Rule: Q[2, 91]

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)
324.69113256813414398 - 8.2918937917340549941e-5979j 3.78e-2011, 3.78e-2011j
244.40635917318100246 + 1.2517548926334437648e-5963j 6.87e-2003, 6.87e-2003j
296.04344724583081233 + 8.1688470789425562193e-5978j 6.03e-2008, 6.03e-2008j
343.83243894029377784 + 4.3477834591009218611e-5985j 2.32e-2013, 2.32e-2013j
262.94815472168451075 + 8.2172229409349431033e-5969j 1.35e-2004, 1.35e-2004j
185.44385259172901082 - 6.4584269531705359739e-5971j 1.6e-1998, 1.6e-1998j
33.311363586267214276 - 8.5134486323332201864e-5999j 1.7e-2006, 1.7e-2006j
219.96467643643978227 + 2.0799912435996783612e-5988j 7.37e-2001, 7.37e-2001j
86.970666824397682552 - 4.0716224937505780414e-5999j 9.74e-1998, 9.74e-1998j
309.35059235427995411 - 3.9062382173393732015e-6025j 2.15e-2009, 2.15e-2009j
15.371303656388614398 - 1.0356375889342097369e-6029j 1.08e-2014, 1.08e-2014j
29.494484844764923557 - 6.7056950555781101796e-6023j 8.55e-2008, 8.55e-2008j
70.664667570853902856 + 2.4523536770508644496e-6012j 3.67e-1999, 3.67e-1999j
19.537306301290598839 - 9.7819493546088537795e-6034j 3.25e-2012, 3.25e-2012j
21.044712520347588028 + 7.9523481169530717579e-6033j 2.1e-2011, 2.1e-2011j
161.84025816181433188 - 1.0429398389187107555e-6017j 2.17e-1997, 2.17e-1997j
131.37055882584785019 + 6.7971906610419394708e-6032j 1.21e-1996, 1.21e-1996j
22.612250709114528646 - 1.4171712025490750928e-6063j 1.17e-2010, 1.17e-2010j
64.725305191191152746 - 7.9976013179696732488e-6053j 6.49e-2000, 6.49e-2000j
53.775701016520176954 - 1.6949781019110145838e-6054j 1.45e-2001, 1.45e-2001j
105.56207432131119838 - 6.8998455160344547496e-6049j 7.08e-1997, 7.08e-1997j
25.929805810895594959 - 9.761121660336278972e-6085j 3.29e-2009, 3.29e-2009j
101.64651605878062548 + 2.0199040547076007926e-6071j 5.21e-1997, 5.21e-1997j
284.08723165745161486 + 2.8898629271735998683e-6093j 1.05e-2006, 1.05e-2006j
27.680950990405932083 - 6.5181947477012263374e-6097j 1.72e-2008, 1.72e-2008j
11.731775478642022173 - 2.0687642263642195815e-6106j 2.36e-2017, 2.36e-2017j
212.51798395184888526 - 4.8438295221469962227e-6085j 2.77e-2000, 2.77e-2000j
18.089555609051687797 - 8.3082143718031362853e-6113j 5.19e-2013, 5.19e-2013j
273.12701460094828304 + 1.752788801662380686e-6096j 1.3e-2005, 1.3e-2005j
83.535511946502302802 - 8.6601418335096216301e-6116j 5.82e-1998, 5.82e-1998j
113.70961350985382331 - 7.7593561988589420027e-6170j 1.13e-1996, 1.13e-1996j
3.4142135623730950488 + 2.3862983923111639494e-6242j 6.64e-2027, 6.64e-2027j
12.886952187896202123 + 9.2310099879370296588e-6233j 1.96e-2016, 1.96e-2016j
41.725008366398000444 - 6.5636160624795697169e-6213j 4.27e-2004, 4.27e-2004j
61.873899339215538696 - 3.1855613003263272527e-6243j 2.72e-2000, 2.72e-2000j
109.58202438954901232 - 6.7414494809152443683e-6350j 9.29e-1997, 9.29e-1997j
156.38577798478090553 - 2.8877997729762169297e-6455j 3.38e-1997, 3.38e-1997j
