Rule: Q[2, 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)
287.7129210880766353 + 7.9329013539189362811e-5971j 2.25e-2006, 2.25e-2006j
347.70310453214707834 - 5.2022025780934275908e-5987j 4.76e-2013, 4.76e-2013j
328.48723974740838357 - 1.0845844737496858029e-5983j 7.76e-2011, 7.76e-2011j
299.72120362574870046 - 5.6964158697537383589e-5975j 1.21e-2007, 1.21e-2007j
239.26461944788173946 + 1.7437081100131252531e-5971j 8.44e-2002, 8.44e-2002j
10.478419632512104838 + 4.1458229892871481407e-6013j 3.24e-2018, 3.24e-2018j
247.84601721324732416 - 4.9732112784602476218e-5992j 1.56e-2002, 1.56e-2002j
231.09033301667435211 - 2.1984905347343209178e-6004j 3.99e-2001, 3.99e-2001j
72.812530938249190252 + 1.3909422703960691927e-6009j 1.55e-1998, 1.55e-1998j
256.89199827160325882 - 1.0636852430934705794e-6017j 2.58e-2003, 2.58e-2003j
36.924185966041659991 - 1.0861634610977568323e-6037j 3.64e-2005, 3.64e-2005j
134.1098270301085222 + 7.764819783448929202e-6028j 3.45e-1996, 3.45e-1996j
63.908749904507116893 + 7.4834264796745334874e-6042j 1.27e-1999, 1.27e-1999j
182.32993738865237767 + 6.2253470321811880946e-6039j 9.16e-1998, 9.16e-1998j
32.898845079812650263 + 7.38957123696140056e-6055j 2.01e-2006, 2.01e-2006j
16.480303112437038867 + 4.6160083788004949984e-6061j 9.16e-2014, 9.16e-2014j
69.765371617060028739 - 5.9200753202198174474e-6046j 7.25e-1999, 7.25e-1999j
66.797955319623323189 - 2.3781078618453646114e-6046j 3.17e-1999, 3.17e-1999j
20.775486653630662871 - 1.0194350256923457193e-6058j 2.25e-2011, 2.25e-2011j
89.304702483036430355 + 2.4955428906813694145e-6043j 3.61e-1997, 3.61e-1997j
116.30161392286442958 + 1.3934893769055179849e-6042j 3.37e-1996, 3.37e-1996j
215.79042878164052719 + 3.5780033287276751769e-6059j 6.09e-2000, 6.09e-2000j
124.96753293802015807 - 2.5483294852646699215e-6060j 3.82e-1996, 3.82e-1996j
266.47744771822422045 + 6.9278439131434285344e-6080j 2.83e-2004, 2.83e-2004j
15.165130979848496333 - 4.4395583743207203615e-6090j 1.3e-2014, 1.3e-2014j
201.67570127930211752 + 1.1466847825624969832e-6070j 5.95e-1999, 5.95e-1999j
148.7994282360282087 + 5.1374543451799680946e-6077j 1.81e-1996, 1.81e-1996j
25.604532655642656389 - 8.0843745870832142506e-6104j 3.76e-2009, 3.76e-2009j
50.587747449185753052 + 5.4409288675715120325e-6095j 7.77e-2002, 7.77e-2002j
48.139898027267210361 + 1.0761609990090145689e-6095j 2.54e-2002, 2.54e-2002j
22.325198464242115791 + 8.7164623121123946655e-6104j 1.3e-2010, 1.3e-2010j
55.696283895049421523 + 5.4726913604069658034e-6094j 6.75e-2001, 6.75e-2001j
75.941054107232081826 - 6.3655391866319545916e-6092j 3.11e-1998, 3.11e-1998j
13.907620524090817277 - 2.2005189849604805178e-6109j 1.64e-2015, 1.64e-2015j
208.5981070215824138 + 3.5871475414435891237e-6091j 2.11e-1999, 2.11e-1999j
188.55859758000295073 + 5.4006141933636280074e-6089j 3.88e-1998, 3.88e-1998j
79.152657346660111678 + 5.2900460364121853468e-6098j 6.17e-1998, 6.17e-1998j
164.80269735004507414 - 7.6982596310200672023e-6095j 5.85e-1997, 5.85e-1997j
