Rule: Q[1, 5, 80]

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)
291.43337516073994617 + 6.6586386274968333579e-5933j 1.5e-2013, 1.5e-2013j
241.90207700976165026 - 3.5020862148140214451e-5931j 2.56e-2008, 2.56e-2008j
276.66921447740953592 - 2.4852512912002070299e-5943j 6.74e-2012, 6.74e-2012j
263.88068037951350142 - 1.5068896482357022362e-5971j 1.48e-2010, 1.48e-2010j
87.823119914312507858 - 5.6412098526375638219e-6004j 3.58e-2001, 3.58e-2001j
19.137311509221022337 + 9.3326957936958763627e-6049j 6.07e-2014, 6.07e-2014j
22.338777445656685906 + 3.7062159959189815061e-6047j 1.8e-2012, 1.8e-2012j
50.022717419033933122 + 2.0292989790561423884e-6035j 6.85e-2005, 6.85e-2005j
223.04088706475941869 + 6.4360183961518196019e-6081j 1.46e-2006, 1.46e-2006j
164.54097720055556038 + 1.2052922537661817316e-6121j 2.8e-2002, 2.8e-2002j
14.829781217182764814 - 1.2038430547645681217e-6153j 3.09e-2016, 3.09e-2016j
67.263498352277393048 + 1.4840888229791273067e-6139j 1.18e-2002, 1.18e-2002j
121.45313189801656015 - 1.5074567647952937751e-6136j 8.64e-2001, 8.64e-2001j
198.56645609270923525 + 1.9948100777601111162e-6155j 1.6e-2004, 1.6e-2004j
4.4397107602374876125 + 5.88170402453132667e-6194j 1.65e-2025, 1.65e-2025j
7.1139361143676779684 + 1.3200564220626294897e-6190j 5.65e-2022, 5.65e-2022j
99.519533801234453815 - 5.5059631629846091818e-6168j 7.68e-2001, 7.68e-2001j
84.144342826089282552 + 8.0476022173677507519e-6174j 2.24e-2001, 2.24e-2001j
64.172049663808438208 + 3.9745770932267185062e-6181j 6.27e-2003, 6.27e-2003j
191.17837708577946838 + 4.4641583100167714044e-6179j 5.87e-2004, 5.87e-2004j
31.534567353861168981 - 3.9818353264755148648e-6200j 3.87e-2009, 3.87e-2009j
37.902486320319623039 + 3.756789333527510628e-6198j 2.41e-2007, 2.41e-2007j
35.706772745472354557 - 7.7451466298085503803e-6199j 5.69e-2008, 5.69e-2008j
116.80053758350250636 + 9.8643951911345946506e-6190j 9.92e-2001, 9.92e-2001j
33.584475755946114551 - 1.237052517312794375e-6214j 1.64e-2008, 1.64e-2008j
170.81243161723044336 - 1.5537304459224470728e-6206j 1.27e-2002, 1.27e-2002j
61.17029408895990776 - 5.023442345901284047e-6226j 2.67e-2003, 2.67e-2003j
80.57013962820182642 + 5.4657982267532437e-6223j 1.45e-2001, 1.45e-2001j
13.524010033138084729 + 1.1690002760911539112e-6239j 4.66e-2017, 4.66e-2017j
252.40634866099435705 + 4.1290332888408393125e-6232j 2.32e-2009, 2.32e-2009j
184.10864920021279629 + 1.8193235330745657554e-6222j 1.86e-2003, 1.86e-2003j
309.88512685631133501 - 8.0269375925755978828e-6248j 1.05e-2015, 1.05e-2015j
16.200346435751097653 - 7.33394095201724893e-6248j 1.89e-2015, 1.89e-2015j
131.19808403877111994 + 9.5755024856679146793e-6232j 5.85e-2001, 5.85e-2001j
29.556077089675672273 - 9.8052966578031098803e-6251j 9.03e-2010, 9.03e-2010j
