Rule: Q[2, 85]

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)
273.81641365990624408 + 3.1897537170836390753e-5341j 8.89e-2010, 8.89e-2010j
320.41624548009292669 - 8.9684809899933167332e-5355j 5.6e-2015, 5.6e-2015j
251.52531220107717326 - 8.8351732877128131894e-5366j 1.72e-2007, 1.72e-2007j
301.73432630008644949 + 3.9164617583298296173e-5379j 7.96e-2013, 7.96e-2013j
286.77787789764020177 - 1.045569200696653204e-5386j 3.8e-2011, 3.8e-2011j
63.738553462731882151 + 1.2851996963113957168e-5433j 3.27e-2002, 3.27e-2002j
262.18147481175050668 + 9.8940508519731586121e-5538j 1.44e-2008, 1.44e-2008j
133.75581366696418707 - 1.7451027215377394463e-5643j 9.72e-2000, 9.72e-2000j
44.860005194710322041 - 6.3754892762488259971e-5694j 2.99e-2005, 2.99e-2005j
160.74679610347671338 - 1.6711188057315963507e-5718j 1.11e-2000, 1.11e-2000j
27.795959705686264389 + 8.2982928674567269813e-5758j 5.77e-2010, 5.77e-2010j
10.21267211628408987 - 2.7949718984127549989e-5768j 1.07e-2019, 1.07e-2019j
20.91190478789978248 - 7.6278679227889234037e-5762j 7.39e-2013, 7.39e-2013j
76.378307796337947169 + 4.8560531836313866189e-5747j 5.96e-2001, 5.96e-2001j
13.757724498238241449 - 4.8700961299901993255e-5788j 5.98e-2017, 5.98e-2017j
179.25431666071751855 - 9.193802660058538808e-5770j 1.1e-2001, 1.1e-2001j
55.165990832265479277 - 1.8670258428516851032e-5793j 2.38e-2003, 2.38e-2003j
42.474925665413768519 + 1.7427872238990307927e-5795j 1.04e-2005, 1.04e-2005j
102.22244807390416449 + 1.2359873033280917587e-5788j 1.11e-1999, 1.11e-1999j
83.253119318632728821 + 1.836560485354347209e-5803j 2.03e-2000, 2.03e-2000j
2.8341896862686306771 + 1.6865030215527903566e-5851j 7.9e-2029, 7.9e-2029j
57.940685062967498376 + 1.180084348927181914e-5821j 5.93e-2003, 5.93e-2003j
232.37861376118252053 - 4.6979655575467716245e-5835j 1.07e-2005, 1.07e-2005j
215.37745588245630559 + 3.5736931623507046213e-5891j 2.93e-2004, 2.93e-2004j
12.514681069354138208 - 5.0600913482404068819e-5954j 7.31e-2018, 7.31e-2018j
144.03970264675594923 - 1.1666080042877324342e-5958j 5.23e-2000, 5.23e-2000j
5.5152280978324484031 - 1.0815791962262173604e-6029j 1.23e-2024, 1.23e-2024j
241.63757384262492498 - 1.5179176944200883826e-6004j 1.5e-2006, 1.5e-2006j
25.975637144996450045 + 5.1994571917503296154e-6047j 1.17e-2010, 1.17e-2010j
40.163954715436900012 - 8.4685795968829881408e-6037j 2.77e-2006, 2.77e-2006j
11.333132161197038208 + 1.4894467637778111486e-6067j 9.33e-2019, 9.33e-2019j
7.2143209775140745686 + 8.6702914313613553566e-6071j 1.25e-2022, 1.25e-2022j
1.1312336912978502806 - 7.1956465442812239568e-6083j 3.53e-2033, 3.53e-2033j
86.837569604151477895 - 1.3601129069829750452e-6083j 2.9e-2000, 2.9e-2000j
22.534311039292506774 + 1.7560503165588356071e-6162j 4.1e-2012, 4.1e-2012j