43.451763231337187195 + 7.2943373186257463759e-6109j 2.11e-2003, 2.11e-2003j
30.98175779352430351 + 1.8625829631817645321e-6112j 4.45e-2007, 4.45e-2007j
108.08052197276225899 + 1.4358877669464550727e-6101j 2.28e-1996, 2.28e-1996j
112.13725238980765108 - 1.3907727482509115627e-6109j 3.02e-1996, 3.02e-1996j
313.08439541420953101 - 7.3367699542063997039e-6134j 4.29e-2009, 4.29e-2009j
5.9129706796882245366 - 2.8987997040977963439e-6146j 6.28e-2023, 6.28e-2023j
96.524628436472689472 + 1.3839295316524480188e-6119j 8.71e-1997, 8.71e-1997j
159.31069024590587848 + 8.1862760941748184769e-6130j 8.88e-1997, 8.88e-1997j
92.867973998436723697 + 2.6343592451767017024e-6143j 5.98e-1997, 5.98e-1997j
276.70344879154782903 - 9.3339319302935940622e-6156j 2.92e-2005, 2.92e-2005j
12.707473530681080561 - 2.0149101635250146586e-6166j 2.23e-2016, 2.23e-2016j
104.12816373394318293 - 2.1316411819933541608e-6145j 1.68e-1996, 1.68e-1996j
27.335248441674994212 - 3.9702761356240414966e-6187j 2e-2008, 2e-2008j
176.30221897835454479 - 1.0808578002999717186e-6173j 1.72e-1997, 1.72e-1997j
6.707557486165180127 - 9.9241306081599359741e-6234j 5.38e-2022, 5.38e-2022j
5.1835562812615549948 - 7.8813840906443884414e-6235j 6.64e-2024, 6.64e-2024j
1.9649798060697712591 + 4.2496677026322199728e-6241j 2.59e-2030, 2.59e-2030j
58.359250628799555106 + 7.6270471732561379203e-6208j 1.87e-2000, 1.87e-2000j
170.46336789742887334 + 1.6911125167799842704e-6218j 3.13e-1997, 3.13e-1997j
100.27714297374098494 + 3.0478779227257413335e-6265j 1.28e-1996, 1.28e-1996j
4.5258787574366277216 - 9.3798858542318294584e-6341j 7.96e-2025, 7.96e-2025j
1.5486603696061750717 - 1.3408351701761783806e-6346j 1.47e-2031, 1.47e-2031j
82.449159707490280111 - 1.6416025495357440334e-6311j 1.19e-1997, 1.19e-1997j
53.106172704674634959 - 8.9375383193916437459e-6358j 2.42e-2001, 2.42e-2001j
153.97882400787678742 + 6.0084883666186457407e-6432j 1.32e-1996, 1.32e-1996j
61.096305829252704974 - 2.9605202900763112181e-6514j 4.93e-2000, 4.93e-2000j
2.4218567241639113052 + 1.06654192326093514e-6618j 4.6e-2029, 4.6e-2029j
7.5631067793654209346 - 1.5598076032665859793e-6606j 5.25e-2021, 5.25e-2021j
39.033952636938154676 + 6.5924276147228531241e-6635j 1.46e-2004, 1.46e-2004j
195.00193603628023945 - 4.4444307206040466901e-6877j 1.67e-1998, 1.67e-1998j
143.76556794021722264 + 4.4897855097711168216e-7104j 2.44e-1996, 2.44e-1996j
29.127446965097798777 + 2.2963586703559936282e-7188j 9.58e-2008, 9.58e-2008j
3.9425700238611410551 - 2.7789263903439625729e-7243j 8.62e-2026, 8.62e-2026j
23.934703663871306448 - 3.4116522097217748396e-7256j 7.12e-2010, 7.12e-2010j
129.47696061347679272 - 5.0430877403072194927e-7406j 3.83e-1996, 3.83e-1996j
9.449343505952531185 - 7.5964510072092985037e-7514j 3.94e-2019, 3.94e-2019j
85.832491306729050578 - 1.0836573999790117363e-7568j 2.11e-1997, 2.11e-1997j
3.4142135623730950488 - 5.2867999177768568758e-7667j 8.34e-2027, 8.34e-2027j
19.285070528855372982 - 1.4706092751784046055e-7638j 3.62e-2012, 3.62e-2012j
