Rule: Q[1, 7, 83]

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)
305.69452693522917101 - 1.1552635718660873834e-6034j 2.01e-2012, 2.01e-2012j
265.96391792199993691 + 3.8058643590116709328e-6030j 4.1e-2008, 4.1e-2008j
255.25633467836748893 - 3.2811476831609605687e-6029j 5.07e-2007, 5.07e-2007j
277.65319193070868505 - 7.1910904453795426196e-6032j 2.61e-2009, 2.61e-2009j
85.803174358556022983 + 1.0708396541521325212e-6019j 1.69e-1999, 1.69e-1999j
89.425670272895336696 - 1.7186910434452043885e-6028j 2.6e-1999, 2.6e-1999j
324.45413645493831334 + 5.7618770332584766922e-6060j 1.29e-2014, 1.29e-2014j
203.44639017510660342 - 8.8360193128485386795e-6049j 1.75e-2002, 1.75e-2002j
245.31936562759453937 - 2.1334492312959577234e-6075j 4.69e-2006, 4.69e-2006j
176.15141706851962829 - 9.2162960150384510017e-6122j 1.22e-2000, 1.22e-2000j
14.79287086189956479 + 1.1483086211111762745e-6191j 1.31e-2014, 1.31e-2014j
211.00496739122382005 - 7.7543271933563408336e-6175j 4.76e-2003, 4.76e-2003j
60.188731287458316061 - 1.7277149207629294457e-6208j 1.07e-2001, 1.07e-2001j
141.8680097720844705 + 2.1572851390555699889e-6255j 4.24e-1999, 4.24e-1999j
39.889533072129195882 + 1.891743599068493519e-6318j 2.89e-2005, 2.89e-2005j
96.978674043678490616 - 9.2629472264371324379e-6312j 5.17e-1999, 5.17e-1999j
16.084709557140512866 - 4.7569739751204582795e-6356j 8.55e-2014, 8.55e-2014j
24.428022870772643214 + 1.5918254329258908032e-6351j 1.17e-2009, 1.17e-2009j
51.994573330056185375 + 2.0546939636086920469e-6341j 6.6e-2003, 6.6e-2003j
17.410438084598255983 + 1.2197262294114760352e-6364j 5.65e-2013, 5.65e-2013j
290.67311949194941196 + 2.2866803862985799442e-6350j 9.69e-2011, 9.69e-2011j
44.505381084225455872 - 8.7662738455855873867e-6382j 2.77e-2004, 2.77e-2004j
13.54631847067413194 - 1.6062157914114685666e-6420j 1.73e-2015, 1.73e-2015j
182.58424000860752157 - 2.3773103938297201816e-6492j 4.91e-2001, 4.91e-2001j
93.149851720440567714 - 1.8681284138514283031e-6690j 3.7e-1999, 3.7e-1999j
169.94678455371769859 + 5.3417883045096540266e-6860j 2.61e-2000, 2.61e-2000j
33.517437383774929615 + 5.7083208019035559345e-6940j 6.81e-2007, 6.81e-2007j
12.35199612685986194 - 1.3330299856851007235e-6972j 2.59e-2016, 2.59e-2016j
147.12872118084602004 - 3.1491781962776328413e-7027j 2.9e-1999, 2.9e-1999j
66.061516881562140812 + 1.2206339834326542202e-7136j 4.87e-2001, 4.87e-2001j
113.40776644758494455 + 1.0927564041406286211e-7251j 9.84e-1999, 9.84e-1999j
7.9509208918881512072 - 3.2252921441610182933e-7336j 1.22e-2019, 1.22e-2019j
31.540312063501960501 + 1.3958266576596162796e-7321j 1.91e-2007, 1.91e-2007j
10.144087188455837365 + 4.0564086047528991654e-7343j 7.5e-2018, 7.5e-2018j
152.55702281791938853 - 8.8138918664198384267e-7360j 1.82e-1999, 1.82e-1999j
63.083081917942735301 - 3.3606507305215291658e-7401j 2.45e-2001, 2.45e-2001j
7.1182795564148503466 + 1.8579903875549330207e-7452j 7.23e-2021, 7.23e-2021j
