Rule: Q[1, 99]

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)
323.86547251965831271 + 4.6545491303057011534e-5727j 9.68e-2006, 9.68e-2006j
373.06686474531403005 - 3.4417587493652559116e-5738j 2.6e-2011, 2.6e-2011j
311.52838005774523643 - 6.0326257677676276775e-5723j 2.04e-2004, 2.04e-2004j
300.20798874071995255 + 1.1059436017181800874e-5719j 2.9e-2003, 2.9e-2003j
108.80932532788781379 + 1.3224469177245116255e-5724j 1.5e-1993, 1.5e-1993j
29.719168785945047105 - 1.3304269518555146406e-5737j 4.89e-2006, 4.89e-2006j
37.301350584882456501 + 6.9249543301162677779e-5735j 2.45e-2003, 2.45e-2003j
105.01557035965908911 - 2.7370784092707194886e-5725j 1.19e-1993, 1.19e-1993j
94.169847452858836068 - 1.0834870417503882173e-5725j 2.94e-1994, 2.94e-1994j
289.6845374456148247 + 1.6079822216394015126e-5723j 2.95e-2002, 2.95e-2002j
17.287720413659205154 - 1.0524662512278374803e-5746j 2.66e-2012, 2.66e-2012j
60.565675064949319708 - 3.8331304505512268265e-5732j 5.39e-1998, 5.39e-1998j
43.616077958738489738 - 1.0954082114771113393e-5735j 1.45e-2001, 1.45e-2001j
55.395069242419481491 + 1.7274146448953508813e-5733j 6.57e-1999, 6.57e-1999j
24.639306871431281147 - 5.4003488179592372696e-5743j 2.89e-2008, 2.89e-2008j
124.94163858612031704 + 1.0359320391980262701e-5726j 4e-1993, 4e-1993j
35.317381653258614155 + 1.7768698256713268023e-5747j 5.68e-2004, 5.68e-2004j
27.969016585487799386 + 2.8502807908155939334e-5750j 9.25e-2007, 9.25e-2007j
152.35156027298808349 - 4.265554956927465264e-5735j 3.43e-1993, 3.43e-1993j
129.22808598974621074 - 1.5219622838725540994e-5773j 4.66e-1993, 4.66e-1993j
45.84431105191190611 + 4.0299106066089164729e-5832j 5.62e-2001, 5.62e-2001j
147.48792794732098641 - 5.1878649152632380162e-5878j 3.97e-1993, 3.97e-1993j
157.34392569896361044 - 2.8505225865892414832e-5973j 2.4e-1993, 2.4e-1993j
237.37906227212154068 - 1.1562915557982581394e-6057j 1.2e-1997, 1.2e-1997j
215.84266757989185268 + 1.5622721382610550738e-6117j 4.46e-1996, 4.46e-1996j
245.12253901146757443 + 7.1646212267838473159e-6163j 2.83e-1998, 2.83e-1998j
173.14951962960872598 - 2.7651995964192299275e-6205j 8.23e-1994, 8.23e-1994j
261.63516100010364102 - 1.6450539109056991452e-6245j 1.19e-1999, 1.19e-1999j
77.759268576690544567 + 2.3514105993626630885e-6270j 1.12e-1995, 1.12e-1995j
87.364882844398076148 - 1.3429893696342953382e-6265j 9.04e-1995, 9.04e-1995j
337.5827680157293981 + 2.2230823393461296917e-6265j 2.92e-2007, 2.92e-2007j
74.711470387152164258 - 7.3842613346759575459e-6276j 5.2e-1996, 5.2e-1996j
39.345329423957498348 + 8.2523454002239274699e-6302j 9.74e-2003, 9.74e-2003j
142.74811590442015227 - 7.3270191852834504347e-6290j 4.2e-1993, 4.2e-1993j
15.980695857382228125 - 7.4400489552074307532e-6364j 3.58e-2013, 3.58e-2013j
116.6786878444129898 + 1.803279677636177107e-6352j 2.97e-1993, 2.97e-1993j
162.47037767451616103 - 3.2797851294522931241e-6420j 1.85e-1993, 1.85e-1993j
52.909980153538408252 + 2.525405594737336965e-6464j 2.08e-1999, 2.08e-1999j
68.83835084295310997 + 2.7435412803714928708e-6475j 9.75e-1997, 9.75e-1997j
20.063845623662642154 - 5.7297366899217564342e-6525j 1.22e-2010, 1.22e-2010j