1.5434872252877653135 + 2.4555906398665606187e-6532j 1.37e-2031, 1.37e-2031j
48.744147752445808589 + 1.2108138869455956401e-6497j 1.74e-2002, 1.74e-2002j
145.94910621548448881 + 4.8154025058869112338e-6501j 7.6e-1997, 7.6e-1997j
198.4829764963399544 - 2.003827101274784627e-6520j 2.53e-1999, 2.53e-1999j
31.371059465870149148 + 2.8765730946436679156e-6545j 4.27e-2007, 4.27e-2007j
253.40819040462512433 - 5.8382174535867625719e-6535j 1.16e-2003, 1.16e-2003j
227.73585483938412635 + 9.6585116321300392521e-6536j 1.86e-2001, 1.86e-2001j
9.5946554519362521423 + 4.7788760703847381523e-6603j 3.58e-2019, 3.58e-2019j
10.6343595633983883 - 5.4569989758790595798e-6603j 3.06e-2018, 3.06e-2018j
191.84838977781217387 + 2.638377388077225283e-6580j 6.6e-1999, 6.6e-1999j
6.0191411707514292479 + 1.1712353489422906719e-6688j 5.74e-2023, 5.74e-2023j
2.8935060407180993245 + 1.0287767494941088678e-6692j 5.47e-2028, 5.47e-2028j
205.36577100791919549 + 1.3431334651261763704e-6661j 8.92e-2000, 8.92e-2000j
24.240432870930038649 - 2.9399490050978817239e-6737j 5.97e-2010, 5.97e-2010j
167.46321299313310925 + 4.2347472263080413065e-6724j 1.29e-1997, 1.29e-1997j
67.655053280754271976 - 3.2788132002499089865e-6747j 1.54e-1999, 1.54e-1999j
73.755760607782874938 - 1.94677639312778486e-6769j 7.64e-1999, 7.64e-1999j
37.386106163828962146 + 2.8553117980341461211e-6811j 3.01e-2005, 3.01e-2005j
16.70102116408371281 + 5.9441045460566288002e-6823j 8.07e-2014, 8.07e-2014j
140.95235478237480658 + 1.0189723268115162103e-6804j 9.39e-1997, 9.39e-1997j
179.25366433597596055 + 2.4673655385321123702e-6854j 3.51e-1998, 3.51e-1998j
59.099394288768224164 - 1.1007122950471774572e-6895j 1.02e-2000, 1.02e-2000j
0.36590647325299858674 + 9.7001261927765041151e-7003j 4.34e-2037, 4.34e-2037j
173.26413034657957537 + 1.1243282706545562195e-6961j 7.1e-1998, 7.1e-1998j
90.496953041599984951 - 1.1849960142787688026e-7056j 1.64e-1997, 1.64e-1997j
51.223995560384305053 - 9.7299699017541315677e-7140j 5.24e-2002, 5.24e-2002j
136.09474557075027164 - 4.536894349946801111e-7229j 1.17e-1996, 1.17e-1996j
4.5954357458426939429 + 1.9358373732228970778e-7325j 6.54e-2025, 6.54e-2025j
1.9552937680525841165 + 3.1845585822446364659e-7331j 2.3e-2030, 2.3e-2030j
39.522117661414107459 + 3.8821484125045992596e-7297j 1.16e-2004, 1.16e-2004j
76.930040209351588689 - 1.3728955187137667611e-7388j 1.65e-1998, 1.65e-1998j
151.09127619195407469 + 2.6580266543085439014e-7546j 5.07e-1997, 5.07e-1997j
6.8241142165104218123 + 4.9327607558492461056e-7640j 5.5e-2022, 5.5e-2022j
0.5857864376269049512 - 4.1719426641083615645e-7673j 1.15e-2035, 1.15e-2035j
14.100048320935160048 - 2.2787403865171438487e-7635j 1.51e-2015, 1.51e-2015j
8.6127691859032486488 - 2.1918696977981610698e-7642j 4.38e-2020, 4.38e-2020j
7.6890334093837043884 + 9.6818867343749212012e-7644j 4.9e-2021, 4.9e-2021j
80.189316865677127174 + 1.4656733746847524775e-7700j 3.32e-1998, 3.32e-1998j
0.19728356327190158997 - 2.5762134836171618555e-7852j 1.58e-2038, 1.58e-2038j