163.95488863415407965 + 1.3300393831093255455e-7434j 5.9e-2000, 5.9e-2000j
29.638336760913198862 + 4.5204512844489242522e-7489j 5.95e-2008, 5.95e-2008j
117.81278491745050091 + 1.2719616446219945756e-7478j 1.01e-1998, 1.01e-1998j
218.92060051417497112 + 2.2338661349115724038e-7527j 1.07e-2003, 1.07e-2003j
1.6737519139767177954 + 7.0459868078105928189e-7592j 1.06e-2030, 1.06e-2030j
4.1002078196590017622 - 3.2271379675224106939e-7587j 2.13e-2025, 2.13e-2025j
54.6459326295243715 - 3.3096512111313066342e-7560j 1.75e-2002, 1.75e-2002j
158.16225044411524482 + 1.1137706325285860948e-7598j 1e-1999, 1e-1999j
236.0128893978350698 - 1.190875197155818266e-7645j 3.46e-2005, 3.46e-2005j
131.81675983350787738 + 3.6748040109452424285e-7677j 7.24e-1999, 7.24e-1999j
49.421472584769959362 + 9.2725018584126281158e-7706j 2.44e-2003, 2.44e-2003j
11.215220252174717318 + 2.8516911923815173852e-7719j 4.22e-2017, 4.22e-2017j
20.095539333837580874 + 1.2185672161944640202e-7713j 1.93e-2011, 1.93e-2011j
26.074466089446763895 - 1.0540049433865090066e-7711j 4.19e-2009, 4.19e-2009j
196.20895428867183506 - 4.884170033489869062e-7701j 6.04e-2002, 6.04e-2002j
75.519174737191624244 + 1.6029067252184905161e-7710j 3.61e-2000, 3.61e-2000j
69.125761566419631191 - 3.5161155498362346064e-7714j 1.07e-2000, 1.07e-2000j
37.692301862516275882 + 2.4452278440109631501e-7738j 8.61e-2006, 8.61e-2006j
100.91531484648177706 - 6.6511753655666835502e-7731j 6.81e-1999, 6.81e-1999j
2.0718527327016358395 - 4.5182480021814311903e-7807j 1.57e-2029, 1.57e-2029j
22.887965149653082438 + 7.0792097897444955616e-7788j 3.1e-2010, 3.1e-2010j
0.74055419263685543493 + 3.8589285261749580424e-7812j 2.67e-2034, 2.67e-2034j
18.75251539166561618 + 6.5062323611924277909e-7790j 3.33e-2012, 3.33e-2012j
6.2835064224773224016 - 5.0558361598092155645e-7800j 4.6e-2022, 4.6e-2022j
2.5000206754193299535 + 1.163701657922242256e-7805j 1.91e-2028, 1.91e-2028j
189.263126558989179 - 1.4359686664761433068e-7776j 1.82e-2001, 1.82e-2001j
42.160350464991130548 + 4.3161235793775808372e-7817j 9.63e-2005, 9.63e-2005j
2.969165807853543769 - 4.4227200613194027801e-7839j 1.98e-2027, 1.98e-2027j
136.76652980146494175 - 1.7297542797659321255e-7809j 5.29e-1999, 5.29e-1999j
8.5164777017183299349 - 3.551172276186641554e-7866j 6.31e-2019, 6.31e-2019j
109.12601527440040259 - 8.2323065296362044752e-7845j 9.7e-1999, 9.7e-1999j
104.96319703628073644 + 1.4652303311287627237e-7900j 7.91e-1999, 7.91e-1999j
0.5252765299407710844 - 3.3326673111181452339e-7987j 1.55e-2035, 1.55e-2035j
1 - 2.3796362785136210366e-7984j 3.71e-2033, 3.71e-2033j
35.568277323507317843 - 1.59433500577444234e-7957j 2.46e-2006, 2.46e-2006j
127.0119012543382932 - 2.3697309338788616475e-7948j 8.61e-1999, 8.61e-1999j
9.1727921287267737614 - 1.0842915015696325118e-7990j 1.72e-2018, 1.72e-2018j
