Rule: Q[5, 62]

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)
237.26790003053807043 + 1.5247930474371088682e-4077j 7.14e-2021, 7.14e-2021j
207.04097047469093331 - 1.4042706374204763635e-4071j 1.66e-2017, 1.66e-2017j
14.844120721407922953 + 1.2441889303999892664e-4076j 3.32e-2019, 3.32e-2019j
16.379501012884029428 - 2.2992958102298031768e-4076j 1.1e-2018, 1.1e-2018j
21.571211929007168317 + 1.0422516590344806012e-4074j 7.88e-2017, 7.88e-2017j
8.1520869076516652718 + 6.9017349485831438128e-4083j 6.69e-2024, 6.69e-2024j
6.0965852838405064943 + 1.3258070540266292207e-4083j 5.44e-2026, 5.44e-2026j
9.2933368142929086459 - 5.3133021957239408381e-4081j 6.95e-2023, 6.95e-2023j
11.729478038549467064 - 2.5077696888736239382e-4078j 1.03e-2020, 1.03e-2020j
220.44163307810334055 + 6.255590726826706339e-4075j 5.59e-2019, 5.59e-2019j
2.9210583191070599945 - 1.3117160851119395997e-4089j 3.56e-2030, 3.56e-2030j
2.3283443117657386272 - 1.5011147797580427689e-4088j 3.03e-2031, 3.03e-2031j
7.0858100058588375569 - 7.5559660620785917433e-4083j 5.95e-2025, 5.95e-2025j
12.640800844275782659 - 1.46703047739050861e-4077j 5.25e-2020, 5.25e-2020j
1.4134030591065167922 + 1.5376289535802872441e-4090j 3.07e-2033, 3.07e-2033j
0.10788462532792876335 - 3.1471578193960108076e-4098j 5.33e-2040, 5.33e-2040j
4.35149453981455575 - 1.3404529995954621075e-4086j 4.68e-2028, 4.68e-2028j
10.501498462975188679 + 3.6173664450245582746e-4079j 8.29e-2022, 8.29e-2022j
1.0708454833955383369 - 5.5132698240608959899e-4092j 2.87e-2034, 2.87e-2034j
3.5964257710407220812 - 2.0314716515333232469e-4086j 4.29e-2029, 4.29e-2029j
1.8243856322334551588 + 6.654037479224600135e-4091j 2.98e-2032, 2.98e-2032j
0.2635603197181409102 - 1.2788599288019995656e-4096j 2.02e-2038, 2.02e-2038j
18.017867969014129126 - 1.2031839834602049873e-4075j 5.07e-2018, 5.07e-2018j
0.48378984054023711523 + 8.0403745764618158254e-4095j 5.46e-2037, 5.46e-2037j
5.1850446726230692927 - 1.2074646750367759423e-4084j 5.1e-2027, 5.1e-2027j
0.020532874159420331382 + 4.2669186721220009043e-4146j 9.05e-2042, 9.05e-2042j
19.749086442622459019 + 5.5120067623715695423e-4075j 2.01e-2017, 2.01e-2017j
0.75907438161763777949 + 1.4844869231354162354e-4093j 1.46e-2035, 1.46e-2035j
13.48028339709395593 - 7.9953169400494580892e-4077j 1.51e-2019, 1.51e-2019j
195.48311662762786977 + 2.553310009579379552e-4067j 2.39e-2016, 2.39e-2016j
185.15565194674824342 - 7.3537289416380488816e-4074j 2.41e-2015, 2.41e-2015j
151.32408548473945346 + 7.3440393593815538115e-4101j 1.92e-2012, 1.92e-2012j
167.04159442539367515 - 2.363458301935648559e-4151j 1.04e-2013, 1.04e-2013j
118.86019348163876075 + 5.5296616680951018084e-4216j 1.85e-2010, 1.85e-2010j
158.93340879300852102 - 1.0035403671856353594e-4286j 5.24e-2013, 5.24e-2013j
107.85909998933850795 + 5.9141229297640619144e-4350j 5.41e-2010, 5.41e-2010j
92.979786606379694761 - 1.3671754242037576203e-4390j 1.09e-2009, 1.09e-2009j
50.978990216839375835 - 9.900721865295215739e-4414j 3.72e-2011, 3.72e-2011j
71.736710573245619716 + 2.4755064838331688065e-4441j 7.53e-2010, 7.53e-2010j
27.5877877796376345 - 3.8854149556168232672e-4478j 4.6e-2015, 4.6e-2015j
64.295835744324135777 - 7.7227543080203926233e-4474j 3.61e-2010, 3.61e-2010j
47.951296410127606464 + 4.2349661872055657681e-4512j 1.64e-2011, 1.64e-2011j
113.24125539117083452 - 6.4315758359578860587e-4561j 3.31e-2010, 3.31e-2010j
75.670351874428793185 + 4.285551397171209232e-4613j 9.66e-2010, 9.66e-2010j
175.73954582233904119 + 2.5337920739650778048e-4659j 1.84e-2014, 1.84e-2014j
42.233480564719475631 - 4.9140325075460796004e-4712j 3.13e-2012, 3.13e-2012j
130.88867351862157661 + 1.5671785074958278464e-4765j 4.45e-2011, 4.45e-2011j
34.458252342209352057 + 1.9797304547447029617e-4817j 1.55e-2013, 1.55e-2013j
88.400822143132943629 + 3.0855380663274228742e-4872j 1.23e-2009, 1.23e-2009j
124.73510703065810596 + 2.9528810498552072907e-4920j 1.04e-2010, 1.04e-2010j
97.741654640735664656 - 3.2241423501254521213e-4946j 9.11e-2010, 9.11e-2010j
32.070372949132885135 + 1.227785638660760993e-4967j 5.33e-2014, 5.33e-2014j
23.484374156976317334 - 4.2341829619432475505e-4970j 3.26e-2016, 3.26e-2016j
67.947078636315459056 - 2.006067806139429502e-4962j 5.45e-2010, 5.45e-2010j
57.388526277175700377 + 2.552778504521130867e-4983j 1.28e-2010, 1.28e-2010j
54.12353561855539708 - 1.3489787583499681905e-5019j 6.93e-2011, 6.93e-2011j
39.537483861177641689 - 2.2908565271593919663e-5092j 1.18e-2012, 1.18e-2012j
60.777871892474755525 + 6.1857803918713399505e-5223j 2.15e-2010, 2.15e-2010j
137.34804180408143211 - 5.0394925367897790612e-5386j 1.89e-2011, 1.89e-2011j
29.780848413769572742 - 1.8079730773244565362e-5569j 1.54e-2014, 1.54e-2014j
144.14621977028035688 - 1.2000444051672211608e-5749j 6.28e-2012, 6.28e-2012j
79.754205908161428016 - 1.6141893733963976423e-5891j 1.04e-2009, 1.04e-2009j
45.037144389960740813 + 3.8539934652101833759e-5997j 7.55e-2012, 7.55e-2012j
102.6972995215439459 - 4.2955396923637732156e-6045j 7.46e-2010, 7.46e-2010j
83.995146275849234978 - 2.309570158469505218e-6075j 1.13e-2009, 1.13e-2009j
25.489472105177605085 - 7.0718675135137221566e-6087j 1.25e-2015, 1.25e-2015j
36.946545544045947008 - 1.6695663389628387193e-6084j 4.33e-2013, 4.33e-2013j