126.7745637935139087 + 4.1320935109125589997e-7809j 1.34e-1996, 1.34e-1996j
35.316123824015147558 + 8.694397851508681417e-7873j 7.5e-2006, 7.5e-2006j
117.94833624757316687 + 2.5598067365012352624e-7872j 1.28e-1996, 1.28e-1996j
97.832326042570584822 + 1.5334831678945322476e-7907j 3.73e-1997, 3.73e-1997j
5.2757367111702050261 - 5.9126439002173430926e-7952j 6.2e-2024, 6.2e-2024j
1.1761021832270065938 - 3.6412697155566140124e-7960j 6.47e-2033, 6.47e-2033j
43.995673465848397887 + 5.2873176178058445643e-7931j 1.48e-2003, 1.48e-2003j
235.86801150114345815 - 3.0606587872251521105e-7924j 3.74e-2002, 3.74e-2002j
0.015250944921622228546 + 4.8995988358518159107e-7979j 9.48e-2042, 9.48e-2042j
46.335055655747661044 - 1.5585111170026714522e-7940j 5.15e-2003, 5.15e-2003j
0.85623382974717044969 + 4.3379306863536333333e-7972j 2.75e-2034, 2.75e-2034j
2.406947019662028999 + 2.1761279443943517009e-7967j 3.65e-2029, 3.65e-2029j
56.400425636086310613 - 4.1552366647479528395e-7937j 4.19e-2001, 4.19e-2001j
3.9773411844348711648 + 2.7805354278169727518e-7963j 7.5e-2026, 7.5e-2026j
122.30196153879868313 - 6.0903960397518199686e-7933j 1.33e-1996, 1.33e-1996j
0.08032783177027119325 + 7.6232332806714552823e-7999j 5.43e-2040, 5.43e-2040j
94.116683670280474648 - 3.0506844016110877983e-7954j 2.63e-1997, 2.63e-1997j

Weights

Weight (ball center) Error (ball radius)
1.632326994380922145e-140 - 8.9546540546297808568e-6079j 2.62e-367, 5.17e-1870j
6.2825639091241662554e-106 + 2.8041059755091463164e-6061j 1.31e-356, 2.59e-1859j
3.3789488142850381116e-128 - 1.4978213645036808898e-6072j 4.53e-364, 8.94e-1867j
1.0658830657079048794e-148 + 6.5945942122378833967e-6083j 2.03e-370, 4.01e-1873j
6.2525162749439451952e-114 + 2.4768991959508872862e-6065j 6.18e-360, 1.22e-1862j
1.8270429687163810574e-80 + 2.425369580328921259e-6048j 9.64e-349, 1.91e-1851j
6.730624031767969325e-15 + 2.9690557618054359154e-6013j 3.56e-287, 7.04e-1790j
2.2468069822714238889e-95 - 6.3307348922827112103e-6056j 2.61e-354, 5.16e-1857j
5.898504102818827832e-38 - 1.8365902456818174933e-6026j 4.03e-323, 7.97e-1826j
6.3379433016485914901e-134 + 1.9091197522108469664e-6075j 4.06e-366, 8.01e-1869j
2.7441955804628946467e-07 - 3.408581195052096818e-6010j 3.9e-262, 7.71e-1765j
2.8621397155330541468e-13 + 1.0546421739519283755e-6012j 1e-284, 1.98e-1787j
6.2378602440417965493e-31 + 9.60328032538061991e-6023j 3.69e-316, 7.29e-1819j
4.8370856958709328209e-09 + 4.9663620579993749066e-6011j 3.68e-271, 7.26e-1774j
1.1147602477597987595e-09 - 2.5453209284160984569e-6011j 1.02e-273, 2.01e-1776j
2.8639209501076424274e-70 + 3.848632152779576899e-6043j 9.31e-346, 1.84e-1848j
4.1191524761299495661e-57 + 2.1332575619589672509e-6036j 4.97e-339, 9.81e-1842j
2.416234494296909949e-10 + 1.2951907195709247571e-6011j 5.82e-278, 1.15e-1780j
2.2444221887020384324e-28 + 2.2731228683768178021e-6021j 9.93e-315, 1.96e-1817j
1.1441337481651146952e-23 + 8.7357621050796828665e-6019j 4.67e-309, 9.23e-1812j