46.925435925679186168 - 1.1239645604202137239e-7975j 8.11e-2004, 8.11e-2004j
0.18807558052466950658 + 8.7377662188809833294e-8011j 2.53e-2038, 2.53e-2038j
4.7673099177671066141 + 6.8081441089746080626e-7998j 2.63e-2024, 2.63e-2024j
78.852410777586490239 + 1.8729451856908374786e-7970j 6.28e-2000, 6.28e-2000j
57.376850727646399417 + 3.0243178103460332917e-7985j 4.23e-2002, 4.23e-2002j
27.814499346567591071 - 6.3673607311147333286e-8005j 1.47e-2008, 1.47e-2008j
1.312775374421956876 - 2.0076073343222647802e-8028j 6.62e-2032, 6.62e-2032j
0.34035539027236206802 + 9.2732903998381059703e-8033j 6.77e-2037, 6.77e-2037j
82.279610764067722788 + 3.9344250473634497659e-7994j 1.05e-1999, 1.05e-1999j
5.4966763587415661649 + 8.877373624003715684e-8038j 3.21e-2023, 3.21e-2023j
122.3457834867184007 - 1.4835742551212805278e-8012j 9.82e-1999, 9.82e-1999j
72.277658491607025743 + 9.0585742141608367354e-8024j 1.96e-2000, 1.96e-2000j
3.4999249477323155088 - 1.9145940667015842562e-8050j 1.95e-2026, 1.95e-2026j
0.014838522071812053902 + 2.641253372889747604e-8066j 1.29e-2041, 1.29e-2041j
21.455885401079092388 + 9.1180583776568531118e-8035j 8.04e-2011, 8.04e-2011j
227.23778280673283337 - 1.2304315070100900771e-8028j 1.99e-2004, 1.99e-2004j
0.077644024104282953764 - 3.9637809992586008565e-8064j 6.69e-2040, 6.69e-2040j

Weights

Weight (ball center) Error (ball radius)
2.8442906410048767934e-132 - 3.1241206593824664418e-6108j 5.46e-384, 2.51e-1888j
3.4738189197631829622e-115 + 2.2057200241477438965e-6099j 7.25e-379, 3.32e-1883j
1.4327897651976681493e-110 - 5.5291264085829127392e-6097j 1.17e-377, 5.38e-1882j
3.2056933008787279006e-120 - 5.3836603505899313345e-6102j 9.96e-381, 4.57e-1885j
1.9459767035217589669e-37 - 1.1380969857918718583e-6056j 9.64e-340, 4.42e-1844j
5.3447778570134256807e-39 - 8.0971621338175702133e-6058j 2.8e-341, 1.28e-1845j
2.7230227445684496426e-140 + 2.2719490480807225653e-6112j 1.68e-388, 7.73e-1893j
3.2595174540375901841e-88 - 2.7507689844961968029e-6085j 4.84e-372, 2.22e-1876j
2.7639843955791587977e-106 + 9.425433921250175557e-6095j 1.09e-377, 4.99e-1882j
1.9899925942462645377e-76 - 4.7592378611576589865e-6079j 2.8e-368, 1.28e-1872j
4.781417174166487561e-07 + 8.8708814193469379066e-6040j 4.61e-286, 2.11e-1790j
1.7779279550877238824e-91 + 5.2805375801479140556e-6087j 2.22e-373, 1.02e-1877j
2.0684542191680313775e-26 - 1.1278181723339040793e-6051j 4.59e-334, 2.1e-1838j
1.2642041767535332532e-61 - 4.3307884777587448174e-6071j 4.52e-362, 2.08e-1866j
1.0599050522169577742e-17 - 9.0812650816567350535e-6047j 9.19e-322, 4.22e-1826j
2.9632816409261868935e-42 - 4.4985265031927411652e-6060j 4.13e-349, 1.89e-1853j
1.3557085894263972854e-07 - 4.1082105351551773458e-6040j 5.2e-293, 2.38e-1797j
3.9254104128387253784e-11 - 2.1805583996860189676e-6042j 5.07e-307, 2.33e-1811j
6.8552065272496091906e-23 + 9.2431310601726874019e-6050j 2.26e-330, 1.04e-1834j
