Rule: Q[1, 3, 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)
1.8140052216398370587 - 1.7344614115594381542e-5193j 2.02e-2032, 2.02e-2032j
1.3941001065258449138 + 1.3941938974570807132e-5194j 1.47e-2033, 1.47e-2033j
1 + 6.8974648449644590125e-5196j 7.05e-2035, 7.05e-2035j
2.2432515555021113989 + 2.407423796058613386e-5192j 1.82e-2031, 1.82e-2031j
0.38766885667794714321 + 2.8533312780998537611e-5199j 9.32e-2038, 9.32e-2038j
0.056897625001077184683 + 1.1350701134881464638e-5201j 6.36e-2041, 6.36e-2041j
0.66053416156490857934 + 4.8876024531261388103e-5197j 2.63e-2036, 2.63e-2036j
0.18585323911106078637 + 1.9805474182605538577e-5200j 2.75e-2039, 2.75e-2039j
0.001850203994642906245 - 3.1758794149344980579e-5262j 4.93e-2043, 4.93e-2043j
236.16937730022646204 + 2.0290556549691602784e-5181j 5.67e-2021, 5.67e-2021j
166.09067957380803546 + 1.0681761791152456058e-5170j 7.96e-2014, 7.96e-2014j
194.46933095031594685 - 2.4557122982004400087e-5179j 1.81e-2016, 1.81e-2016j
206.00290398383513311 + 5.6512455755011161693e-5184j 1.32e-2017, 1.32e-2017j
158.00131258860077342 - 6.2101120195583667931e-5197j 3.72e-2013, 3.72e-2013j
14.33445721760110642 + 1.3540863331908680588e-5242j 1.27e-2020, 1.27e-2020j
136.46824469374680008 + 4.2463718878854261049e-5240j 1.32e-2011, 1.32e-2011j
184.16416030846556132 + 2.4735228401880088918e-5303j 1.95e-2015, 1.95e-2015j
143.2495870347057445 - 1.3167403895346165506e-5376j 4.43e-2012, 4.43e-2012j
36.377808914171052958 - 2.588222086773541885e-5435j 1.11e-2013, 1.11e-2013j
7.8232631436879996743 - 6.0137303459575414436e-5467j 7.02e-2025, 7.02e-2025j
21.069730372358274495 + 2.4876099041790982575e-5502j 1.07e-2017, 1.07e-2017j
74.963043212739449692 - 1.7435999952320898651e-5656j 4.85e-2010, 4.85e-2010j
38.958136508120321049 + 2.036541659858530816e-5904j 3.32e-2013, 3.32e-2013j
96.967848560353129068 + 5.1134063628718942334e-6039j 5.53e-2010, 5.53e-2010j
87.65437493765376378 + 3.5663256251162355761e-6140j 6.72e-2010, 6.72e-2010j
10.179617115692389247 + 6.7078299555427307822e-6188j 4.23e-2023, 4.23e-2023j
27.059618020371698029 + 1.1423372237658375351e-6176j 7.86e-2016, 7.86e-2016j
219.37624403432206522 - 3.6751017885983939069e-6184j 4.28e-2019, 4.28e-2019j
83.261985963750947059 - 8.7895963443465468782e-6209j 6.18e-2010, 6.18e-2010j
41.643361616795944221 - 1.2747337620233122545e-6230j 9.14e-2013, 9.14e-2013j
19.254535434558206019 + 5.3458000067118019697e-6259j 2.19e-2018, 2.19e-2018j
53.488710942947522084 - 7.0735246764757301729e-6261j 2.78e-2011, 2.78e-2011j
71.041988288547072486 + 1.0666593897009341306e-6297j 3.54e-2010, 3.54e-2010j
33.899959413704609015 + 1.779967104510313167e-6330j 3.32e-2014, 3.32e-2014j
101.90939157961978886 + 1.4113433201955687589e-6353j 4.44e-2010, 4.44e-2010j
12.865785577489110287 - 2.6089040149674328703e-6388j 1.98e-2021, 1.98e-2021j
6.7674114701871861735 + 2.1024807944251421352e-6392j 8.6e-2026, 8.6e-2026j
56.742100299518290821 - 1.313140378812026787e-6377j 5.92e-2011, 5.92e-2011j
79.034088006084771677 - 2.16924947473552438e-6406j 5.64e-2010, 5.64e-2010j
63.625654805014783875 + 4.8576237508867549952e-6443j 1.61e-2010, 1.61e-2010j
3.369839231310923141 + 1.6083756580577874253e-6496j 1.18e-2029, 1.18e-2029j
31.522343049200972463 + 1.2319204694671276637e-6476j 9.98e-2015, 9.98e-2015j
130.02520617878835942 + 8.0540276651292364291e-6534j 3.48e-2011, 3.48e-2011j
118.02806302440738213 - 1.5127338520193927449e-6607j 1.36e-2010, 1.36e-2010j
4.9001371421013381584 - 9.5520050391962584629e-6671j 9.27e-2028, 9.27e-2028j
