Rule: Q[1, 4, 92]

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)
334.37600421468430769 + 2.2695202951958229657e-5116j 2.17e-2010, 2.17e-2010j
293.34896302728502453 + 1.0891429309413346704e-5107j 6.85e-2006, 6.85e-2006j
318.88074249592541365 + 7.7562090228565037243e-5114j 1.21e-2008, 1.21e-2008j
262.31779482357580664 - 3.5825049154363811808e-5102j 8.54e-2003, 8.54e-2003j
271.9706291496135118 + 1.8551082396628454735e-5115j 1.02e-2003, 1.02e-2003j
76.270638047919589611 + 3.1289096687616116611e-5127j 1.79e-1997, 1.79e-1997j
29.731985761074942709 + 5.1187593831513968064e-5172j 7.43e-2007, 7.43e-2007j
108.07488374329990142 + 5.9584749027162809117e-5161j 1.47e-1995, 1.47e-1995j
353.7024965811074811 + 5.266505515283491056e-5195j 1.27e-2012, 1.27e-2012j
253.20642280686275756 - 7.2190413514966052888e-5233j 6.07e-2002, 6.07e-2002j
64.334737523111929921 - 2.2767169347345004695e-5287j 7.3e-1999, 7.3e-1999j
37.50251629450195473 + 1.1171827232784658071e-5330j 2.42e-2004, 2.42e-2004j
163.91003957172476614 + 7.5596132759014721266e-5390j 5.08e-1996, 5.08e-1996j
143.25099328327878511 + 5.8621029955037512216e-5452j 1.96e-1995, 1.96e-1995j
305.43443749066779295 - 1.0244376446457708491e-5480j 3.81e-2007, 3.81e-2007j
8.4466517811210281678 + 2.7304248325502517527e-5503j 2.86e-2019, 2.86e-2019j
12.291077805409495598 + 1.0154329122388334668e-5499j 7.13e-2016, 7.13e-2016j
79.453780282730175105 + 3.2974050097382975103e-5478j 3.66e-1997, 3.66e-1997j
53.604328719629029049 + 1.4547942023593322227e-5495j 1.48e-2000, 1.48e-2000j
206.67068064501353141 - 1.3965069985357594976e-5489j 2.64e-1998, 2.64e-1998j
13.405334716538062419 - 1.3395496793637694805e-5540j 4.84e-2015, 4.84e-2015j
11.242378555161742866 + 4.2996324848822896494e-5542j 1.1e-2016, 1.1e-2016j
120.41049018336919079 + 8.8566610262359966009e-5520j 2.52e-1995, 2.52e-1995j
6.0165843328122930598 + 1.116406381457040342e-5581j 2.6e-2022, 2.6e-2022j
58.824076695840359729 + 4.4154779163280108048e-5554j 1.2e-1999, 1.2e-1999j
100.36319404917048836 - 6.3298327978396534549e-5577j 8.49e-1996, 8.49e-1996j
187.15278827047089562 - 5.5863997277167631682e-5650j 4.11e-1997, 4.11e-1997j
21.404067690452799986 - 4.1681059453892750821e-5727j 2.15e-2010, 2.15e-2010j
67.202293318011064697 + 2.7155692719916215328e-5725j 1.81e-1998, 1.81e-1998j
31.580715078011907472 + 1.9634538026357455485e-5770j 3.42e-2006, 3.42e-2006j
124.7400837690575435 + 2.5378697999864322788e-5809j 2.69e-1995, 2.69e-1995j
39.603836586173998958 - 1.2539948492068112066e-5871j 9.76e-2004, 9.76e-2004j
18.494493018462859549 + 1.3650287554718523608e-5881j 7.21e-2012, 7.21e-2012j
56.17843208149705282 - 5.7189361905710372014e-5865j 4.2e-2000, 4.2e-2000j
199.93898947860144546 - 3.202362314902490231e-5904j 7.25e-1998, 7.25e-1998j
5.2844912448592332343 - 2.1462856860008807927e-5993j 2.5e-2023, 2.5e-2023j
89.508480377270990834 - 4.5464640510579624073e-5965j 2.18e-1996, 2.18e-1996j
282.26648530753948608 + 7.5889938007958195774e-5999j 9.45e-2005, 9.45e-2005j
153.28874161599731661 - 3.23625605985677261e-6054j 1.16e-1995, 1.16e-1995j