3.6724696458940446681e-08 + 1.9624567410644203646e-6040j 2.92e-296, 1.34e-1800j
8.0197508372377074814e-126 + 6.7551611860659596429e-6105j 2.18e-386, 9.98e-1891j
1.1183358378611271859e-19 - 6.165956071913471886e-6048j 4.97e-326, 2.28e-1830j
1.5986512114189316002e-06 - 1.9920572691920900041e-6039j 8.07e-291, 3.7e-1795j
3.3196241066154539513e-79 + 1.5892816090482714398e-6080j 2.13e-370, 9.78e-1875j
1.3260637965150045674e-40 + 5.3577480547926130268e-6059j 7.44e-349, 3.41e-1853j
9.5079013491253639037e-74 + 1.2756914804610207176e-6077j 1.5e-368, 6.86e-1873j
5.5930616491402314055e-15 + 4.4537388941718882591e-6045j 1.22e-321, 5.59e-1826j
5.0403711061623041392e-06 + 4.7011622667870973791e-6039j 4.23e-294, 1.94e-1798j
6.770121334342201521e-64 + 2.5275868042149583196e-6072j 6.11e-365, 2.8e-1869j
6.1660156006539546875e-29 - 5.4112727464490267524e-6053j 8.59e-342, 3.94e-1846j
2.4287672119464961485e-49 - 2.8488728776006815019e-6064j 3.97e-358, 1.82e-1862j
0.0002697713330725031675 - 3.0454875043120407805e-6037j 2.3e-289, 1.06e-1793j
3.8903956795118599741e-14 - 1.5809831564883403634e-6044j 2.71e-322, 1.24e-1826j
4.058397856284689933e-05 + 3.4236013648337442404e-6038j 9.19e-295, 4.21e-1799j
3.068186287268219253e-66 - 1.3651004103111739986e-6073j 2.05e-366, 9.41e-1871j
1.1779819457819783299e-27 + 2.4903263695266012995e-6052j 2.11e-341, 9.67e-1846j
0.0006893668655253162282 + 2.593444028393442484e-6037j 6.41e-291, 2.94e-1795j
3.6764119058417276569e-71 - 3.0858645135962730031e-6076j 7.44e-369, 3.41e-1873j
2.5036985395352478904e-13 + 5.5445474330308687363e-6044j 7.6e-324, 3.49e-1828j
3.0527354649939809837e-51 + 2.3810240242000671193e-6065j 2.18e-360, 9.99e-1865j
6.806318309482453693e-95 - 8.4916023010044042847e-6089j 1.29e-380, 5.92e-1885j
0.071546839552499245118 - 3.560016035072874168e-6036j 1.47e-270, 6.74e-1775j
0.010512482070143975067 + 8.7045797712895888952e-6037j 5.69e-288, 2.61e-1792j
4.9827914855847793082e-24 - 2.1761994213254253309e-6050j 1.82e-340, 8.35e-1845j
1.1658956837339978326e-68 + 6.7854121013291911741e-6075j 4.75e-368, 2.18e-1872j
2.8604684584269215079e-102 - 1.172328185909337705e-6092j 6.48e-384, 2.97e-1888j
2.7592644922913079579e-57 - 1.0281358207105052035e-6068j 1.67e-364, 7.65e-1869j
8.7176348674774746383e-22 - 3.8358729432714500644e-6049j 6.01e-340, 2.76e-1844j
1.4894593192797798444e-05 - 1.1925720495045021858e-6038j 4.09e-311, 1.88e-1815j
2.5189964045703260039e-09 + 4.4326752916059702796e-6041j 7.45e-323, 3.42e-1827j
8.039715317834001927e-12 + 6.568330721930403596e-6043j 1.06e-327, 4.85e-1832j
4.3451613468576737403e-85 + 1.2225466051341168017e-6083j 6.28e-377, 2.88e-1881j
5.2389077135275497627e-33 + 5.539659871524865002e-6055j 8.44e-352, 3.87e-1856j
2.9614866133561880994e-30 + 1.1643824880947077497e-6053j 3.62e-349, 1.66e-1853j
9.2260030093404394887e-17 + 3.3821209101467904288e-6046j 3.78e-337, 1.74e-1841j