1.1783917519916491492 + 5.7291366885738598927e-7692j 6.91e-2033, 6.91e-2033j
8.4774032390334073064 + 1.0568923783341678089e-7661j 4.58e-2020, 4.58e-2020j
45.761570364636956618 - 9.712486718581704843e-7679j 7.21e-2003, 7.21e-2003j
0.85695184641295526826 + 1.0389005665106149956e-7767j 3.09e-2034, 3.09e-2034j
0.19707594847116643627 + 5.2346014606646919329e-7782j 1.95e-2038, 1.95e-2038j
17.853485791294285042 + 1.2928303699856642874e-7757j 5.46e-2013, 5.46e-2013j
138.87094689932390047 + 3.6002204486757103392e-7852j 3.13e-1996, 3.13e-1996j
41.209525330555165855 + 3.3398573978235211842e-7912j 5.55e-2004, 5.55e-2004j
34.87940876018931206 + 1.4015994701712823299e-7918j 8.69e-2006, 8.69e-2006j
0.36568083716078184577 + 5.351321055254313925e-7972j 4.5e-2037, 4.5e-2037j
0.015228235567258860329 - 5.3857233078109527709e-7978j 1.43e-2041, 1.43e-2041j
120.57711345273503916 - 7.0600197133906111105e-7930j 3.67e-1996, 3.67e-1996j
223.27780453043739137 + 4.2109579062048343739e-7956j 1.72e-2000, 1.72e-2000j
0.080220450284055052698 + 6.6727280772855702958e-8015j 5.92e-2040, 5.92e-2040j
0.5857864376269049512 + 1.3036782218182798684e-8010j 1.3e-2035, 1.3e-2035j
2.9090719318918163598 - 4.8131469655061086329e-8003j 8.69e-2028, 8.69e-2028j
11.564455776239028646 - 5.2824749988530045381e-7992j 2.74e-2017, 2.74e-2017j

Weights

Weight (ball center) Error (ball radius)
1.2800390312117682833e-124 - 1.1870944864440761051e-6080j 2e-354, 5.25e-1861j
2.2302400161689491947e-150 - 1.1692429796749660223e-6093j 1.49e-362, 3.9e-1869j
3.680492806402509939e-142 + 1.6397322893137236466e-6089j 3.11e-360, 8.15e-1867j
8.5784624993000953661e-130 + 2.8844549830733139351e-6083j 1.39e-356, 3.63e-1863j
1.0265755448512171348e-103 + 4.4785006317101456305e-6070j 1.44e-349, 3.77e-1856j
2.9756893997212846132e-05 - 7.3238726425346543564e-6018j 7.29e-234, 1.91e-1740j
2.025196184713390139e-107 - 5.9539994104576833353e-6072j 6.29e-351, 1.65e-1857j
3.476235042755912982e-100 - 2.7515798981970993882e-6068j 4.76e-349, 1.25e-1855j
7.3711539762106357275e-32 - 2.6160430602478369015e-6033j 1.61e-310, 4.2e-1817j
2.5221573175814942545e-111 + 6.2835868975119785264e-6074j 1.49e-352, 3.89e-1859j
1.9120331062219129751e-16 - 4.6428415094598324719e-6025j 5.06e-287, 1.33e-1793j
2.682777780554418611e-58 - 5.7276004996010451921e-6047j 5.9e-333, 1.55e-1839j
5.008610859730655769e-28 + 2.7048165008704300177e-6031j 1.21e-306, 3.17e-1813j
4.0021627611329003271e-79 + 1.355044993847130761e-6057j 1.47e-343, 3.84e-1850j
1.0045218637372385576e-14 - 4.2608713761586394591e-6024j 6.83e-285, 1.79e-1791j
9.3568978624482229002e-08 - 7.7960951198100415963e-6020j 1.91e-262, 5.01e-1769j
1.5115452653799409574e-30 + 1.2753227265279706471e-6032j 9.13e-310, 2.39e-1816j
2.8615211226593429634e-29 - 5.9840008022111821616e-6032j 2.56e-308, 6.7e-1815j
1.4426458701016189697e-09 + 4.7591224243901933222e-6021j 1.51e-272, 3.96e-1779j
5.7766775032145114744e-39 + 5.1796898683207963468e-6037j 1.95e-320, 5.1e-1827j