Weights

Weight (ball center) Error (ball radius)
1.7928114443513375115e-102 + 7.8497966345490508319e-4136j 1.46e-400, 4.05e-1916j
1.4943030543459109782e-89 + 3.4302978581310752328e-4129j 1.16e-396, 3.22e-1912j
5.2683203958043678834e-07 + 6.3129445464666244194e-4083j 1.79e-323, 4.97e-1839j
1.2242579336652764575e-07 - 8.1943590141788377162e-4083j 2.61e-326, 7.26e-1842j
7.9985483342090523205e-10 - 1.0310174261293425915e-4083j 1.41e-334, 3.93e-1850j
0.00031819725129569951842 + 3.8534859079972430594e-4082j 5.86e-309, 1.63e-1824j
0.0021390037258190928031 + 7.4967407938633447049e-4082j 4.91e-302, 1.36e-1817j
0.00010833414608260603451 - 2.8726920088313386604e-4082j 1.55e-312, 4.3e-1828j
9.4745309324436811301e-06 - 2.7135906094525038029e-4082j 6.18e-319, 1.72e-1834j
2.6936077837867689244e-95 - 3.8054201601067672904e-4132j 4.05e-401, 1.13e-1916j
0.034198359594807458044 + 3.2105074570040421793e-4081j 5.03e-287, 1.4e-1802j
0.053566854292450426724 - 4.688320259147559206e-4081j 6.67e-282, 1.85e-1797j
0.00086026154511362367577 - 5.3232375757587995649e-4082j 6.01e-307, 1.67e-1822j
2.0572654948369848059e-06 + 8.3304496662492651005e-4083j 3.04e-321, 8.45e-1837j
0.089778302108966598644 - 8.3481059560282475494e-4081j 3.23e-274, 8.98e-1790j
0.1094077785423678553 + 1.1442155732489806764e-4081j 2.86e-271, 7.95e-1787j
0.01023823921111124247 + 1.5315711139254788588e-4081j 9.87e-298, 2.74e-1813j
3.3932068186835188677e-05 + 2.4169878821067023269e-4082j 1.05e-316, 2.92e-1832j
0.11111950451804429472 + 8.1070969747889351779e-4081j 1.39e-271, 3.86e-1787j
0.019620682145302609523 - 2.2096031238320385899e-4081j 4.88e-294, 1.36e-1809j
0.073723048345946943516 + 6.6809335632481851742e-4081j 4.73e-281, 1.31e-1796j
0.14513430871157401434 - 2.3464427072558257466e-4081j 1.42e-271, 3.96e-1787j
2.5214453403469094296e-08 + 5.3391722354133230563e-4083j 2.36e-332, 6.56e-1848j
0.15416096555605729795 + 3.9917536352003909721e-4081j 4.5e-273, 1.25e-1788j
0.0048862703658107997312 - 1.0678541966767246021e-4081j 1.05e-302, 2.93e-1818j
0.051591259307515873864 - 3.1979128458752832259e-4082j 8.88e-275, 2.47e-1790j
4.706600387259358661e-09 + 1.4356523075119183523e-4084j 2.12e-335, 5.9e-1851j
0.13910082913525077658 - 6.1255044483121494095e-4081j 9.52e-277, 2.65e-1792j
1.6575092844147552028e-06 + 4.5301650651807540827e-4083j 8.42e-324, 2.34e-1839j
1.3776600456417325715e-84 - 1.240594343427096149e-4126j 1.16e-401, 3.23e-1917j
3.8068503473914807072e-80 + 2.4329526057904925712e-4124j 9e-401, 2.5e-1916j
1.4095099270991335847e-65 + 8.6588868704922352654e-4117j 3.41e-397, 9.48e-1913j
2.3893592294797443336e-72 + 2.6377738132509091408e-4120j 1.94e-399, 5.39e-1915j
1.3767268473775537206e-51 - 1.7860837408783509142e-4109j 3.93e-393, 1.09e-1908j