5.9455245612646598385e-44 + 4.0368442936928156581e-6061j 8.24e-359, 3.78e-1863j
0.052042564578810894899 + 3.2369773414121379945e-6036j 1.1e-299, 5.05e-1804j
1.7033089884000989502e-10 + 6.7807818670673048366e-6042j 5.66e-329, 2.6e-1833j
0.11182565313742335686 + 4.0226795050834621493e-6036j 1.37e-298, 6.3e-1803j
9.642796164805970774e-09 - 9.488875582130079543e-6041j 1.24e-325, 5.71e-1830j
0.0015183866461076566937 - 2.9465866490489647096e-6037j 1.81e-314, 8.31e-1819j
0.036534973684228628689 - 2.7267295131537214093e-6036j 5.82e-305, 2.67e-1809j
4.3363648653881647816e-82 - 4.706267248301279464e-6082j 8.18e-377, 3.75e-1881j
1.1302931457734537071e-18 + 2.3911683823181190226e-6047j 3.11e-340, 1.43e-1844j
0.025528851697187059612 + 2.027551815222683818e-6036j 5.06e-310, 2.32e-1814j
2.014364402114873692e-59 + 6.9019256219728797591e-6070j 4.39e-367, 2.01e-1871j
8.9041575276367671198e-05 + 2.7215978595646178226e-6037j 6.04e-321, 2.77e-1825j
1.7086376085528434376e-47 + 3.2782571977270861623e-6063j 6.02e-362, 2.76e-1866j
1.0674443422750268656e-45 - 3.664010841345659238e-6062j 5.79e-361, 2.66e-1865j
0.11765031901593593049 - 3.2940666091876697828e-6036j 1.14e-311, 5.25e-1816j
0.10522037154185711775 - 4.1015317894857727718e-6036j 6.66e-312, 3.06e-1816j
7.4561196194158512186e-16 - 1.2372068627914393489e-6045j 1.01e-340, 4.64e-1845j
3.2711992236524856538e-55 + 1.4385152636202526987e-6067j 2.03e-366, 9.3e-1871j
9.1298406290475253049e-05 - 1.2159973901911588894e-6037j 4e-327, 1.83e-1831j
1.0258927190295957915e-20 + 1.5554687600149798479e-6048j 1.38e-345, 6.34e-1850j
0.10993848277418210894 - 1.2230170532207823057e-6036j 2.52e-320, 1.15e-1824j
0.0059435218322954836236 - 5.690964593250651457e-6037j 4.05e-326, 1.86e-1830j
1.9218883643128277627e-34 - 1.3192973305284370843e-6055j 2.57e-356, 1.18e-1860j
3.3435778311230611606e-25 + 5.0082182258869739606e-6051j 5.92e-350, 2.72e-1854j
1.4842638928442119221e-12 - 1.922413525426970827e-6043j 1.14e-340, 5.22e-1845j
0.091078235989800450468 + 3.8456285977071560502e-6036j 1.11e-326, 5.08e-1831j
0.12108393084805253879 + 2.1870139526233246309e-6036j 3.61e-326, 1.66e-1830j
6.417559616319970753e-36 + 4.0118109345926686897e-6056j 3.18e-357, 1.46e-1861j
0.0031122424130168347338 + 3.9197498081498948692e-6037j 1.4e-332, 6.43e-1837j
3.3770149002227631473e-53 - 1.89983893491093445e-6066j 8.09e-367, 3.71e-1871j
1.3027723071976218706e-31 - 2.5094598685248729231e-6054j 6.76e-355, 3.1e-1859j
0.017077683061284903956 - 1.3549148948512957821e-6036j 3.2e-334, 1.47e-1838j
0.037462030069361433392 - 1.5108906205250824599e-6037j 6.95e-335, 3.18e-1839j
6.6643624934301515673e-10 - 1.8662816351157241993e-6041j 7.11e-341, 3.26e-1845j
1.7503137545190882636e-98 + 1.1183500098737531214e-6090j 9.02e-391, 4.14e-1895j
0.080721171828668156935 + 5.6185241788847671956e-6037j 8.9e-335, 4.05e-1839j

Download

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