175.1737876627094761 + 1.6400592967296517575e-6105j 1.61e-1996, 1.61e-1996j
27.944893741561270698 - 6.2402209209847306345e-6135j 1.55e-2007, 1.55e-2007j
22.948833933502370182 + 8.5124882983402396282e-6137j 1.22e-2009, 1.22e-2009j
61.542433355973209084 - 5.5638487457893368681e-6126j 2.96e-1999, 2.96e-1999j
9.3291180490733064372 - 6.3836487257883485826e-6146j 2.11e-2018, 2.11e-2018j
51.100656903498980508 - 4.1096701279212488811e-6128j 4.56e-2001, 4.56e-2001j
104.16980035191923786 + 2.1585967609918988882e-6123j 1.2e-1995, 1.2e-1995j
93.034945822105070414 + 1.7874808250189575488e-6129j 3.5e-1996, 3.5e-1996j
73.168746644263575827 - 1.9763703542307927595e-6145j 8.6e-1998, 8.6e-1998j
1 + 1.7734245922032789164e-6192j 4.45e-2033, 4.45e-2033j
193.43829843412327587 - 1.4913769441310215576e-6155j 1.92e-1997, 1.92e-1997j
112.08128934014547238 + 7.9714076644291296804e-6222j 1.91e-1995, 1.91e-1995j
41.770060695106487782 + 1.9957666688668491784e-6279j 3.59e-2003, 3.59e-2003j
15.826239886641738547 + 2.5262208555939583904e-6323j 1.97e-2013, 1.97e-2013j
19.91927718121048399 - 2.3164737870760705036e-6316j 3.7e-2011, 3.7e-2011j
17.129965184944930593 - 1.7584750101787327668e-6321j 1.13e-2012, 1.13e-2012j
228.45089509178054218 - 6.5379356806997261013e-6337j 7.28e-2000, 7.28e-2000j
138.43545786416615214 - 2.3312996734204795899e-6429j 2.31e-1995, 2.31e-1995j
70.146477953177152356 + 4.3799222495924475621e-6473j 4.13e-1998, 4.13e-1998j
10.257382160766360565 - 2.053010641070827041e-6528j 1.78e-2017, 1.78e-2017j
1.6496517805970149606 + 3.3825895334815886559e-6540j 1.74e-2030, 1.74e-2030j
158.5230438511370379 - 3.5065406123362702184e-6504j 8.01e-1996, 8.01e-1996j
213.65166758908769928 + 4.6324653459511447406e-6540j 8.55e-1999, 8.55e-1999j
82.719897600294260752 - 4.5796164291029381964e-6554j 6.82e-1997, 6.82e-1997j
35.465349931203581438 - 6.0047296113327374742e-6589j 6.23e-2005, 6.23e-2005j
3.9606042071370736716 - 2.8574198132642869401e-6610j 1.72e-2025, 1.72e-2025j
4.5979728630500204374 - 1.6014583217157773732e-6608j 2.05e-2024, 2.05e-2024j
96.652405681458720891 + 4.6288941188943686653e-6579j 5.36e-1996, 5.36e-1996j
181.06866088266248143 - 2.3896163821142094619e-6636j 8.59e-1997, 8.59e-1997j
129.18464728000765018 - 1.6921809538213596326e-6696j 2.87e-1995, 2.87e-1995j
6.7902215031945192171 + 3.7048996394760609045e-6776j 2.9e-2021, 2.9e-2021j
0.72196585820194206812 + 9.102983085653165571e-6791j 1.83e-2034, 1.83e-2034j
46.300455732653759179 + 2.421464008309112547e-6751j 4.91e-2002, 4.91e-2002j
236.32462306484052676 - 1.5771214447037742392e-6756j 1.61e-2000, 1.61e-2000j
148.20016640357975741 - 6.3348043717238007939e-6800j 1.54e-1995, 1.54e-1995j
116.19206659817080867 - 3.5995583711511147426e-6822j 2.3e-1995, 2.3e-1995j
0.062753379659813789868 - 3.7980563275422704522e-6892j 5.09e-2040, 5.09e-2040j
3.3761674306651932729 - 2.6216814898391251522e-6879j 1.56e-2026, 1.56e-2026j
244.56127829392270579 - 2.9525194672458996388e-6847j 3.3e-2001, 3.3e-2001j
133.74828821997448354 - 3.5105026054878121835e-6894j 2.63e-1995, 2.63e-1995j