120.75954012947059235 + 1.1561160626747890995e-6553j 3.5e-1993, 3.5e-1993j
14.72720173879784658 - 4.1460330085854685767e-6629j 4.43e-2014, 4.43e-2014j
196.4175171343983271 + 2.8247819548653667306e-6637j 6.86e-1995, 6.86e-1995j
50.490419875181545503 - 5.9227335829865212635e-6677j 6.21e-2000, 6.21e-2000j
97.698001218802200133 + 1.5242556874446757312e-6669j 4.51e-1994, 4.51e-1994j
353.37944406064132499 - 8.2912781980739481689e-6673j 5.03e-2009, 5.03e-2009j
209.15544447059467084 + 7.4904034476208877677e-6688j 1.24e-1995, 1.24e-1995j
13.526890094147069521 - 2.5865355677794233467e-6734j 5.63e-2015, 5.63e-2015j
5.8028685852727890121 - 5.2270329368283280886e-6743j 5.96e-2023, 5.96e-2023j
63.253232623415123063 + 7.0855701580729292971e-6717j 1.43e-1997, 1.43e-1997j
178.71570143088509948 + 6.8861747254134870096e-6711j 5.17e-1994, 5.17e-1994j
3.1675983269338018075 + 1.7855692014126130429e-6764j 1.89e-2027, 1.89e-2027j
71.738279630105532068 - 8.6676773502573615734e-6733j 2.23e-1996, 2.23e-1996j
5.0683213709224200121 + 5.1291201432520199534e-6761j 4.73e-2024, 4.73e-2024j
9.2511233185516993769 - 5.5112140632863250954e-6757j 7.72e-2019, 7.72e-2019j
11.284511203202253188 - 1.2680531876948557548e-6754j 7.83e-2017, 7.83e-2017j
3.7508585436064956197 - 2.4206245668746920022e-6764j 2.74e-2026, 2.74e-2026j
84.084437284028853491 - 2.2935469856787924241e-6731j 4.7e-1995, 4.7e-1995j
10.241835242717066379 - 8.6792914648271676152e-6755j 8.18e-2018, 8.18e-2018j
1 - 3.5627124744009435566e-6770j 1.91e-2033, 1.91e-2033j
1.717862694669777856 + 7.7718828855137447455e-6768j 5.93e-2031, 5.93e-2031j
33.392771430758043261 + 4.8890657576413755467e-6741j 1.17e-2004, 1.17e-2004j
253.19546521115440779 + 6.6597620297016281679e-6729j 6.69e-1999, 6.69e-1999j
41.450000334003238834 + 3.2470616850381902362e-6763j 4e-2002, 4e-2002j
18.648641832606983605 + 4.1382509328208713044e-6773j 1.78e-2011, 1.78e-2011j
12.379430835973453969 + 2.9851160970251171998e-6777j 6.62e-2016, 6.62e-2016j
21.533737045585933582 - 5.0147346190383417189e-6771j 8.35e-2010, 8.35e-2010j
8.3121116441054008027 + 4.6829279400399987624e-6782j 7.17e-2020, 7.17e-2020j
101.31254095918165513 + 2.1006157346291860823e-6753j 8.2e-1994, 8.2e-1994j
167.73676874360472553 - 4.0486731661480528504e-6764j 1.3e-1993, 1.3e-1993j
0.71519875566934043837 - 9.5271870858375331328e-6896j 1.06e-2034, 1.06e-2034j
2.6344416859030440746 - 2.0092692926670256202e-6889j 1.32e-2028, 1.32e-2028j
270.48787083013201156 - 2.3341206442272812374e-6853j 2.06e-2000, 2.06e-2000j
190.34050570610387975 + 6.8714094849536018139e-6962j 1.43e-1994, 1.43e-1994j
57.946635703182841248 + 1.4024045358420761675e-7018j 1.86e-1998, 1.86e-1998j
0.15348960066604030065 + 5.1643886768099179759e-7088j 8.72e-2039, 8.72e-2039j
1.3341636010974179478 + 8.638983835233073359e-7082j 3.58e-2032, 3.58e-2032j
66.010406479471738726 + 7.6772003558658645478e-7042j 3.87e-1997, 3.87e-1997j
6.5882104506427248972 - 5.8139199093661564566e-7124j 6.51e-2022, 6.51e-2022j
229.93435134685269827 - 2.4657803195449330263e-7143j 4.43e-1997, 4.43e-1997j
7.424551831564227806 + 2.6146772946141463194e-7285j 7.48e-2021, 7.48e-2021j
0.47951685481741179811 - 3.5020683948234862381e-7301j 5.32e-2036, 5.32e-2036j