52.68416567515317255 + 1.0557338359409016168e-6245j 1.98e-2004, 1.98e-2004j
232.1596673191329978 - 4.5460064727851853775e-6244j 2.13e-2007, 2.13e-2007j
44.941334437606650676 + 3.5137294257289932331e-6246j 8.23e-2006, 8.23e-2006j
20.704691359102993693 - 1.3649937185510374485e-6253j 3.44e-2013, 3.44e-2013j
73.723965439773477493 - 5.750830586455166087e-6242j 4.64e-2002, 4.64e-2002j
206.30833720034170916 + 3.7582119140209438237e-6241j 4.1e-2005, 4.1e-2005j
17.63604030690071415 + 2.1646303745588013464e-6264j 1.06e-2014, 1.06e-2014j
55.428139733866864662 - 4.4415988939937268885e-6253j 4.62e-2004, 4.62e-2004j
1 - 7.2093161842037139343e-6284j 2.97e-2033, 2.97e-2033j
91.609611429211496976 + 9.9475389945983431936e-6250j 4.88e-2001, 4.88e-2001j
177.32811813052202809 - 5.2219944394115854653e-6265j 5.07e-2003, 5.07e-2003j
136.30458315423929758 - 5.7752725434917492548e-6295j 4.39e-2001, 4.39e-2001j
24.040224988993079079 - 1.3090294471739522313e-6330j 8.86e-2012, 8.86e-2012j
0.54521540802690686802 + 1.1770800116881383694e-6354j 1.41e-2035, 1.41e-2035j
5.8077860482980055671 + 3.2513546605680912902e-6342j 2.5e-2023, 2.5e-2023j
58.256271509059151742 + 6.284107949087933254e-6319j 1.16e-2003, 1.16e-2003j
95.507199433062643926 - 7.7323629872300833276e-6323j 6.51e-2001, 6.51e-2001j
3.1544165044377107647 + 2.2870929910861030513e-6396j 7.26e-2028, 7.26e-2028j
112.28619955911064744 - 7.4591697406058316844e-6368j 1.05e-2000, 1.05e-2000j
9.9957815789095006435 + 1.2492257574548517059e-6415j 1.35e-2019, 1.35e-2019j
40.172704964640858158 - 1.9657029431918178667e-6396j 7.71e-2007, 7.71e-2007j
47.442257092792849207 - 2.3641391458593370524e-6409j 2.49e-2005, 2.49e-2005j
147.02703706347141243 + 6.0565591164762953317e-6471j 1.92e-2001, 1.92e-2001j
6.4020551035846217575 - 2.457209800739280989e-6557j 1.25e-2022, 1.25e-2022j
0.77343672429322291799 - 1.1569471025804699624e-6586j 2.84e-2034, 2.84e-2034j
3.7722776243921486754 - 1.0307257346079891024e-6554j 1.05e-2026, 1.05e-2026j
107.90456624441758096 + 1.1383049909670715154e-6555j 1.03e-2000, 1.03e-2000j
141.5778278244153548 - 2.1243680593723133453e-6640j 3.12e-2001, 3.12e-2001j
103.65056244802969061 + 3.9045141328190173198e-6705j 9.19e-2001, 9.19e-2001j
7.9848413107483397296 - 2.0033694574668958138e-6770j 3.21e-2021, 3.21e-2021j
5.1384848875831238418 - 4.5610440324607545407e-6771j 2.35e-2024, 2.35e-2024j
0.01390375421532508014 - 3.4703678232914208022e-6790j 1.54e-2041, 1.54e-2041j
42.518581012210393489 + 1.1674944008740952701e-6749j 2.91e-2006, 2.91e-2006j
11.106533822766615235 - 6.6131979372082084423e-6787j 9.95e-2019, 9.95e-2019j
2.5922508199253002476 - 2.9865607194531409737e-6794j 4.85e-2029, 4.85e-2029j
