159, 1.09e-904j
1.5109885639718706789e-45 + 4.8492779167790569551e-2130j 3.6e-163, 2.79e-908j
0.053721003916372748347 + 5.8357293750087956824e-2106j 2.31e-129, 1.79e-874j
0.10939754673294087848 - 1.7125842958541946242e-2106j 3.08e-127, 2.39e-872j
0.14524226924040711237 + 3.4641634662941558979e-2106j 3.55e-127, 2.75e-872j
1.676932284274289078e-13 - 5.2675878097816996273e-2113j 3.89e-144, 3.01e-889j
0.05156082773336425154 + 4.8246285915437043628e-2107j 1.9e-128, 1.47e-873j
4.8807611232768188893e-61 + 6.9238056923495030152e-2138j 5.38e-172, 4.17e-917j
3.4829656406759100852e-30 + 4.3156160570073171137e-2122j 4.86e-156, 3.76e-901j
0.1544319069342618335 - 5.788427421291444389e-2106j 3.6e-133, 2.79e-878j
0.11083147012295646176 - 1.1335751580052836039e-2105j 5.98e-134, 4.63e-879j
1.404987476472188225e-28 - 3.0201544748420037237e-2121j 3.54e-155, 2.74e-900j
3.9174115580318545583e-58 - 1.9952535822052130538e-2136j 7.64e-171, 5.92e-916j
3.5005977836100265198e-06 - 5.3951310796482770391e-2108j 1.73e-141, 1.33e-886j
0.073693142020444066319 - 8.7673062156846961946e-2106j 1.55e-138, 1.15e-883j
1.1955291064677544481e-11 - 6.6441237120670467246e-2112j 9.97e-146, 7.73e-891j

Download

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