33.664840805714787699 - 5.4994794579346144338e-6151j 5.39e-2008, 5.39e-2008j
90.523661092529163014 + 8.9457620768333022183e-6195j 4.24e-2000, 4.24e-2000j
0.84016511752394913613 - 1.3556222368420371349e-6310j 2.33e-2034, 2.33e-2034j
6.334928173461732621 + 4.4427605773697696681e-6294j 1.25e-2023, 1.25e-2023j
124.07885314176489877 - 2.0025977270040656861e-6275j 1.42e-1999, 1.42e-1999j
154.99410454699223211 - 1.2158947123215167925e-6323j 2.06e-2000, 2.06e-2000j
16.430086262040016328 + 3.1454792898172402922e-6367j 2.9e-2015, 2.9e-2015j
24.221994555140937444 - 4.0212076860175465864e-6364j 2.35e-2011, 2.35e-2011j
185.89176613426810226 - 3.5630217473996805302e-6351j 4.38e-2002, 4.38e-2002j
47.320370773927445758 - 1.5374665763487880413e-6372j 9.97e-2005, 9.97e-2005j
223.64964150563838515 + 8.1394935982914781254e-6367j 5.89e-2005, 5.89e-2005j
79.767556092340366475 + 3.0826641771357294051e-6372j 1.05e-2000, 1.05e-2000j
73.082968483113589298 + 1.0900889954053036932e-6379j 3.15e-2001, 3.15e-2001j
1.8598864667245530874 - 6.3589252886916231643e-6424j 4.94e-2031, 4.94e-2031j
69.879284345445123632 - 2.9586029374881897224e-6392j 1.52e-2001, 1.52e-2001j
19.354131509718847801 + 8.8148282725309996641e-6447j 1.21e-2013, 1.21e-2013j
192.79564071515899678 - 9.6385397469516549042e-6433j 1.51e-2002, 1.51e-2002j
138.81823257763659816 - 4.1186707631693311117e-6492j 7.61e-2000, 7.61e-2000j
166.69844267106779803 + 1.4300347262642488874e-6550j 5.79e-2001, 5.79e-2001j
110.5903499074125966 + 2.5339072384583753978e-6596j 1.5e-1999, 1.5e-1999j
35.759939665554210437 - 5.1104793673546714343e-6628j 2.09e-2007, 2.09e-2007j
128.84494678955372777 - 2.953426727053490373e-6619j 1.17e-1999, 1.17e-1999j
49.857266881175473695 + 3.6732245448293667085e-6632j 3.03e-2004, 3.03e-2004j
98.212804246125232268 - 5.3039637352006693651e-6626j 8.28e-2000, 8.28e-2000j
1.466962545065950051 - 4.6680146661718392183e-6662j 4.47e-2032, 4.47e-2032j
31.639734515536973848 - 1.4666265453891118828e-6638j 1.27e-2008, 1.27e-2008j
199.9905284784078523 - 5.7964450833180870776e-6630j 4.61e-2003, 4.61e-2003j
106.34696717093487185 + 2.5521114726761144052e-6641j 1.3e-1999, 1.3e-1999j
94.314347857251432278 + 1.0825725318628346475e-6672j 6.33e-2000, 6.33e-2000j
29.683723981188203691 + 8.7431934912917293529e-6705j 2.6e-2009, 2.6e-2009j
4.7551410584629453901 + 5.1525917319860392152e-6720j 1.14e-2025, 1.14e-2025j
66.765141224519800455 + 2.8152925965453015705e-6694j 6.88e-2002, 6.88e-2002j
60.797653928063719959 + 1.0758607379359832219e-6720j 1.4e-2002, 1.4e-2002j
0.20174278709177494999 + 6.9229333508418959217e-6818j 2.03e-2038, 2.03e-2038j
8.1535764578403712015 + 2.0584332010593019404e-6780j 1.25e-2021, 1.25e-2021j
2.315646920107089163 + 1.5390066516055480426e-6810j 6.37e-2030, 6.37e-2030j