1.6485513575962662028 + 3.3787237769887566599e-6809j 2.99e-2031, 2.99e-2031j
214.44793531989100026 + 6.9870121203371206484e-6834j 8.53e-2006, 8.53e-2006j
77.097588348463253592 + 3.3568708512010103205e-7001j 8.31e-2002, 8.31e-2002j
70.44672804930681925 + 5.0453685004124084524e-7179j 2.47e-2002, 2.47e-2002j
8.9529512477548957267 - 5.7687739273814136263e-7289j 2.04e-2020, 2.04e-2020j
1.2800252063485622098 + 8.7683530361553109225e-7353j 2.61e-2032, 2.61e-2032j
0.34167103814193398265 + 6.9712770800950416415e-7382j 4.5e-2037, 4.5e-2037j
0.18296039898248679851 + 2.0545531769994247458e-7425j 1.32e-2038, 1.32e-2038j
152.66256417269811705 - 1.1374514216836879338e-7517j 1.1e-2001, 1.1e-2001j
27.648089567472917962 + 4.9633736587845028236e-7606j 1.94e-2010, 1.94e-2010j
0.073784282453942895586 - 2.7805569520906511465e-7675j 4.55e-2040, 4.55e-2040j
2.08901715600306432 - 2.482284111691741807e-7638j 3.71e-2030, 3.71e-2030j
25.809742440497612171 - 7.7288593877052397374e-7710j 4.3e-2011, 4.3e-2011j
158.49610773564038143 - 5.368220813125366496e-7836j 5.89e-2002, 5.89e-2002j
12.282875475077860533 - 4.924024318062746781e-7914j 6.61e-2018, 6.61e-2018j
126.25007612635400232 - 1.099721175750616472e-7911j 8.13e-2001, 8.13e-2001j

Weights

Weight (ball center) Error (ball radius)
4.3667347526296120922e-126 - 8.992409384024796478e-6048j 4.65e-389, 6.64e-1895j
8.8594016621740106025e-105 + 1.5812325349172270097e-6035j 9.52e-383, 1.36e-1888j
9.5132374158756793726e-120 + 2.1362644150399142312e-6044j 1.63e-387, 2.32e-1893j
3.0152254784295020189e-114 - 2.1254859273295586292e-6041j 6.51e-386, 9.29e-1892j
2.6968446412004962516e-38 + 3.5842848455989353687e-6003j 6.46e-350, 9.22e-1856j
7.4931078904238979779e-09 - 4.5809057069638074969e-5987j 2.37e-297, 3.38e-1803j
3.3151099166531317074e-10 - 6.6229141962432088987e-5988j 9.18e-303, 1.31e-1808j
4.9411503914687960092e-22 + 1.393457091991399173e-5994j 3.59e-331, 5.12e-1837j
1.2053851480559325945e-96 + 2.3180233655136245819e-6032j 1.8e-381, 2.56e-1887j
2.1380625172248904991e-71 + 4.8086618097122490424e-6020j 1.76e-372, 2.51e-1878j
4.8529331693461039629e-07 + 7.1432914901345665302e-5986j 3.92e-293, 5.6e-1799j
1.9246226231165923772e-29 + 1.544104868770007608e-5998j 6.64e-343, 9.48e-1849j
8.4694997292238371843e-53 + 1.2312182541026750188e-6010j 6.5e-363, 9.28e-1869j
4.3864858516129724127e-86 - 2.5202322276308653479e-6027j 1.03e-378, 1.47e-1884j
0.0081195151725514253061 - 1.636310697544963058e-5982j 4.23e-261, 6.04e-1767j
0.00065498455745986664725 - 4.1982245479425809116e-5983j 2.17e-275, 3.1e-1781j
2.4485919288210292504e-43 - 8.8051268845213537558e-6006j 1.4e-356, 2e-1862j
1.0375339300473496965e-36 - 2.3920713775279163385e-6002j 6.86e-351, 9.79e-1857j