5.6684100444425671736e-46 + 1.205537191844696175e-6030j 3.01e-332, 5.95e-1835j
9.4275115952078906747e-12 + 3.3934933008040000898e-6012j 8.65e-286, 1.71e-1788j
2.7705096697411157492e-44 - 9.0920437365560343138e-6030j 6.38e-331, 1.26e-1833j
4.7854440791582474461e-123 + 6.0312826305349205961e-6070j 3.74e-367, 7.38e-1870j
1.6954321535877523274e-12 - 1.810297024626907096e-6012j 1.17e-289, 2.32e-1792j
9.0489915791226302341e-06 + 2.0117909754890969606e-6009j 2.84e-268, 5.6e-1771j
3.6951492591939695925e-92 + 2.7218118503104218949e-6054j 1.52e-357, 3.01e-1860j
1.974714316621180321e-08 - 9.5793378433145542902e-6011j 3.06e-279, 6.04e-1782j
2.5429252258504012558e-118 - 1.4834250832304290737e-6067j 9.98e-366, 1.97e-1868j
1.7833203114836046535e-36 + 1.1026180488479602477e-6025j 8.8e-327, 1.74e-1829j
1.7297511221556004423e-49 + 1.8193495340971939503e-6032j 3.34e-337, 6.6e-1840j
0.017761085501573246092 + 1.7659668745033864889e-6007j 1.06e-244, 2.1e-1747j
2.9967952219779412715e-06 - 1.1332202445782455064e-6009j 1.24e-275, 2.46e-1778j
1.692981649301743338e-18 - 9.4508046830818174475e-6016j 4.88e-308, 9.64e-1811j
3.7812354704560056446e-27 - 1.0520581866317029617e-6020j 9.13e-319, 1.8e-1821j
1.0448841605170279048e-47 - 1.5200317759160751216e-6031j 1.04e-335, 2.05e-1838j
6.4975336682146420053e-68 - 6.1626840047262326882e-6042j 1.89e-349, 3.73e-1852j
0.083367627079526210222 + 1.71114780179628407e-6007j 3.12e-236, 6.17e-1739j
1.6551544635440083415e-21 + 1.4730064433155408048e-6017j 1.3e-314, 2.56e-1817j
2.0891824627119585153e-63 - 1.2517059099569754371e-6039j 1.91e-347, 3.78e-1850j
4.2617867900237547552e-86 + 3.2846111392132614371e-6051j 2.86e-358, 5.65e-1861j
4.5328726628914040228e-14 - 7.9487621776792221569e-6013j 1.81e-304, 3.58e-1807j
8.1785287185435662702e-110 - 3.0121123691609984641e-6063j 5.9e-367, 1.17e-1869j
9.9007016194244046105e-99 + 1.2532553759329380307e-6057j 3.04e-363, 6e-1866j
6.8829037658342316231e-05 + 6.0139035302590259912e-6009j 8.27e-286, 1.63e-1788j
2.5725060948439457878e-05 - 3.5086751094482394942e-6009j 3.8e-287, 7.51e-1790j
3.128488164819223832e-83 - 9.4324240440803310797e-6050j 9.22e-358, 1.82e-1860j
0.0018833724057245780535 + 4.3825173398736508669e-6008j 4.45e-281, 8.79e-1784j
0.027860996790457133624 - 1.9668046379941539836e-6007j 5.63e-268, 1.11e-1770j
4.5365398740402045707e-89 - 1.0109566354155961252e-6052j 8.35e-360, 1.65e-1862j
4.9235380453369724638e-11 - 6.5898209364897571122e-6012j 1.15e-304, 2.26e-1807j
1.0673500282071754365e-72 - 2.2115552803673128049e-6044j 1.8e-354, 3.56e-1857j
1.2315592781736103819e-29 - 4.7531551783528324032e-6022j 2.04e-330, 4.03e-1833j
2.9117659143450127062e-32 - 1.8719271566491174736e-6023j 4.82e-333, 9.52e-1836j
1.2196368142904879483e-16 - 1.7666590913494478328e-6014j 3.31e-318, 6.54e-1821j
7.5871424603884407462e-08 + 1.8215249843642647187e-6010j 3.03e-302, 5.99e-1805j
3.0038666992198373562e-61 + 1.5994400740380540654e-6038j 8.96e-351, 1.77e-1853j