7.4257466442475454795e-69 - 1.7113503719817632941e-4118j 1.91e-398, 5.31e-1914j
7.5709888507193760594e-47 - 5.6264606373565495905e-4107j 2.55e-391, 7.1e-1907j
1.9435209300393338636e-40 + 1.4119599782761507979e-4103j 1.26e-388, 3.51e-1904j
2.2358248749576606395e-22 - 7.6841284282531198313e-4094j 6.35e-376, 1.77e-1891j
2.7027341178432824772e-31 - 1.1326104818362352401e-4098j 7.74e-384, 2.15e-1899j
2.2402043600601710808e-12 - 5.2666944795690302387e-4087j 7.99e-362, 2.22e-1877j
4.2757864027161597142e-28 - 6.1237905234286494729e-4097j 1.14e-381, 3.17e-1897j
4.4445782043759317981e-21 + 3.7531220235189313833e-4093j 2.83e-375, 7.87e-1891j
3.6317898102018905128e-49 + 3.3612201083490981914e-4108j 1.01e-393, 2.82e-1909j
5.4912943805434026533e-33 + 1.383438611111587443e-4099j 1.52e-385, 4.24e-1901j
4.2957972346848796675e-76 - 3.029940788416013241e-4122j 1.38e-404, 3.84e-1920j
1.2516040365689787543e-18 + 5.9703195167379831236e-4092j 3.88e-375, 1.08e-1890j
9.0201945618192727582e-57 - 3.4087657045476476617e-4112j 3.26e-398, 9.07e-1914j
2.6421445850804241703e-15 + 8.0852348862323026849e-4090j 2.51e-372, 6.98e-1888j
1.8211076603621311504e-38 - 1.5903931648138689192e-4102j 5.89e-390, 1.64e-1905j
4.0468295126760610354e-54 + 8.3609221321381208491e-4111j 4.81e-397, 1.34e-1912j
1.7285878756638030072e-42 - 1.1455261330421969144e-4104j 5.9e-392, 1.64e-1907j
2.7601186663390031325e-14 - 7.9480864695505602517e-4089j 3.69e-373, 1.03e-1888j
1.2384753239177319997e-10 - 5.768415348090679903e-4085j 1.48e-367, 4.1e-1883j
1.151989590445889578e-29 + 8.6265388086768023722e-4098j 9.16e-386, 2.55e-1901j
3.967032214961010856e-25 - 2.5058489260130306433e-4095j 7.75e-384, 2.15e-1899j
1.0003665300146020366e-23 + 1.4416043598996358272e-4094j 5.95e-383, 1.65e-1898j
1.7831760829961122463e-17 - 1.378305023271228906e-4091j 3.4e-379, 9.46e-1895j
1.3889646931817637166e-26 + 4.0557879016188564009e-4096j 7.31e-385, 2.03e-1900j
1.4843563760681528117e-59 + 1.1939882181006278557e-4113j 1.81e-403, 5.03e-1919j
2.6108508645347382663e-13 + 6.5521948397525530509e-4088j 4.85e-377, 1.35e-1892j
1.7457174861502163674e-62 - 3.5339372998504564362e-4115j 6.61e-405, 1.84e-1920j
9.6029816229908573733e-35 - 1.5682126287693266372e-4100j 6.63e-392, 1.84e-1907j
7.8839273815979621134e-20 - 1.6378580108677029815e-4092j 1.82e-383, 5.06e-1899j
1.2675970292906494106e-44 + 8.4470642481364642763e-4106j 3.11e-397, 8.66e-1913j
1.4356628909674338951e-36 + 1.6447593274916886169e-4101j 4.49e-393, 1.25e-1908j
1.7463371930422048711e-11 + 4.654123813717879829e-4086j 2.36e-379, 6.55e-1895j
2.2857094916796969067e-16 - 3.4723835195552318534e-4091j 2.25e-382, 6.25e-1898j

Download

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