4.113397121105740457e-28 - 7.8019672199761868489e-5998j 5.94e-343, 8.49e-1849j
6.7770106934647388248e-83 + 9.2390256204139923802e-6026j 6.47e-378, 9.24e-1884j
4.0623747754122749291e-14 + 3.3395755768886292526e-5990j 1.1e-323, 1.57e-1829j
7.7268979332345397753e-17 - 9.7869232995254842769e-5992j 2.26e-329, 3.22e-1835j
6.7137300711023115812e-16 + 3.277130620133692745e-5991j 1.18e-327, 1.69e-1833j
8.6153582028055758947e-51 - 1.3067630335935863687e-6009j 9.59e-364, 1.37e-1869j
5.4168714949657002159e-15 - 1.062630980736876723e-5990j 2.78e-326, 3.97e-1832j
4.1940329277359853523e-74 - 2.126535725200223454e-6021j 2.82e-376, 4.03e-1882j
8.0355244043010520158e-27 + 3.7794124316071232999e-5997j 3.41e-344, 4.87e-1850j
3.5952921131707481099e-35 + 1.5189518808956414344e-6001j 5.08e-352, 7.26e-1858j
1.7044243075705522213e-06 - 1.7315064555949510723e-5985j 4.16e-308, 5.94e-1814j
2.6338385198254226154e-109 + 1.4583712502001392756e-6038j 2.47e-390, 3.53e-1896j
7.6344956810009814024e-80 - 2.9691382236501872138e-6024j 4.67e-379, 6.67e-1885j
5.6920723870405246536e-134 + 6.4746098423011479624e-6052j 6.84e-401, 9.77e-1907j
1.292278348656698313e-07 - 2.9093264989386904019e-5986j 1.88e-316, 2.68e-1822j
5.2797614558844322037e-57 + 8.8702637681204710699e-6013j 6.81e-370, 9.73e-1876j
2.8343397665155544109e-13 - 1.0181495390021894594e-5989j 3.09e-330, 4.42e-1836j
3.5588918173796443505e-23 - 3.3706648495704942992e-5995j 2.4e-344, 3.42e-1850j
1.406049007953703173e-100 - 4.4153670322903616487e-6034j 1.29e-387, 1.83e-1893j
7.4721716727406134301e-20 + 2.1313424837049616531e-5993j 2.71e-341, 3.87e-1847j
1.6306370378554238096e-09 + 1.7621794640154792179e-5987j 5.13e-325, 7.33e-1831j
3.19067789581865788e-32 + 5.3059388885230400501e-6000j 2.8e-353, 4e-1859j
1.9991336221206466812e-89 + 5.9950990965406691129e-6029j 8.1e-384, 1.16e-1889j
3.2181733297837304323e-08 + 1.1655875749715341951e-5986j 1.23e-323, 1.76e-1829j
2.3594482554045035767e-24 + 7.8478556243000618685e-5996j 2.23e-346, 3.19e-1852j
0.08775001599580353019 + 1.9881360326276652428e-5981j 3.44e-296, 4.91e-1802j
6.2942934036562382493e-40 - 5.1022078489444240051e-6004j 1.05e-359, 1.5e-1865j
6.4540455605579047857e-77 + 8.4249859448484479434e-6023j 3.55e-379, 5.07e-1885j
3.301466337760355895e-59 - 6.7394366744867134727e-6014j 9.73e-373, 1.39e-1878j
6.2929249814050546516e-11 + 2.4281598211925462334e-5988j 8.29e-334, 1.18e-1839j
0.12836150847630354524 + 1.2894643829307822362e-5981j 3.44e-296, 4.91e-1802j
0.0018637517276941680536 - 1.3439743706591881226e-5982j 6.34e-316, 9.05e-1822j
1.4375487657054493476e-25 - 1.7570903104801715585e-5996j 4.8e-349, 6.86e-1855j
1.3146892650430041414e-41 + 6.8885007375303141626e-6005j 8.6e-362, 1.23e-1867j