114.95692045409597084 + 2.7093650492826772123e-6800j 1.5e-1999, 1.5e-1999j
9.152930780088460631 - 2.7882287734844848325e-6877j 1.12e-2020, 1.12e-2020j
172.86248108284147884 - 2.0871545080068255147e-6908j 2.59e-2001, 2.59e-2001j
3.4142135623730950488 - 3.7517671136585740762e-7004j 9.26e-2028, 9.26e-2028j
0.015716050110067403418 + 6.6754967440951980686e-7020j 1.03e-2041, 1.03e-2041j
37.925977815354803303 + 5.4748151219293574072e-6979j 8.36e-2007, 8.36e-2007j
149.42855751842131039 + 1.3152546488628856208e-7065j 3.39e-2000, 3.39e-2000j
207.50586749795961727 - 3.0524025135075929369e-7171j 1.24e-2003, 1.24e-2003j
52.472009462612130055 - 5.9226876578040848315e-7253j 8.33e-2004, 8.33e-2004j
4.054718678079677722 + 1.1048993679809725561e-7315j 8.92e-2027, 8.92e-2027j
0.5857864376269049512 - 7.7510009481120573068e-7331j 1.31e-2035, 1.31e-2035j
15.062701993493282628 - 3.4462095241499593485e-7296j 4.23e-2016, 4.23e-2016j
0.082566097341622897616 - 1.4217228048128230316e-7339j 5.11e-2040, 5.11e-2040j
119.45137972035267189 - 5.9714930597414093517e-7311j 1.49e-1999, 1.49e-1999j
17.860383057724812417 + 1.481732702429070988e-7360j 1.96e-2014, 1.96e-2014j
0.37093410995890393508 - 2.626218239591256527e-7383j 5.18e-2037, 5.18e-2037j

Weights

Weight (ball center) Error (ball radius)
1.4798702221638719491e-118 - 2.3688911175208662118e-5459j 8.32e-375, 1.92e-1880j
1.537886983158628341e-138 - 9.5410695833038678213e-5471j 3.58e-381, 8.26e-1887j
5.9486806440887541729e-109 - 1.4012708924979252989e-5455j 1.75e-372, 4.03e-1878j
1.4860103540223532048e-130 + 1.6135147081019609578e-5466j 3.99e-379, 9.2e-1885j
3.9257520954613294077e-124 - 5.7951433554394123384e-5463j 3.57e-377, 8.23e-1883j
6.2146335819560348829e-28 + 9.6554073414337273389e-5416j 6.5e-329, 1.5e-1834j
1.518600833980657388e-113 + 1.3283827835698008074e-5457j 3.73e-374, 8.61e-1880j
4.0578233256494206292e-58 + 8.0144570535821944512e-5431j 9.86e-355, 2.27e-1860j
7.976544867867774565e-20 - 1.2040475826992547723e-5411j 8.41e-319, 1.94e-1824j
9.0305647837109371641e-70 - 1.349318381035565733e-5436j 8.26e-361, 1.9e-1866j
1.5720176638180111663e-12 - 6.403984167660564048e-5408j 7.33e-304, 1.69e-1809j
4.0007012024196189477e-05 - 5.2843591857710311717e-5404j 2.64e-272, 6.09e-1778j
1.316643778099608044e-09 - 2.1026514149553508427e-5406j 4.99e-295, 1.15e-1800j
2.2558831907151398965e-33 + 1.7835973004539897642e-5418j 4.69e-337, 1.08e-1842j
1.3497186273772263596e-06 + 8.269915978020642775e-5405j 5.3e-283, 1.22e-1788j
9.2154563255431514831e-78 + 1.5424519228304836734e-5440j 5.05e-365, 1.16e-1870j
3.0097235630201201524e-24 - 6.9557737120635175845e-5414j 1.23e-326, 2.83e-1832j
8.3954043894208193258e-19 + 3.9778298645628832852e-5411j 1.45e-318, 3.35e-1824j
