Rule: Q[5, 63]

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)
224.50961838985233426 + 1.7685764123830158641e-2193j 1.76e-997, 1.76e-997j
188.99722680557892197 - 3.2862998521246823745e-2190j 8.14e-994, 8.14e-994j
199.39433629826344843 + 1.0450181759742171762e-2214j 8.01e-995, 8.01e-995j
162.58295249925514475 + 4.2205445484836440676e-2255j 1.64e-991, 1.64e-991j
241.43360104462915741 - 1.9401932259457233092e-2291j 2.16e-999, 2.16e-999j
27.277030009836712903 - 1.0741267685468443774e-2314j 8.72e-994, 8.72e-994j
96.001119928002579552 - 2.0942557705351410715e-2354j 4.45e-988, 4.45e-988j
91.366652632889518266 - 3.6122194944983451028e-2397j 5.1e-988, 5.1e-988j
179.51483713545656914 - 9.3152331612003883883e-2410j 6.07e-993, 6.07e-993j
170.75307102031290086 + 4.686700909381341516e-2409j 3.57e-992, 3.57e-992j
36.500688940991617245 + 4.5052439975242765195e-2422j 9.65e-992, 9.65e-992j
19.520898495153572217 - 2.3072169830216806228e-2426j 3.28e-996, 3.28e-996j
66.926130567490615853 - 1.4290173116605692792e-2417j 1.73e-988, 1.73e-988j
140.81945582168165194 + 1.2652219389560288796e-2448j 6.4e-990, 6.4e-990j
105.82972298796430164 + 4.2759923979588767741e-2487j 2.85e-988, 2.85e-988j
47.321052703718097623 - 1.3246275776787324096e-2507j 4.07e-990, 4.07e-990j
7.0858100058588375569 + 2.3020257488470294577e-2534j 1.03e-1003, 1.03e-1003j
29.440753124124991312 + 1.0002740835163267419e-2523j 3.11e-993, 3.11e-993j
1.8252375335498964645 + 2.7980313532372182786e-2542j 3.79e-1011, 3.79e-1011j
147.6760011529059619 + 9.8892650323440614557e-2518j 2.25e-990, 2.25e-990j
211.02668930187716424 - 1.7811225324048227596e-2541j 5.02e-996, 5.02e-996j
17.796705860358404806 + 1.8189132080026356436e-2569j 7.23e-997, 7.23e-997j
100.81849997436520319 + 3.857672564842914085e-2576j 3.72e-988, 3.72e-988j
34.050609601842330439 - 6.3171904139035501584e-2608j 3.45e-992, 3.45e-992j
78.469223272282909337 + 1.8008094879239345278e-2629j 4.32e-988, 4.32e-988j
12.07635015280852735 + 4.3113198529138764601e-2691j 1.31e-998, 1.31e-998j
23.222822527705975688 + 2.5233096647191362032e-2680j 5.66e-995, 5.66e-995j
10.564123414844551099 - 1.3502307620304873681e-2701j 1.92e-1000, 1.92e-1000j
74.479625761356417125 + 1.6522883819747463117e-2700j 3.65e-988, 3.65e-988j
134.30246694075131205 + 3.937188837689808778e-2805j 1.57e-989, 1.57e-989j
12.640800844275782659 - 1.4752318908604761311e-2869j 1.27e-997, 1.27e-997j
116.48529134545790614 - 4.133977687191216688e-2920j 1.26e-988, 1.26e-988j
2.9216901667522666983 + 3.108790523585484763e-2993j 4.38e-1009, 4.38e-1009j
4.3507455848476271076 - 5.7852637453165612552e-2991j 6.14e-1007, 6.14e-1007j
82.608852612074829913 - 3.4730613554454046843e-2972j 4.81e-988, 4.81e-988j
44.457983522756413124 + 1.0325801975500763193e-2993j 1.78e-990, 1.78e-990j
9.3126397252097980391 - 2.8062744024447629474e-3006j 1.38e-1001, 1.38e-1001j
3.5964257710407220812 + 1.9224604045091329583e-3011j 5.2e-1008, 5.2e-1008j
41.701979517177876034 - 4.9815841653629216775e-2994j 7.11e-991, 7.11e-991j
63.351422676376636519 - 2.5747921611043807164e-2991j 1.1e-988, 1.1e-988j
56.582534318369522034 - 1.0650252467029691686e-3007j 3.64e-989, 3.64e-989j
25.20497786705817444 - 8.088297701323223682e-3035j 2.48e-994, 2.48e-994j
21.328777036402404075 + 7.2316468732499712475e-3036j 1.49e-995, 1.49e-995j
0.75861331218000151582 + 1.2191512361409316844e-3055j 1.73e-1014, 1.73e-1014j
5.1836621195104547082 - 6.2429277638590078357e-3047j 7.66e-1006, 7.66e-1006j
86.905430775424436623 - 6.9110546431678353358e-3028j 5.14e-988, 5.14e-988j
0.02053861724381469098 - 2.6440004015761588206e-3076j 1.55e-1020, 1.55e-1020j
59.90499144204425133 - 3.4984102676227221284e-3043j 6.08e-989, 6.08e-989j
0.48365486446255778099 + 7.2789950281746077723e-3080j 9.77e-1016, 9.77e-1016j
31.697974239725853609 + 2.9787495707938985952e-3057j 1.02e-992, 1.02e-992j
111.04723038312265177 + 1.814864268809753338e-3052j 1.93e-988, 1.93e-988j
70.633815083326494852 + 7.4301877180616483795e-3062j 2.54e-988, 2.54e-988j
39.050374706662693243 + 6.428778294778601176e-3072j 2.77e-991, 2.77e-991j
8.1571548072283289725 - 1.1161660923790083411e-3084j 1.17e-1002, 1.17e-1002j
2.3293351929848361754 - 2.6270474086077775075e-3091j 4.07e-1010, 4.07e-1010j
53.380101714363157 + 7.1186886091325338602e-3070j 1.77e-989, 1.77e-989j
154.91316561080308162 - 1.0095856629311786222e-3076j 6.64e-991, 6.64e-991j
50.294058832168681076 - 6.2305874351460239251e-3094j 8.7e-990, 8.7e-990j
6.0951387729251138384 + 1.107528617208191206e-3142j 9.19e-1005, 9.19e-1005j
0.2635603197181409102 - 2.2317552849586168425e-3155j 2.42e-1017, 2.42e-1017j
0.10790436156901972008 - 1.4733707578337201725e-3157j 7e-1019, 7e-1019j
16.151854076755070385 - 5.8809598255327055051e-3131j 1.78e-997, 1.78e-997j
128.09187685038031944 - 2.2495650866570274783e-3125j 3.38e-989, 3.38e-989j
14.572974326978428728 - 3.0783708267048805264e-3177j 4.71e-998, 4.71e-998j
1.0701624724261145008 + 5.393027318717959545e-3193j 3.01e-1013, 3.01e-1013j
1.4134030591065167922 + 2.8847926518262926739e-3192j 3.95e-1012, 3.95e-1012j
12.78148575356269764 - 4.561050962255373679e-3177j 1.29e-997, 1.29e-997j
122.16041248009988599 - 2.2568573223457466128e-3166j 6.59e-989, 6.59e-989j