24.970771272424497404 - 1.3080793031866474748e-6663j 2.05e-2016, 2.05e-2016j
92.219795487378648316 - 4.7341187223256752527e-6742j 6.35e-2010, 6.35e-2010j
123.887514730993629 - 1.5620652063111918213e-6843j 6.98e-2011, 6.98e-2011j
50.35559159185245999 - 2.2501927311583224647e-6928j 1.31e-2011, 1.31e-2011j
112.42420786546886736 + 5.2179132855402166278e-7012j 2.26e-2010, 2.26e-2010j
150.41004714226090753 - 8.3459426153413420189e-7072j 1.43e-2012, 1.43e-2012j
4.0908896242867985101 - 3.6679986365767539054e-7116j 1.07e-2028, 1.07e-2028j
2.7488673519096523852 + 7.2083718473053367137e-7124j 1.54e-2030, 1.54e-2030j
29.242875007960464542 + 1.9574534097475168215e-7103j 2.89e-2015, 2.89e-2015j
174.76890323797878957 - 1.9997113376713891544e-7138j 1.47e-2014, 1.47e-2014j
8.9605300353960174383 - 6.2006604869348166077e-7177j 5.74e-2024, 5.74e-2024j
15.888090919872913685 - 6.1225011153467651407e-7170j 7.39e-2020, 7.39e-2020j
107.05678518978004703 + 7.642037547302864038e-7169j 3.29e-2010, 3.29e-2010j
11.481122867472712326 - 1.8375145706255106095e-7194j 2.9e-2022, 2.9e-2022j
67.264729336046040823 + 1.9368750089940924712e-7180j 2.6e-2010, 2.6e-2010j
47.339154392272342161 - 9.293922430027003142e-7185j 5.76e-2012, 5.76e-2012j
60.119662854876954374 + 1.2413822598358577643e-7182j 9.88e-2011, 9.88e-2011j
22.974660674483330326 - 8.6485386255800665315e-7192j 4.37e-2017, 4.37e-2017j
44.436094413664006752 + 3.8044106560763263647e-7187j 2.32e-2012, 2.32e-2012j
5.7928782121422054367 - 1.8065452872544675821e-7201j 9.6e-2027, 9.6e-2027j
17.527735708445867153 + 4.9339176239176405512e-7194j 4.11e-2019, 4.11e-2019j

Weights

Weight (ball center) Error (ball radius)
0.068595575748667911957 + 3.1581729078509914592e-5193j 3.64e-264, 1.22e-1775j
0.1025639664664359771 - 1.7560183287092008336e-5193j 4e-257, 1.34e-1768j
0.13606241359599903767 + 1.0323166893338817682e-5193j 1.44e-252, 4.83e-1764j
0.048041750933256375536 - 8.1662797882635555666e-5194j 1.76e-270, 5.92e-1782j
0.16136478104549110789 + 5.0649097278693391703e-5194j 7.2e-253, 2.42e-1764j
0.087104416583349045669 + 2.6700428674025156211e-5194j 3.32e-253, 1.11e-1764j
0.15873342680822829698 - 6.8930128456703130496e-5194j 3.27e-254, 1.1e-1765j
0.13749273595881097049 - 3.7978962576278777298e-5194j 1.99e-253, 6.67e-1765j
0.016909134649344754756 - 1.0499097878711013248e-5194j 1.55e-253, 5.21e-1765j
5.3675609923486893368e-102 - 1.1688857167497437052e-5248j 7.48e-403, 2.51e-1914j
6.1696522530602470177e-72 - 2.7831595824022469432e-5233j 2.16e-393, 7.26e-1905j
3.7887609928775357715e-84 + 1.527776744475511034e-5239j 7.33e-398, 2.46e-1909j
4.2108006503439839938e-89 - 4.4694337312673414636e-5242j 1.48e-399, 4.96e-1911j
1.8815844105785005533e-68 + 1.7194232667420959322e-5231j 6.98e-393, 2.34e-1904j
8.9925879343486765437e-07 + 2.4848828814749290528e-5198j 4.09e-334, 1.37e-1845j
3.56895467777115554e-59 - 1.0393100421751139256e-5226j 2.01e-390, 6.75e-1902j
1.0237978783344114373e-79 - 2.8405524412806051712e-5237j 2.36e-397, 7.93e-1909j
4.2688497923609445708e-62 + 3.2255515663506288652e-5228j 2.28e-391, 7.65e-1903j
4.0199041201804229499e-16 - 6.3747524481155947079e-5204j 1.07e-361, 3.6e-1873j
0.00043894834816039281292 - 2.5450823474877873686e-5196j 3.64e-325, 1.22e-1836j
1.3152423358967716522e-09 + 3.8920561030798121566e-5200j 9.85e-349, 3.31e-1860j
1.110393619345908453e-32 - 6.8839606219655801131e-5213j 2.27e-379, 7.63e-1891j
3.1698682264511485646e-17 + 1.5399661060019857026e-5204j 7.41e-364, 2.49e-1875j