1.6389645119740511512e-44 - 4.7662402069811650435e-5424j 8.8e-348, 2.03e-1853j
2.4658432298935630292e-36 + 5.8458028409961270024e-5420j 1.19e-340, 2.75e-1846j
0.032291389820280500502 + 3.5098307974175109933e-5402j 8.85e-246, 2.04e-1751j
1.933060940568019515e-25 + 1.7407269561897062747e-5414j 1.5e-328, 3.46e-1834j
1.0777711906925286047e-100 - 1.0559412722607668647e-5451j 1.04e-374, 2.4e-1880j
2.3404030448244820854e-93 - 3.6254019938852738605e-5448j 5.42e-373, 1.25e-1878j
4.4517068244026153146e-06 - 1.5783416772874595444e-5404j 2.04e-291, 4.71e-1797j
1.4754711143905767514e-62 + 5.0234692508997299333e-5433j 1.25e-360, 2.88e-1866j
0.0031793123450820554243 + 6.8317860390901960206e-5403j 4.24e-273, 9.78e-1779j
1.0922625939830085198e-104 + 1.3421873788682240927e-5453j 1.03e-375, 2.37e-1881j
9.3543675104920802066e-12 + 1.6080477529068579195e-5407j 3.06e-312, 7.05e-1818j
8.2009195797706932156e-18 - 1.2675290339846686672e-5410j 3.65e-323, 8.43e-1829j
1.377640274225565881e-05 + 2.9283375777384266499e-5404j 1.1e-291, 2.54e-1797j
0.00066921008983417747303 + 2.6458167189379320643e-5403j 2e-282, 4.61e-1788j
0.10039288332770036534 + 9.6810840160894222811e-5402j 3.36e-242, 7.76e-1748j
7.0372458080846678959e-38 - 9.8502681370609974889e-5421j 2.5e-345, 5.78e-1851j
2.7055393323774118278e-10 + 9.2103078420274657005e-5407j 5.99e-310, 1.38e-1815j
4.9363038002361197747e-15 + 3.3202168691355681565e-5409j 2.82e-320, 6.5e-1826j
1.8142568083097876673e-39 + 1.5794990918616506248e-5421j 5.04e-347, 1.16e-1852j
0.1175928869500905056 - 9.1127377231661409424e-5402j 1.03e-250, 2.38e-1756j
0.0015064392382337035563 - 4.3022939403297931318e-5403j 1.59e-284, 3.66e-1790j
6.0946519210890483563e-54 + 9.5441872388390556043e-5429j 6.07e-358, 1.4e-1863j
2.7512035617400642021e-67 + 2.2828456308328638928e-5435j 1.84e-364, 4.25e-1870j
1.0238713197408860495e-07 + 2.0817408302030775989e-5405j 2.66e-307, 6.13e-1813j
5.2022086496468484427e-11 - 3.9100163898793609898e-5407j 1.17e-314, 2.71e-1820j
1.2549374071108099833e-80 - 6.0102431546695288961e-5442j 5.07e-371, 1.17e-1876j
7.0256923288097033791e-21 + 3.513105571323288296e-5412j 1.18e-331, 2.73e-1837j
6.2965557237453634668e-97 + 6.7966171700490632624e-5450j 1.43e-376, 3.29e-1882j
7.8265254507896765946e-35 - 3.3058365398458369771e-5419j 4.41e-345, 1.02e-1850j
5.9188805695826161606e-32 - 9.1916645819926979442e-5418j 1.42e-343, 3.28e-1849j
0.066023522992853099846 + 6.8608883005381404839e-5402j 8.37e-282, 1.93e-1787j
1.4167826694226340583e-30 + 4.5294614042490975638e-5417j 7.72e-343, 1.78e-1848j
5.998821547489949536e-09 + 4.6541196809925337641e-5406j 1.75e-317, 4.04e-1823j
1.3115752540469004878e-83 + 2.070106532110191457e-5443j 7.88e-374, 1.82e-1879j
2.6486458263544928417e-60 - 6.5924435003384600585e-5432j 1.91e-363, 4.42e-1869j