23.058741816326494811 + 6.8415266696300301829e-7258j 4.92e-2009, 4.92e-2009j
184.44313414276647546 + 1.8019710256865682337e-7259j 2.84e-1994, 2.84e-1994j
133.6222129701803281 - 3.9067789346734836599e-7339j 4.7e-1993, 4.7e-1993j
90.726097792424725341 + 6.898668651474291438e-7418j 1.63e-1994, 1.63e-1994j
4.3843774849001910432 + 3.5577934646984968725e-7531j 3.78e-2025, 3.78e-2025j
0.060723226673385535988 - 5.1434458971911129643e-7558j 3.49e-2040, 3.49e-2040j
222.76278176949107211 + 2.2023464981236626878e-7510j 1.46e-1996, 1.46e-1996j
279.81220360229113796 - 4.9012165105172378741e-7590j 2.66e-2001, 2.66e-2001j
48.135484232277049507 - 3.4590203066009402971e-7644j 1.9e-2000, 1.9e-2000j
2.1512428630776431776 - 1.6974594257345561736e-7673j 9.66e-2030, 9.66e-2030j
31.526898274754132044 + 2.4521552085890158052e-7649j 2.45e-2005, 2.45e-2005j
112.69618561651350525 - 3.5861911595147821576e-7635j 2.16e-1993, 2.16e-1993j
80.883092268725288853 - 1.1102349307090134084e-7669j 2.44e-1995, 2.44e-1995j
202.685061155413594 - 4.1659145812298415048e-7699j 3.06e-1995, 3.06e-1995j
26.275901174751507592 + 3.0047615067955587585e-7729j 1.74e-2007, 1.74e-2007j
0.29254532443108880274 - 7.0746433896224804035e-7759j 2.24e-2037, 2.24e-2037j
0.011268233891119390087 + 2.6652703127682886654e-7864j 1.34e-2041, 1.34e-2041j
138.12760217102923216 - 1.3662167923849984989e-7713j 4.67e-1993, 4.67e-1993j

Weights

Weight (ball center) Error (ball radius)
2.8789717367221397984e-140 + 4.29675773325684443e-5815j 5.04e-351, 1.63e-1852j
2.2045050923759453996e-161 - 1.0144480793740777375e-5825j 1.16e-357, 3.78e-1859j
5.9733515821433572764e-135 - 2.0454261880457184724e-5812j 1.22e-349, 3.94e-1851j
4.5548059288616067571e-130 + 5.8919559917788866614e-5810j 1.86e-348, 6.03e-1850j
2.1331930637243950419e-47 - 4.7266058263738861451e-5768j 3.44e-309, 1.12e-1810j
2.2042862214461203208e-13 - 3.3833023209029773874e-5750j 2.97e-257, 9.62e-1759j
1.271332524193066249e-16 - 4.5038120903261272992e-5751j 1.49e-266, 4.83e-1768j
9.2494899086765266004e-46 + 3.2935373305497487482e-5767j 6.22e-308, 2.02e-1809j
4.4140404392870161515e-41 - 8.2790646529737403605e-5765j 3.57e-304, 1.16e-1805j
1.5821944124421488644e-125 - 1.1440292292125096497e-5807j 8.53e-349, 2.76e-1850j
4.1415705260656869238e-08 - 6.9375631747606318203e-5748j 5.31e-240, 1.72e-1741j
1.319527396734642788e-26 + 3.9701449064573483581e-5757j 5.74e-288, 1.86e-1789j
2.5096522095918365913e-19 - 5.8348358615690405183e-5753j 1.69e-275, 5.46e-1777j
2.2045067579994363355e-24 + 6.0524614120140982174e-5756j 1.19e-284, 3.87e-1786j
3.2040992181938701601e-11 + 2.8060411494340676735e-5749j 3.04e-255, 9.86e-1757j
2.3187810165850240144e-54 - 1.2674603566391034173e-5771j 1.57e-317, 5.08e-1819j
8.9705978208443781007e-16 + 1.2139237248798683296e-5750j 5.07e-268, 1.64e-1769j
1.2278039326038056211e-12 + 5.3457998329528495141e-5750j 6.36e-260, 2.06e-1761j
3.3663046744296407957e-66 - 1.1610067143389903462e-5777j 6.06e-327, 1.96e-1828j
3.2690100163690172601e-56 + 1.4341298186593176447e-5772j 1.1e-319, 3.58e-1821j
2.7803171993865458116e-20 + 1.5012680518802352169e-5753j 1.38e-280, 4.46e-1782j