48.666364820068955035 + 1.2103135316841242329e-6952j 1.53e-2001, 1.53e-2001j
24.553707786538941699 - 4.5250863704598063498e-6972j 6.2e-2009, 6.2e-2009j
0.48726973549270874252 + 6.563900549938319666e-6999j 7.67e-2036, 7.67e-2036j
14.584246147584025461 + 3.3788526629473408131e-6978j 2.89e-2014, 2.89e-2014j
220.90332180987621329 - 5.3867563675424071531e-6958j 2.65e-1999, 2.65e-1999j
7.6011349062722800267 - 1.4222550712275874569e-7037j 2.87e-2020, 2.87e-2020j
1.3139937123083044615 + 4.5601844308662828252e-7049j 9.18e-2032, 9.18e-2032j
0.29892053287437948505 - 9.7558897436869930523e-7055j 2.87e-2037, 2.87e-2037j
2.3902045572501654536 + 4.1329604334678034142e-7046j 1.8e-2028, 1.8e-2028j
26.218944077283985961 - 5.405818856468277912e-7026j 3.14e-2008, 3.14e-2008j
44.001985536291720989 - 1.9816456693909730709e-7013j 1.33e-2002, 1.33e-2002j
0.011704210699467513387 - 1.1643766588200549667e-7068j 1.23e-2041, 1.23e-2041j
2.8500082985710811872 + 8.0135737620045118499e-7054j 1.72e-2027, 1.72e-2027j
0.15769548012154955374 - 3.2180067451458237677e-7065j 1.3e-2038, 1.3e-2038j
1.9990968979678377934 - 2.5681280669061385603e-7056j 1.83e-2029, 1.83e-2029j
86.070817785318953622 - 1.9941295727825702404e-7021j 1.29e-1996, 1.29e-1996j
169.45743384946060687 - 5.4155841874384663346e-7077j 2.95e-1996, 2.95e-1996j
33.491634585631923819 - 4.9344558287625768847e-7113j 1.47e-2005, 1.47e-2005j

Weights

Weight (ball center) Error (ball radius)
1.0256468356141790265e-144 - 2.7664492906691669202e-5219j 1.78e-372, 3.14e-1876j
4.5956696695656232375e-127 + 2.8739634101823509949e-5210j 1.79e-367, 3.14e-1871j
4.6504876763411623812e-138 + 6.9019138646464416706e-5216j 9.39e-371, 1.65e-1874j
1.1180578728404370138e-113 - 2.0776910943301006931e-5203j 7.18e-364, 1.26e-1867j
7.6327409633736748814e-118 + 1.5159434814390312063e-5205j 3.44e-365, 6.05e-1869j
2.3622279180573814801e-33 - 3.904405296216328544e-5160j 8.79e-319, 1.55e-1822j
2.2238949794165339839e-13 + 1.315981480824992245e-5150j 1.14e-282, 2.01e-1786j
4.5798233689591205628e-47 - 1.5408202658138989906e-5168j 1.92e-332, 3.39e-1836j
5.5627168856149438477e-153 + 1.690914144813260797e-5223j 2.51e-377, 4.43e-1881j
9.5861446916699405187e-110 + 2.1744212541195116664e-5201j 3.29e-363, 5.8e-1867j
3.2472813695531433697e-28 - 3.3216535905777319826e-5158j 2.86e-314, 5.04e-1818j
1.0681943260301655587e-16 + 1.9833214791647056963e-5152j 7.22e-295, 1.27e-1798j
3.5680546780486708704e-71 - 2.070217626853488008e-5181j 1.39e-349, 2.45e-1853j
2.9883519722821482441e-62 - 1.0365519525909745848e-5176j 1.04e-344, 1.83e-1848j
2.8505104372462144195e-132 - 6.244902660539145151e-5213j 1.18e-370, 2.08e-1874j
0.00018521911080895446138 + 6.5217632897733712732e-5145j 4.33e-247, 7.62e-1751j
4.9667828930708392287e-06 + 5.2842522713223344306e-5146j 3.98e-260, 7.01e-1764j
1.0048510348918565894e-34 - 4.3857887693052113946e-5161j 2.42e-323, 4.25e-1827j
1.3321358242652069104e-23 - 5.299489845897066656e-5156j 1.16e-310, 2.05e-1814j
1.202120840265971715e-89 + 5.008586692050797696e-5191j 1.42e-358, 2.5e-1862j
1.7283793978933438774e-06 - 2.4466827821562166126e-5146j 1.81e-265, 3.19e-1769j