Weights

Weight (ball center) Error (ball radius)
4.6368437074620403873e-97 + 1.2852268637108406791e-2280j 2.45e-166, 4.01e-911j
8.225734502696758185e-82 + 1.3799300053168748025e-2271j 1.07e-161, 1.75e-906j
2.7757292645611502895e-86 + 1.3583918084239133961e-2274j 3.17e-163, 5.2e-908j
1.9459631277016900258e-70 - 6.7065868101121850221e-2267j 1.33e-158, 2.17e-903j
2.7979168481827181477e-104 - 1.8515753856861188884e-2284j 1.11e-169, 1.82e-914j
3.0170191455668960682e-12 - 5.9356131874600937784e-2237j 3.04e-113, 4.98e-858j
9.5845774282235562954e-42 + 1.2051339673865452064e-2252j 2.65e-146, 4.34e-891j
9.4979023055568077494e-40 - 1.2617883851340675197e-2251j 4.13e-145, 6.78e-890j
9.9212588512917966165e-78 - 3.4667595399780360435e-2270j 1.96e-161, 3.21e-906j
5.8836618690614868626e-74 + 1.5321271075035894218e-2268j 2.42e-160, 3.96e-905j
3.514043399584481532e-16 - 3.3667558042357327651e-2239j 7.97e-126, 1.31e-870j
5.8756960628100037868e-09 - 6.7086897796276209101e-2235j 3.23e-111, 5.3e-856j
3.1296602659960354081e-29 - 3.4383862980880643489e-2246j 1.55e-140, 2.54e-885j
4.6527202516546430805e-61 + 2.3905214051947832621e-2262j 1.27e-157, 2.08e-902j
5.5890626329471309418e-46 + 8.4695399490905366908e-2255j 3.51e-151, 5.76e-896j
8.1986976759039230614e-21 - 9.8829829320111891533e-2242j 2.8e-134, 4.59e-879j
0.00086255806120361680092 - 6.390085662437058167e-2232j 1.21e-94, 1.98e-839j
3.6179895556736389152e-13 + 1.7178453132268065491e-2237j 2.36e-123, 3.87e-868j
0.07374090302375630798 + 1.0401388910957140543e-2230j 2.54e-67, 4.16e-812j
5.1600307871231441895e-64 - 8.4468410557275997393e-2264j 9.8e-159, 1.61e-903j
2.7937641563669744984e-91 - 1.8179842386428738168e-2277j 1.52e-168, 2.5e-913j
3.141966344747722097e-08 + 2.1766299584456627113e-2234j 6.48e-116, 1.06e-860j
8.0606906331303348578e-44 - 1.0568672763022921015e-2253j 4.48e-150, 7.34e-895j
3.9120271460236517389e-15 + 1.2974546678732245317e-2238j 9.51e-129, 1.56e-873j
3.3896254565911829303e-34 + 9.0443079290481034416e-2249j 2.44e-146, 4e-891j
1.4662629085630338365e-05 - 7.9026322901956855292e-2232j 1.47e-112, 2.42e-857j
1.5913455113923350912e-10 - 6.5176385481111108587e-2236j 6.4e-123, 1.05e-867j
3.3870411982006759645e-05 + 2.6896495804015743031e-2232j 1.24e-110, 2.03e-855j
1.7653525369271502855e-32 - 7.0015535097177795968e-2248j 1.43e-145, 2.34e-890j
2.9960940771035724584e-58 - 5.870147071526452645e-2261j 1.28e-158, 2.09e-903j
-2.5477068236818814902e-05 + 2.7256558748651671681e-2231j 1.52e-115, 2.49e-860j
1.4310592679756718183e-50 + 4.0603560605300974113e-2257j 1.16e-155, 1.9e-900j
0.034148671097043711913 + 4.7877115459663856395e-2231j 1.43e-97, 2.35e-842j
0.010236329708776498938 + 2.1340693346906056141e-2231j 2.91e-103, 4.77e-848j