1.3064527958515482021e-50 - 5.0355408764516988569e-6043j 3.19e-330, 8.34e-1837j
1.4087201538826072995e-93 - 6.1662017314158055396e-6065j 6.71e-351, 1.76e-1857j
2.3745068017215157342e-54 - 6.0400224747804393724e-6045j 5.16e-333, 1.35e-1839j
1.8422090336891274262e-115 - 5.0727123743984889061e-6076j 2.71e-358, 7.09e-1865j
3.3358398325655006104e-07 + 2.0120352584112721498e-6019j 2.3e-270, 6.01e-1777j
1.7600848153649673545e-87 - 7.66495705141505973e-6062j 2.8e-349, 7.33e-1856j
1.2169426158546468264e-64 + 3.2644292935344928368e-6050j 5.39e-340, 1.41e-1846j
1.28999074137155961e-11 - 2.6569405073499282243e-6022j 1.02e-287, 2.67e-1794j
2.6606616333637401404e-22 - 2.9985197014731694788e-6028j 1.85e-307, 4.85e-1814j
2.9898567222842417402e-21 + 1.1016324283956379057e-6027j 2.93e-306, 7.68e-1813j
3.1828443698599681819e-10 - 1.8480999124718697033e-6021j 1.5e-285, 3.92e-1792j
1.7012259764723849164e-24 - 2.0128877114803449247e-6029j 2.22e-310, 5.81e-1817j
3.3131938432558072296e-33 + 5.160271851992063005e-6034j 2.63e-319, 6.89e-1826j
1.1206567841159787585e-06 - 5.4086344360355715585e-6019j 6.65e-276, 1.74e-1782j
1.8005264480520404285e-90 + 2.3249131523713100225e-6063j 3.12e-352, 8.15e-1859j
8.1599806478126613764e-82 - 5.8023783920945055387e-6059j 1.13e-349, 2.95e-1856j
1.3703156591898281711e-34 - 9.7789615213105505203e-6035j 2.07e-322, 5.42e-1829j
1.4904945905886336621e-71 - 9.7066053962388899203e-6054j 1.49e-346, 3.9e-1853j
3.0639809973859547047e-19 + 1.3524069408373491382e-6026j 3.39e-308, 8.88e-1815j
6.6105830178290168797e-14 + 1.2409735475128921585e-6023j 2.19e-300, 5.73e-1807j
4.6102238041394124378e-47 - 3.3725197757660599428e-6041j 5.12e-334, 1.34e-1840j
8.1893625258834113042e-49 + 4.2314769452339077312e-6042j 6.77e-335, 1.77e-1841j
1.5211517316932130283e-135 - 3.590319983048389527e-6086j 1.6e-373, 4.18e-1880j
0.0020630461617694831206 + 4.5562876399019116497e-6017j 1.29e-274, 3.39e-1781j
4.4522138019154952779e-42 + 1.2631439095556498929e-6038j 1.53e-331, 4e-1838j
3.5114870113463136796e-69 + 1.5724557809341640358e-6052j 3.99e-347, 1.05e-1853j
1.6803742855141874736e-40 - 8.2751157712325482631e-6038j 1.67e-330, 4.37e-1837j
7.1463689036340190291e-120 + 2.9799305062297207341e-6078j 9.9e-368, 2.59e-1874j
3.5479300069128299057e-06 + 1.5988988593717226397e-6018j 9.53e-294, 2.49e-1800j
2.3383603695184623945e-45 + 2.5536300335693204125e-6040j 5.15e-334, 1.35e-1840j
2.367551042686841502e-12 + 9.7857251372042433321e-6023j 1.4e-307, 3.66e-1814j
1.6072227650834880643e-76 - 2.8638465057947003611e-6056j 1.1e-350, 2.87e-1857j
0.0010085508210297754337 - 3.2048171765498345416e-6017j 1.88e-288, 4.92e-1795j
0.0038961723777712188316 - 6.6616184857788084719e-6017j 7.31e-285, 1.91e-1791j
0.061367412542104840566 - 9.8955621648262439378e-6017j 2.09e-271, 5.48e-1778j
1.2196383651761701573e-25 + 4.9568162207863525544e-6030j 2.46e-322, 6.45e-1829j
5.3483895729721448473e-74 + 5.5107920655998777491e-6055j 9.91e-350, 2.59e-1856j