1.3318714772870033808e-05 - 1.0944425507238343101e-5145j 1.1e-259, 1.93e-1763j
2.1735118896976872692e-52 + 1.9273967063032891954e-5171j 2.61e-339, 4.59e-1843j
0.0018372253710621515253 - 2.387571281954243313e-5144j 4.13e-243, 7.26e-1747j
7.6112241764926898688e-26 - 4.2352360381530385985e-5157j 1.35e-314, 2.38e-1818j
9.7231385962269627795e-44 - 1.0956925668237997236e-5166j 3.97e-333, 6.99e-1837j
3.2490226819813593964e-81 - 1.1875299268622201576e-5186j 5.84e-356, 1.03e-1859j
7.6679229112598116676e-10 - 1.5235428235487430265e-5148j 5.14e-286, 9.05e-1790j
1.8952032916121657987e-29 + 9.6033549633802317674e-5159j 2.71e-319, 4.76e-1823j
3.6204675201139588404e-14 - 4.7720065174063648034e-5151j 1.2e-297, 2.12e-1801j
2.9388690200822226709e-54 - 1.8955387532863382826e-5172j 4.77e-341, 8.39e-1845j
1.3470822927012485556e-17 - 6.5564940746938426743e-5153j 8.72e-305, 1.53e-1808j
1.295479659743917122e-08 - 8.8959293849322200584e-5148j 4.94e-284, 8.69e-1788j
1.0437701623911831189e-24 + 1.5077680860866688604e-5156j 3.96e-314, 6.96e-1818j
9.727980086597268069e-87 - 1.6081371296263852988e-5189j 5.93e-359, 1.04e-1862j
0.003599061849557802446 + 3.5875827774737225953e-5144j 5.3e-255, 9.33e-1759j
4.6639457365806644996e-39 + 5.5684058899174595708e-5164j 8.44e-331, 1.48e-1834j
2.7606003283425289887e-122 - 8.0289491817299543628e-5208j 1.17e-371, 2.05e-1875j
1.3810938599947483832e-66 - 5.3244552543168900222e-5179j 6.39e-350, 1.12e-1853j
4.8608556006973141495e-76 - 5.9021022274005373546e-5184j 1.37e-354, 2.41e-1858j
1.283278862765612696e-12 - 3.5494651339483149235e-5150j 7.66e-301, 1.35e-1804j
1.7008648580199284761e-10 + 6.1334110247474000639e-5149j 2.1e-296, 3.69e-1800j
5.1594230560738067717e-27 + 1.1825719551876511131e-5157j 4.03e-320, 7.09e-1824j
8.022916330887982571e-05 - 3.8736823484114844166e-5145j 1.49e-277, 2.62e-1781j
1.583997843942630716e-22 + 1.8313377262406294995e-5155j 2.43e-316, 4.27e-1820j
2.2166568878392561009e-45 + 1.3205927764616216661e-5167j 1.75e-337, 3.07e-1841j
1.4070110463377230015e-40 - 7.0344976570672820767e-5165j 2.52e-334, 4.44e-1838j
5.1191307705239425616e-32 + 1.2132288821895856955e-5159j 6.49e-327, 1.14e-1830j
0.10954841741074793576 - 3.2129932495199020322e-5143j 3.69e-273, 6.5e-1777j
6.2568989696495988278e-84 + 4.6075158494196901776e-5188j 1.44e-360, 2.53e-1864j
8.5513273337637825083e-49 + 1.7320192981951671776e-5169j 1.82e-340, 3.2e-1844j
1.5911314461193086431e-18 + 2.1170887196501867223e-5153j 1.94e-315, 3.41e-1819j
1.704499340085281834e-07 - 4.8446013658457871987e-5147j 4.74e-297, 8.34e-1801j
3.2506758420901553441e-09 + 3.7145421985133472418e-5148j 3.66e-301, 6.43e-1805j
4.8505031101089765039e-08 + 2.0939452966830678798e-5147j 1.58e-298, 2.79e-1802j
4.696958477616284551e-99 - 6.9073641270439121457e-5196j 7.82e-370, 1.38e-1873j
3.5890950378673543993e-60 + 1.3142088201453609744e-5175j 2.59e-350, 4.57e-1854j
1.0242869929649471566e-30 - 3.0116914066396961847e-5159j 1.27e-328, 2.23e-1832j
3.3517984266357303184e-05 + 2.1361991191776528971e-5145j 3.41e-295, 6.01e-1799j