4.2474942125706790769e-64 + 1.3620552675437112918e-5776j 9.27e-326, 3.01e-1827j
2.3465028484637059892e-68 + 9.2878974076449015206e-5779j 6.94e-329, 2.25e-1830j
6.1346975943459524923e-103 - 2.8433964318535299983e-5796j 4.02e-348, 1.3e-1849j
1.2395972682445111712e-93 + 1.4328489464478186171e-5791j 9.37e-345, 3.04e-1846j
2.7695150594000575752e-106 + 5.8157075964600951867e-5798j 1.38e-349, 4.47e-1851j
3.4797761393493373339e-75 - 3.1585964837463385721e-5782j 2.87e-336, 9.3e-1838j
2.0402652570410384465e-113 + 1.4619955435051093595e-5801j 1.26e-352, 4.08e-1854j
5.2349664638025988503e-34 + 4.116974095559643863e-5761j 3.96e-309, 1.28e-1810j
3.7942220969208995471e-38 - 2.8177551293596474351e-5763j 9.05e-313, 2.93e-1814j
3.57960389660900388e-146 - 4.5718433690793340075e-5818j 2.04e-365, 6.6e-1867j
1.0760323054858701261e-32 - 2.0190622811296288429e-5760j 3.89e-308, 1.26e-1809j
1.6958715623438923596e-17 - 1.5414188498154370017e-5751j 2.5e-288, 8.1e-1790j
4.7366882557769386159e-62 - 1.5034274659977019392e-5775j 7.03e-329, 2.28e-1830j
1.4687562771718817961e-07 + 1.2325132307298735854e-5747j 6.87e-269, 2.23e-1770j
8.5610143411082727255e-51 - 8.5122014658792518144e-5770j 2.1e-322, 6.81e-1824j
1.4309702269939976785e-70 - 6.9544781147045211372e-5780j 1.48e-334, 4.8e-1836j
2.576547910161467423e-23 - 2.4098012940763902758e-5755j 4.53e-300, 1.47e-1801j
3.637609008464766124e-30 - 4.3925900732551890957e-5759j 5.38e-308, 1.74e-1809j
2.7892784622258893063e-09 - 2.057793580283552976e-5748j 1.7e-278, 5.52e-1780j
1.4820087560265988844e-52 + 1.0645831413901534975e-5770j 1.55e-323, 5.03e-1825j
4.9300093451161138075e-07 - 2.1408915727158951867e-5747j 4.55e-273, 1.48e-1774j
3.0709033482480755511e-85 - 2.5316269008545588313e-5787j 6.55e-345, 2.12e-1846j
2.8194216159946557549e-22 + 9.557365577962831595e-5755j 2.9e-300, 9.4e-1802j
1.3276629404343248823e-42 + 1.4141798395627075286e-5765j 2.01e-318, 6.51e-1820j
5.8361103697899805211e-153 + 1.7535823853606963742e-5821j 2.39e-372, 7.76e-1874j
9.6145073610439643968e-91 - 4.1462962032383960984e-5790j 1.92e-347, 6.23e-1849j
1.5665785722482957877e-06 + 3.6344608525938125824e-5747j 6.6e-278, 2.14e-1779j
0.0022940835740613174347 + 1.056458383561329376e-5745j 8.55e-264, 2.77e-1765j
9.2126940694458976815e-28 - 8.2533385336621115718e-5758j 3.68e-308, 1.19e-1809j
1.3691610122145438794e-77 + 1.9029480556656158572e-5783j 7.22e-341, 2.34e-1842j
0.023502088655492899612 + 3.0963374573204518513e-5745j 3.05e-255, 9.9e-1757j
2.0524262214857838682e-31 + 9.5743237196620067376e-5760j 3.44e-311, 1.11e-1812j
0.0044630706704975448681 - 1.4385237038121888773e-5745j 2.64e-264, 8.56e-1766j
9.26262535528680682e-05 + 2.3837222360271899772e-5746j 2e-275, 6.49e-1777j
1.3429972363258917168e-05 + 9.7641003852939360693e-5747j 1.39e-278, 4.52e-1780j
0.014295044514066243105 - 2.4642417859745550151e-5745j 7.75e-261, 2.51e-1762j
9.8451339484951820143e-37 + 1.5404704002484330206e-5762j 1.67e-316, 5.42e-1818j
3.6240849350849824636e-05 - 1.5441972724334209867e-5746j 2.04e-277, 6.63e-1779j
0.1138401941460852523 - 6.1216851207804033724e-5745j 9.61e-252, 3.12e-1753j
0.073307983972695946519 - 5.1534671891392693591e-5745j 9.61e-252, 3.12e-1753j