2.4318274705750159763e-72 + 7.2563685021386534302e-5438j 3.72e-369, 8.59e-1875j
4.0282494098060774339e-48 - 7.5468566573556158348e-5426j 1.04e-358, 2.39e-1864j
6.2822901792986369104e-16 - 1.1574087166320591578e-5409j 2.35e-334, 5.42e-1840j
5.3451891743893795004e-56 - 9.0570036698332522908e-5430j 4.9e-362, 1.13e-1867j
5.7298266928430427845e-22 - 9.874542570815784774e-5413j 1.38e-340, 3.19e-1846j
8.7841206834979054979e-43 + 3.4798889024716047345e-5423j 1.79e-355, 4.13e-1861j
0.083635047260593932241 - 8.7072380184278561827e-5402j 6.73e-302, 1.55e-1807j
3.6139412130865662191e-14 - 9.2062391177005393101e-5409j 1.32e-334, 3.04e-1840j
1.0268069950169651381e-86 - 6.2401350789112242946e-5445j 1.04e-377, 2.4e-1883j
2.7265520521024093917e-46 + 6.1732807104002595168e-5425j 6.49e-358, 1.5e-1863j
4.2129387486669257701e-41 - 2.4068244602324043631e-5422j 1.54e-354, 3.55e-1860j
2.4672847917553125439e-13 + 2.4685562126758569682e-5408j 4.01e-336, 9.24e-1842j
0.0062857365593000280902 - 1.0607257916907115031e-5402j 4.61e-322, 1.06e-1827j
3.100361106933561369e-29 - 2.1364807895478570785e-5416j 3.29e-348, 7.59e-1854j
1.1431682760500156547e-26 - 4.1846265893963125737e-5415j 7.15e-347, 1.65e-1852j
0.11827677576229975435 + 3.2738697074151135731e-5402j 5.07e-317, 1.17e-1822j
0.00027886076060372806715 - 1.5872603729353603709e-5403j 9.56e-329, 2.2e-1834j
0.048103517931769177926 - 5.0049669407365711067e-5402j 2.9e-321, 6.7e-1827j
5.2628123573538942779e-50 + 8.6904110294160953102e-5427j 2.87e-361, 6.61e-1867j
0.00010903283779330460507 + 9.2804934234228048286e-5404j 1.64e-330, 3.79e-1836j
5.3015747480810039967e-75 - 3.5295579834324733182e-5439j 2.92e-374, 6.74e-1880j
0.020083261661110859311 - 2.4028388686722411142e-5402j 2.41e-328, 5.56e-1834j
0.039677441997292910021 + 4.7099659527724394516e-5403j 6.21e-326, 1.43e-1831j
7.4428996164557463203e-17 + 3.8978578593572718296e-5410j 1.02e-342, 2.36e-1848j
6.9571380868575679016e-65 - 3.5325793620298295699e-5434j 2.49e-369, 5.75e-1875j
5.8491997282112060397e-90 + 1.6275621456809509777e-5446j 7.86e-382, 1.81e-1887j
4.3213250019916737497e-23 + 2.671992837991189307e-5413j 1.33e-347, 3.07e-1853j
0.011627184643143736329 + 1.6124881391944463539e-5402j 2.85e-334, 6.57e-1840j
0.13118274837827963747 + 7.3475045620809486681e-5402j 2.69e-333, 6.2e-1839j
3.8387549877765011365e-07 - 4.2102629282406669355e-5405j 2.96e-339, 6.82e-1845j
0.085873094549274093349 - 1.6558070587722513321e-5402j 2.31e-334, 5.32e-1840j
6.0519708760777432032e-52 - 9.4054342477657119982e-5428j 4.23e-363, 9.77e-1869j
2.5601225769339010623e-08 - 9.9922650096856091655e-5406j 4.1e-340, 9.46e-1846j
0.13315154854113343126 - 5.2300756495817972752e-5402j 3.42e-335, 7.85e-1841j

Download

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