3.7368139561261848456e-42 + 7.1733001855430613116e-5218j 1.68e-385, 5.65e-1897j
3.8301380509602594363e-38 + 9.0702869708569314671e-5216j 2.45e-383, 8.22e-1895j
4.7805994947293566691e-05 - 4.1944483893610627124e-5197j 8.88e-338, 2.98e-1849j
3.7819012752162765159e-12 - 1.1895932543357556886e-5201j 1.65e-358, 5.55e-1870j
7.8010739434723909456e-95 + 5.2726994919810779962e-5245j 3.13e-406, 1.05e-1917j
2.9794443437176107294e-36 - 8.9565336731856567163e-5215j 2.32e-382, 7.79e-1894j
2.2492353029775557029e-18 - 3.5443578366419266858e-5205j 2.23e-368, 7.47e-1880j
7.6917775409810396121e-09 - 1.1556986579115416899e-5199j 1.34e-353, 4.49e-1865j
1.880601400243331641e-23 - 5.9273694901885936416e-5208j 9.11e-375, 3.06e-1886j
5.3964903625001358247e-31 + 5.39838015383912476e-5212j 3.01e-380, 1.01e-1891j
4.5980228908490054247e-15 + 2.5180972007579942312e-5203j 1.42e-365, 4.78e-1877j
2.7793264114687234641e-44 - 5.5438953941108495805e-5219j 9.85e-389, 3.31e-1900j
3.6875431626857601058e-06 - 6.5208240975769221208e-5198j 8.32e-351, 2.79e-1862j
0.0011681724741815525606 + 6.2509225849051922056e-5196j 9.02e-342, 3.03e-1853j
7.545289932894141798e-25 + 1.0435478101159507945e-5208j 1.27e-376, 4.27e-1888j
1.966972901999535316e-34 + 8.1591331891865831021e-5214j 1.85e-382, 6.23e-1894j
8.329268885717104985e-28 + 2.6994751434525907847e-5210j 3.8e-379, 1.28e-1890j
0.023177942049048690618 + 3.5561350075193698099e-5194j 8.79e-338, 2.95e-1849j
4.7538122627985063837e-14 - 9.5060286001065328078e-5203j 3.71e-367, 1.24e-1878j
2.1335574881643907874e-56 + 2.8303144254492051123e-5225j 4.28e-396, 1.44e-1907j
3.1555965730836031667e-51 + 1.3497684861669398757e-5222j 2.03e-394, 6.8e-1906j
0.0063394364498602120455 + 4.0292310330869959216e-5195j 1.5e-348, 5.03e-1860j
2.9203316677307237333e-11 + 3.9551897830671123361e-5201j 2.22e-367, 7.44e-1879j
4.1435734579298390103e-40 - 8.437021849816347016e-5217j 7.69e-388, 2.58e-1899j
9.4207685267870739815e-54 - 6.6227500086968062688e-5224j 1.16e-395, 3.9e-1907j
4.1550594894776548487e-22 + 3.1790395235064102258e-5207j 1.77e-379, 5.95e-1891j
8.1993799170527453603e-49 - 2.4234640812228114646e-5221j 1.13e-393, 3.79e-1905j
3.507411229045892131e-65 - 8.2899313352300612762e-5230j 1.03e-401, 3.45e-1913j
0.01281658704677943036 - 1.1190458332560327357e-5194j 3.8e-357, 1.28e-1868j
0.036125669699491396519 - 1.4901171537454090083e-5193j 4.94e-354, 1.66e-1865j
4.4513353698709531423e-13 + 3.4347296067170982306e-5202j 3.38e-374, 1.13e-1885j
1.1313939169536929392e-75 + 3.360602910081837302e-5235j 6.4e-407, 2.15e-1918j
0.00015124117885925447081 + 1.0374743225703562802e-5196j 1.64e-365, 5.51e-1877j
2.0093097009503170496e-07 - 9.2145555952995615861e-5199j 2.01e-370, 6.74e-1882j
1.6841909765019440397e-46 + 3.8704190232671523225e-5220j 6.02e-393, 2.02e-1904j
1.3863468528299975532e-05 + 1.6705217646986793407e-5197j 1.77e-368, 5.95e-1880j
2.2717166557627306784e-29 - 3.9474641969736644053e-5211j 1.68e-385, 5.63e-1897j
8.1666455164666440064e-21 - 1.6131803065544730866e-5206j 7.12e-382, 2.39e-1893j
2.6733229908827598395e-26 - 1.7310824344741952497e-5209j 1.57e-384, 5.27e-1896j
2.0527049111395269539e-10 - 1.2643399955526224788e-5200j 2.95e-376, 9.89e-1888j
1.4325147490540167817e-19 + 7.7596031490456623688e-5206j 2.53e-381, 8.48e-1893j
0.0028472934171754278473 - 1.5584535696326081651e-5195j 1.83e-371, 6.12e-1883j
4.1104685063785201501e-08 + 3.3162815893408963254e-5199j 5.95e-375, 2e-1886j

Download

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