0.02519908015427757464 - 2.6733875154678811029e-5982j 5.15e-312, 7.35e-1818j
7.6348452547213811082e-49 + 1.2986491265535408533e-6008j 2.85e-367, 4.07e-1873j
4.9120316501415409195e-05 + 2.4229687863506454798e-5984j 1.34e-327, 1.91e-1833j
8.2494206385214090769e-18 + 2.8279292686057208158e-5992j 1.53e-344, 2.19e-1850j
6.3241381251143825094e-21 - 5.5498141433777468043e-5994j 5.12e-347, 7.3e-1853j
7.771790374344312435e-64 - 3.0605574169273215433e-6016j 7.6e-377, 1.09e-1882j
0.0010238828638325746611 + 9.3814022278948802958e-5983j 4.03e-326, 5.75e-1832j
0.1050430863830684236 - 1.8817861730968197571e-5981j 8.17e-309, 1.17e-1814j
0.014815572508814975044 + 2.0173694732438708959e-5982j 1.88e-321, 2.68e-1827j
5.9268687295942587295e-47 - 1.2115420719220406221e-6007j 7.02e-367, 1e-1872j
1.7484900777344536095e-61 + 4.7332689936345600531e-6015j 1.2e-375, 1.72e-1881j
4.0507034160961157124e-45 + 1.063575751898636184e-6006j 8.05e-366, 1.15e-1871j
0.00031530180249517143284 + 1.5580919159642064421e-5983j 1.67e-333, 2.38e-1839j
0.004107313922657327737 + 1.4645775210159282151e-5982j 1.89e-329, 2.69e-1835j
0.035255644340641373716 + 7.6126592417025480932e-5983j 5.54e-321, 7.92e-1827j
8.1609434743229924476e-19 - 7.8993854132092624098e-5993j 3.05e-349, 4.36e-1855j
1.7172326309344272025e-05 - 1.0000095692296534882e-5984j 2.67e-337, 3.81e-1843j
0.039909841030403805432 + 3.7443317312740342389e-5982j 2.58e-328, 3.68e-1834j
0.078252143101580505623 + 8.69685123852410439e-5982j 6.77e-327, 9.66e-1833j
6.1437515526490240995e-93 - 1.2455854029656144016e-6030j 8.91e-391, 1.27e-1896j
1.1253954323171713695e-33 - 9.1905669558080067637e-6001j 5.73e-360, 8.19e-1866j
8.2140459837767766568e-31 - 2.9266027487175567884e-5999j 2.82e-358, 4.03e-1864j
0.00013029617786898370606 - 6.0116169440496424231e-5984j 1.3e-338, 1.85e-1844j
0.090789176545002593235 - 1.4293435202248068967e-5981j 7.61e-332, 1.09e-1837j
0.12979224434306661573 - 8.2326079484571496452e-5982j 3.46e-331, 4.94e-1837j
0.11170860672457471229 + 5.0462071701912088521e-5982j 1.93e-331, 2.75e-1837j
2.8696697137180098848e-66 + 1.8139025493638922065e-6017j 2.13e-379, 3.03e-1885j
1.8413295430548232716e-12 + 3.0140684986729254615e-5989j 7e-349, 1e-1854j
0.078308619323146560916 - 2.6077394651103653784e-5982j 1.62e-335, 2.31e-1841j
0.05852516435862493528 - 5.5324697356560356462e-5982j 2.42e-337, 3.46e-1843j
1.1147051407358845449e-11 - 8.6726422783220884235e-5989j 2.18e-348, 3.11e-1854j
8.7010215586493435059e-69 - 9.8055661684367851505e-6019j 7.5e-381, 1.07e-1886j
5.5971886241200789041e-06 + 4.1636453851564690955e-5985j 1.04e-345, 1.47e-1851j
7.2099718295224753983e-55 - 1.0831542433074080975e-6011j 1.37e-373, 1.96e-1879j

Download

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