5.9613557544615177939e-15 - 1.6772399753558549256e-5750j 5.56e-297, 1.8e-1798j
9.0163552311185279744e-110 - 1.0099919774440742032e-5799j 2.17e-357, 7.02e-1859j
2.1278587396175372961e-18 + 2.6317984888440571768e-5752j 2.09e-300, 6.78e-1802j
1.1050608683233946425e-08 + 3.8196544843488666844e-5748j 2.94e-288, 9.54e-1790j
4.7134711891433594931e-06 - 6.0279182839584079164e-5747j 1.61e-282, 5.22e-1784j
6.6580571811089143606e-10 + 1.0848766125451549416e-5748j 4.08e-291, 1.32e-1792j
0.00022422465869378211691 - 3.5906361054191577772e-5746j 3.96e-279, 1.28e-1780j
3.6628275206841260847e-44 - 2.1983735488401564368e-5766j 1.55e-322, 5.03e-1824j
7.5903547324374339828e-73 + 4.8595035669020353073e-5781j 6.42e-340, 2.08e-1841j
0.12725848716902140386 + 6.2602183293210422867e-5745j 5.23e-264, 1.69e-1765j
0.03646464195919907387 - 3.7818492723750107938e-5745j 2.04e-271, 6.6e-1773j
3.0660297389022584622e-117 - 1.7240021922826817815e-5803j 3.53e-362, 1.14e-1863j
1.2979794437395612019e-82 + 5.4122673358324669136e-5786j 2.07e-346, 6.71e-1848j
1.7643256610223381128e-25 - 1.6248052942739921839e-5756j 7.78e-312, 2.52e-1813j
0.099099571379718966224 - 4.2438922910216843015e-5745j 5.23e-272, 1.69e-1773j
0.09452799573917709376 + 5.7245311901814964782e-5745j 1.03e-273, 3.33e-1775j
5.9981375396860973722e-29 + 1.9478828411324526386e-5758j 1.78e-314, 5.76e-1816j
0.0011160757786581818985 - 7.5614158470297485629e-5746j 1.87e-287, 6.06e-1789j
1.0100768107429565475e-99 + 1.1984971014729129613e-5794j 3.46e-355, 1.12e-1856j
0.00051406909764209412649 + 5.2763007030953045135e-5746j 1.17e-289, 3.79e-1791j
0.13077298720482562775 - 6.0500141449708029471e-5745j 1.11e-278, 3.61e-1780j
1.5024693886157470178e-10 - 5.5921604355550789137e-5749j 8.55e-301, 2.77e-1802j
4.5878177210303841352e-80 - 1.0584870932632485826e-5784j 2.24e-345, 7.27e-1847j
4.1389119618022628566e-58 - 1.5395038190160393167e-5773j 8.47e-335, 2.75e-1836j
1.3486945734621435807e-39 + 4.9366141301974508155e-5764j 3.1e-324, 1.01e-1825j
0.0082144504218879592002 + 1.9081211249795428626e-5745j 2.77e-293, 8.99e-1795j
0.066340673917266414365 + 2.6089832843578822167e-5745j 8.28e-289, 2.68e-1790j
1.2678872453852275869e-96 - 4.4109305172685110953e-5793j 4.27e-354, 1.39e-1855j
2.8882832411169807405e-121 + 1.6087870837526917038e-5805j 7.73e-366, 2.51e-1867j
2.8910657248228263283e-21 - 3.7588468461142698901e-5754j 2.46e-314, 7.97e-1816j
0.053314501323753556255 + 4.4844589254000524523e-5745j 1.22e-296, 3.97e-1798j
3.733201127148368298e-14 + 3.2874881259980214363e-5750j 3.09e-310, 1e-1811j
4.4825983316347073164e-49 + 6.4892295589464924217e-5769j 1.34e-330, 4.34e-1832j
2.3600777073958093009e-35 - 8.1084294222441712435e-5762j 2.7e-323, 8.74e-1825j
6.0105794963780682102e-88 + 1.0774143117860304635e-5788j 1.38e-350, 4.46e-1852j
6.4546930694304717817e-12 - 1.3441901758333751479e-5749j 1.12e-311, 3.61e-1813j
0.12153101616234952217 + 5.4011142052485828386e-5745j 3.22e-305, 1e-1806j
0.028769566541683205481 - 8.430875915461660828e-5746j 6.67e-306, 2.07e-1807j
4.68950273020096498e-60 + 1.564951840859838255e-5774j 1.5e-336, 4.86e-1838j

Download

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