5.6030361376152772997e-36 - 1.0890116118192319977e-2249j 6.08e-148, 9.97e-893j
1.3826317956019717625e-19 + 4.5500890933886477169e-2241j 2.64e-138, 4.34e-883j
0.00010832658091074610501 - 3.1792442549332156204e-2232j 1.54e-115, 2.52e-860j
0.01960098025771022169 - 3.1954688877428301229e-2231j 2.21e-104, 3.62e-849j
2.0939528424314112324e-18 - 1.9978324102639216904e-2240j 2.72e-137, 4.46e-882j
1.0767420482362155562e-27 + 2.1928353919564700788e-2245j 2.88e-145, 4.73e-890j
8.7091699848675879946e-25 + 7.4757003328877863114e-2244j 5.06e-144, 8.29e-889j
2.2931381491606355768e-11 + 1.9911006604966104693e-2236j 3.92e-131, 6.42e-876j
1.0100559845505650707e-09 + 2.097133246839550116e-2235j 3.19e-129, 5.23e-874j
0.13898094801275821516 - 1.0024233547562203726e-2230j 1.58e-107, 2.59e-852j
0.004890493047250843227 - 1.4241792323908491544e-2231j 5.12e-116, 8.39e-861j
7.9192080858704754359e-38 + 1.2182936387526972583e-2250j 3.99e-151, 6.54e-896j
0.051604244189141560927 - 5.3980687360001701034e-2232j 1.77e-110, 2.91e-855j
3.2583074171727074425e-26 - 1.3175892810293142547e-2244j 4.17e-145, 6.84e-890j
0.15404208663257859304 + 6.6186215677978690197e-2231j 3.97e-111, 6.51e-856j
3.9476648688087056322e-14 - 4.808096426020679282e-2238j 1.01e-135, 1.65e-880j
3.1560174379182674229e-48 - 6.1693075078750451727e-2256j 5.56e-158, 9.11e-903j
7.964132717834697372e-31 + 5.0674339331059530271e-2247j 9.19e-148, 1.51e-892j
2.8553034208460088802e-17 + 8.3817935858458416945e-2240j 1.29e-139, 2.12e-884j
0.00031893980994412827666 + 4.3853453079640600973e-2232j 5.02e-128, 8.23e-873j
0.05349809007016685823 - 7.1639566688054248641e-2231j 7.28e-122, 1.19e-866j
2.064198512774991282e-23 - 4.0136976273134755417e-2243j 1.85e-144, 3.03e-889j
3.9251448927368982187e-67 + 2.5688117046063590623e-2265j 1.39e-168, 2.28e-913j
4.3537679853320218799e-22 + 2.0433364129201624669e-2242j 6.53e-144, 1.07e-888j
0.002143163593639061196 + 9.5088218962629491277e-2232j 2.44e-130, 4e-875j
0.1450876972728335835 - 3.925712012176986107e-2231j 1.63e-125, 2.68e-870j
0.10941227909394909404 + 1.9254505762656158751e-2231j 1.8e-125, 2.94e-870j
1.5545423590086540576e-07 - 7.4681960457947592709e-2234j 1.17e-135, 1.92e-880j
1.4235448329070165588e-55 + 1.2623298634911260461e-2259j 1.22e-163, 2e-908j
7.3114153238910864439e-07 + 3.0623260054696672282e-2233j 8.83e-136, 1.45e-880j
0.11124616292258383348 + 1.304585009790074318e-2230j 4.56e-131, 7.46e-876j
0.090032049424981341222 - 1.3209565392223944054e-2230j 2.07e-131, 3.39e-876j
2.2096141268659575352e-05 - 2.0918314288403136229e-2231j 4.95e-134, 8.09e-879j
5.1265016639849922889e-53 - 2.3985680664251420511e-2258j 2.32e-162, 3.8e-907j

Download

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