0.065582839080175098208 - 4.3482914763037405985e-5143j 3.58e-273, 6.3e-1777j
7.574686992793781987e-69 + 3.4440724211947035353e-5180j 7.4e-355, 1.3e-1858j
1.1595245208978266919e-92 - 1.3791536824836425178e-5192j 6.08e-367, 1.07e-1870j
3.9336648487458582692e-36 + 3.9284229584210202021e-5162j 1.45e-334, 2.56e-1838j
7.9392516126186929744e-16 - 5.8602459653135165022e-5152j 9.51e-319, 1.67e-1822j
0.011652067967551987724 + 8.3094080030588964522e-5144j 1.61e-291, 2.83e-1795j
0.0066730914955331079615 - 5.4249137427739028156e-5144j 9.33e-293, 1.64e-1796j
3.8753964220024316595e-42 + 8.8558099359644116593e-5166j 1.07e-338, 1.88e-1842j
1.3808062412507448368e-78 + 2.7728181597495784857e-5185j 2.69e-360, 4.73e-1864j
3.5429100536895145591e-56 + 1.7719340653305577316e-5173j 5.15e-349, 9.07e-1853j
0.00089184629735024504704 + 1.5849294863337166372e-5144j 2.18e-302, 3.83e-1806j
0.12491055717188756583 + 2.6625404981456637188e-5143j 8.39e-289, 1.48e-1792j
1.818456521707915149e-20 + 2.0586367834566402595e-5154j 1.15e-326, 2.02e-1830j
1.8673723162465616003e-102 + 1.2217320068242790025e-5197j 3.21e-373, 5.65e-1877j
2.1777340878895803931e-64 + 7.6784223726093270632e-5178j 1.03e-353, 1.82e-1857j
1.4386030595037796324e-50 - 1.8683435508149638801e-5170j 3.55e-346, 6.26e-1850j
0.068074544193818180393 + 7.0796170694669735873e-5144j 6.84e-299, 1.2e-1802j
0.019017108431510482998 - 1.2950165615624257784e-5143j 7.74e-306, 1.36e-1809j
5.1801107783367235716e-106 - 1.8042334116395273238e-5199j 3.65e-375, 6.43e-1879j
3.7925709528322947581e-58 - 1.5698162508898953397e-5174j 1.27e-350, 2.24e-1854j
1.7565741763099305671e-21 - 6.2057574298493212309e-5155j 4.85e-331, 8.54e-1835j
3.5479621835704563227e-11 - 2.4215436207038169576e-5149j 2.54e-324, 4.47e-1828j
0.13010841379727063219 - 2.182528567040871972e-5143j 2.97e-308, 5.22e-1812j
5.6128379521720779037e-07 + 1.1005488604776672432e-5146j 1.75e-319, 3.07e-1823j
8.5476435848822016205e-96 + 3.3214066150999927074e-5194j 1.42e-370, 2.51e-1874j
0.00041408654340557256543 - 1.035237232167438915e-5144j 2.13e-316, 3.75e-1820j
0.08807003117363261365 + 3.8519265648265957291e-5143j 6.59e-312, 1.16e-1815j
0.12220235856828122863 + 1.7187611529579052968e-5143j 5.17e-311, 9.1e-1815j
0.038850624179401732054 - 3.1222308206848446324e-5143j 2.5e-314, 4.4e-1818j
6.9592446383572335107e-12 + 9.368796602105376117e-5150j 2.98e-325, 5.25e-1829j
1.758971503678760551e-19 - 6.6781516793037742225e-5154j 1.18e-330, 2.07e-1834j
0.029826630262845642568 - 2.2019693094001424408e-5144j 1.39e-314, 2.45e-1818j
0.028603457712350213216 + 2.0432189575370481048e-5143j 4.05e-316, 7.12e-1820j
0.10062283873459914102 - 1.2300369943980746232e-5143j 2.05e-314, 3.6e-1818j
0.049195022198471907294 + 4.1229671502747823353e-5143j 1.61e-315, 2.83e-1819j
1.414572773727254007e-37 - 4.5032454031059462614e-5163j 3.78e-341, 6.66e-1845j
1.4325455431176528646e-73 + 1.1516360971858765398e-5182j 4.7e-360, 8.27e-1864j
5.5343243037219863971e-15 + 1.6916534487521977307e-5151j 1.57e-328, 2.75e-1832j

Download

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