1.071824391801712049e-43 - 1.8398369695340278387e-6039j 7.29e-334, 1.91e-1840j
0.0067090377989030796855 + 9.602923913146159375e-6017j 2.94e-288, 7.7e-1795j
0.083721052463026655118 + 8.3246007154889296937e-6017j 5.32e-275, 1.39e-1781j
5.205680154581571843e-36 + 1.7785896860616625606e-6035j 1.07e-329, 2.79e-1836j
2.2055477172095552707e-23 + 7.8996983619453593082e-6029j 5.17e-322, 1.35e-1828j
7.0529527394608380227e-67 - 2.352889437287319012e-6051j 1.33e-347, 3.49e-1854j
8.1170921845892045867e-27 - 1.1787552450010658009e-6030j 2.48e-324, 6.5e-1831j
0.042089633705351216236 + 1.1651618845881308973e-6016j 1.05e-288, 2.74e-1795j
0.00045963626111799547946 + 2.3869793051836856495e-6017j 1.24e-300, 3.26e-1807j
2.3916448902445866172e-17 + 1.4705674938993521727e-6025j 6.49e-320, 1.7e-1826j
1.3438687701985314933e-84 + 2.2332050744020219105e-6060j 7.98e-356, 2.09e-1862j
1.8162367339257230837e-62 - 4.2141299034735680105e-6049j 2.13e-346, 5.59e-1853j
4.0825562287195727051e-13 - 3.5259235538783726073e-6023j 8.14e-318, 2.13e-1824j
0.010671498954044703031 - 1.2617177187971387654e-6016j 1.13e-300, 2.96e-1807j
6.6072664510191293935e-11 + 7.0701993691835987369e-6022j 5.63e-316, 1.47e-1822j
2.6842477818708354168e-56 + 6.0637423932837059429e-6046j 1.02e-343, 2.67e-1850j
7.8785272427456989064e-05 + 2.1668931993875051626e-6017j 5.02e-310, 1.32e-1816j
1.8129669080811714359e-37 - 3.1014935505763918655e-6036j 9.42e-333, 2.46e-1839j
0.01687739683969989782 + 1.4052002523214716899e-6016j 5.59e-304, 1.46e-1810j
6.1550058847750785584e-09 - 1.2120751788573221132e-6020j 6.58e-316, 1.72e-1822j
0.10654345891350164814 - 6.9048585585881419302e-6017j 8e-303, 2.09e-1809j
0.00019630579660618896019 - 1.981827151385328337e-6017j 4.68e-310, 1.22e-1816j
3.1328707080044251651e-20 - 3.9203706120747877039e-6027j 2.15e-324, 5.63e-1831j
0.12583956856566180362 + 5.5775590146612784618e-6017j 1.39e-305, 3.63e-1812j
0.11722432835148258153 - 2.0017525084771610392e-6017j 2.08e-306, 5.43e-1813j
2.4727218951393744746e-08 + 3.0698682362816553626e-6020j 1.01e-315, 2.64e-1822j
2.3593235282593741337e-60 + 5.0778303949524660187e-6048j 3.37e-346, 8.82e-1853j
2.7994890246050222885e-18 - 4.5259741858919681608e-6026j 8.9e-324, 2.33e-1830j
1.431563827387329882e-15 + 1.4255634255594452507e-6024j 2.94e-322, 7.7e-1829j
0.13486646316255194946 + 3.1110823992653714042e-6017j 1.57e-312, 4.11e-1819j
0.038488165856602243853 - 2.9896315742454515509e-6018j 3.19e-313, 8.34e-1820j
1.8652797902241630919e-52 + 5.6733569211448414672e-6044j 2.08e-342, 5.46e-1849j
8.2229576054477339395e-97 + 1.4122435851703863823e-6066j 5.75e-365, 1.5e-1871j
0.083920997903970330365 + 1.0365401316477919877e-6017j 1.25e-314, 3.28e-1821j
0.13679041500948411852 - 4.3124616345068160981e-6017j 8.7e-315, 2.28e-1821j
0.027142602537470815256 - 1.3358537003229289619e-6016j 1.69e-315, 4.42e-1822j
1.0585346690552592224e-05 - 6.1685340376844686757e-6018j 3.24e-318, 8.46e-1825j

Download

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