8.6214017813943828626e-78 - 5.5800279406909269052e-6047j 2.36e-357, 4.66e-1860j
5.8973527634062420639e-26 + 4.7206956967417786806e-6020j 3.71e-330, 7.33e-1833j
0.13478711277828437316 + 7.3414768934721007034e-6008j 2.43e-280, 4.8e-1783j
3.3320075688957814429e-75 + 1.1638250122746619513e-6045j 2.1e-356, 4.15e-1859j
1.7809771023763289305e-39 + 2.9312260522033672768e-6027j 7.24e-341, 1.43e-1843j
1.4267271445499107884e-22 - 3.6223911792644369286e-6018j 1.22e-328, 2.42e-1831j
3.7595629639757700159e-59 - 1.9086474337605189357e-6037j 5.67e-351, 1.12e-1853j
0.0065498761264846873009 + 1.0190152290711602325e-6007j 7.26e-301, 1.44e-1803j
0.061223489713245925281 - 1.8861903972247038197e-6007j 3.79e-292, 7.49e-1795j
1.4862201733034570572e-17 + 3.9156196130115445262e-6015j 7.54e-325, 1.49e-1827j
1.2505100960694941014e-33 + 3.5154061486673299293e-6024j 3.37e-337, 6.66e-1840j
1.2569668324610035312e-65 + 9.118914886966434177e-6041j 2.16e-353, 4.26e-1856j
0.000908038564639942881 - 2.7395626398081942545e-6008j 7.74e-308, 1.53e-1810j
0.13655566761213490942 - 9.9721954759131043156e-6008j 4.06e-296, 8.02e-1799j
9.3453136918090497378e-07 + 6.2702333222929424732e-6010j 6.67e-313, 1.32e-1815j
0.0001732066900276671107 - 1.0135501950545358292e-6008j 6.23e-310, 1.23e-1812j
0.00040950799051233498198 + 1.6803137728324454801e-6008j 2.7e-309, 5.34e-1812j
4.9323358095861340261e-35 - 6.3516047695189433541e-6025j 8.96e-339, 1.77e-1841j
0.11726573144123935038 - 4.7926009081414748211e-6008j 1.34e-301, 2.65e-1804j
3.9713961259526239926e-55 - 2.2391618714058937128e-6035j 6.92e-351, 1.37e-1853j
9.3636366254193895769e-16 + 1.0292644512995801524e-6013j 1.04e-326, 2.06e-1829j
2.5627386364900461558e-51 - 2.0632979281801164432e-6033j 2.35e-349, 4.64e-1852j
1.223667912735223263e-42 + 6.5315378289441549779e-6029j 4.95e-345, 9.79e-1848j
0.0036414374724984872119 - 6.8291098225731894157e-6008j 4.43e-316, 8.75e-1819j
0.10612513369117020634 - 1.4957935675502123305e-6007j 1.21e-312, 2.39e-1815j
1.8012201531578121731e-19 + 2.3540307316496189749e-6016j 7.23e-332, 1.43e-1834j
3.0500341859813932014e-102 - 2.0736557564359672333e-6059j 1.87e-374, 3.69e-1877j
0.038543328196665071352 - 7.2641964430391514506e-6009j 2.09e-316, 4.13e-1819j
1.7882739363107349405e-20 - 5.9061079860795920974e-6017j 8.86e-333, 1.75e-1835j
0.12547357260798604002 + 1.2546301037520100652e-6007j 1.03e-317, 2.03e-1820j
0.042324238340227197438 + 1.9899658836831785544e-6007j 5.06e-319, 1e-1821j
8.5261937266266507919e-25 - 2.0578231467414597232e-6019j 1.6e-335, 3.16e-1838j
0.011030385005883644767 - 1.4134723732131094122e-6007j 3.58e-321, 7.07e-1824j
3.3853891336575257007e-53 + 2.2127213156685115209e-6034j 4.59e-351, 9.07e-1854j
0.084008281282649049071 + 2.5055690845416197365e-6008j 3.04e-323, 5.65e-1826j
4.8976250562743386061e-41 - 4.4763775965245870971e-6028j 8.16e-345, 1.61e-1847j

Download

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