Rule: Q[1, 3, 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)
333.66125081806382836 - 6.0945199079626640565e-6039j 1.91e-2010, 1.91e-2010j
318.18544034466022578 - 3.8693408410813390777e-6036j 1.15e-2008, 1.15e-2008j
352.96404195460949004 + 2.8221686375906832476e-6047j 1.09e-2012, 1.09e-2012j
304.75635187079270179 - 1.5291026310513220009e-6033j 3.05e-2007, 3.05e-2007j
168.97384514503259002 - 2.0122290789190432214e-6054j 2.26e-1996, 2.26e-1996j
13.03271658400975535 - 4.131565418882597789e-6126j 5.12e-2016, 5.12e-2016j
147.75080131651276562 - 1.4414042283306995759e-6104j 1.1e-1995, 1.1e-1995j
96.290301737019362203 - 9.2662316302440461517e-6176j 3.97e-1996, 3.97e-1996j
138.00218239947583917 + 2.315097694025244599e-6248j 1.74e-1995, 1.74e-1995j
25.952233173339263399 - 5.3207652917215496969e-6321j 1.17e-2008, 1.17e-2008j
69.830323442000379406 - 2.7779789372090953937e-6312j 2.37e-1998, 2.37e-1998j
37.234343600305512891 - 1.1337868716319798641e-6343j 1.19e-2004, 1.19e-2004j
213.10042553045396429 + 2.9204886091967067162e-6375j 6.85e-1999, 6.85e-1999j
55.885417406791551964 + 3.6580650595003693987e-6418j 2.25e-2000, 2.25e-2000j
292.68662884075102202 - 3.855298380952156278e-6429j 5.94e-2006, 5.94e-2006j
235.74042237740172657 - 2.5589874756763536405e-6475j 1.29e-2000, 1.29e-2000j
75.943961223775541697 + 8.2762232668029983729e-6502j 1.11e-1997, 1.11e-1997j
199.40824472044961506 - 1.302126349881618775e-6518j 5.94e-1998, 5.94e-1998j
33.226260123401965912 - 5.2111230820443083501e-6553j 6.63e-2006, 6.63e-2006j
79.121592880672001815 - 2.3963718321749084052e-6543j 2.17e-1997, 2.17e-1997j
48.384727982577228719 + 1.8235599111929936405e-6563j 8.06e-2002, 8.06e-2002j
180.5668453102191441 - 3.5696583593769280123e-6565j 6.67e-1997, 6.67e-1997j
61.240739593101939502 - 2.5236412805107460381e-6598j 1.56e-1999, 1.56e-1999j
220.34141401145439366 - 4.0539037160959286289e-6594j 2.08e-1999, 2.08e-1999j
174.68118461445530969 - 9.6920095745920670364e-6608j 1.23e-1996, 1.23e-1996j
46.022118176301439717 + 8.9265695761935778178e-6629j 2.37e-2002, 2.37e-2002j
43.726669960667922282 + 8.5973544973545617977e-6629j 6.91e-2003, 6.91e-2003j
64.028407951548747647 + 1.2684672157161938856e-6624j 3.73e-1999, 3.73e-1999j
85.727128731083265217 + 1.3421659489500673841e-6621j 7.89e-1997, 7.89e-1997j
142.80975448887621355 + 2.2600154214046112373e-6622j 1.44e-1995, 1.44e-1995j
163.43527521314440099 + 9.1981693151338803285e-6652j 3.71e-1996, 3.71e-1996j
35.198803145831572298 - 1.8988816159802893266e-6694j 2.66e-2005, 2.66e-2005j
5.3514926872733469054 + 3.1619970353405638143e-6714j 8.11e-2024, 8.11e-2024j
19.634665990318761633 - 1.8696634548895122798e-6701j 9.79e-2012, 9.79e-2012j
58.526824249779044699 - 2.5384698571346361264e-6685j 5.55e-2000, 5.55e-2000j
133.32281646758055944 - 8.1962044811984906083e-6688j 1.88e-1995, 1.88e-1995j
8.7556402755219753057 - 1.456701380623982116e-6756j 7.92e-2020, 7.92e-2020j
82.3820384254804059 + 7.5429901533675876397e-6731j 4.22e-1997, 4.22e-1997j
206.12981926826499919 + 4.9964845344356091836e-6803j 2e-1998, 2e-1998j
10.784134929976865891 - 5.0387861267756402885e-6902j 6.6e-2018, 6.6e-2018j
18.200676252374821016 - 3.8528688591150974447e-6896j 1.38e-2012, 1.38e-2012j
89.158805909280311027 - 2.5718388154841626266e-6903j 1.38e-1996, 1.38e-1996j
29.467333571905964156 + 3.2305721338531613074e-6992j 2.94e-2007, 2.94e-2007j
3.9750174695909860102 - 3.4176699032918727935e-7030j 7.32e-2026, 7.32e-2026j
271.33682825931776579 - 1.7796111365415095453e-7137j 7.96e-2004, 7.96e-2004j
243.96538208632418234 + 1.1630192422655389324e-7292j 2.61e-2001, 2.61e-2001j
50.81546332312872651 + 4.8798391720920398402e-7362j 2.65e-2001, 2.65e-2001j
261.69716887547733718 - 6.9152737726165809789e-7416j 6.94e-2003, 6.94e-2003j
281.61883362916459247 + 1.9080638927192617959e-7474j 8.1e-2005, 8.1e-2005j
107.69300772114227456 - 2.1792414205189360811e-7527j 9.93e-1996, 9.93e-1996j
1.948038458417908552 - 5.1482994957461646376e-7594j 7.46e-2030, 7.46e-2030j
14.240314837033824304 + 5.7988883192356171192e-7579j 3.94e-2015, 3.94e-2015j
53.315337751661903099 - 6.0242898946869562812e-7560j 7.3e-2001, 7.3e-2001j
92.679132504639947148 + 3.1132153735250716473e-7588j 2.38e-1996, 2.38e-1996j
7.8232631436879996743 - 6.4343576114741500617e-7650j 7.96e-2021, 7.96e-2021j
27.679618094949116983 + 4.8322009592985693134e-7636j 5.95e-2008, 5.95e-2008j
227.87801129130552305 + 1.4825372073611925266e-7623j 5.44e-2000, 5.44e-2000j
99.99464894374368896 + 1.0101065540961215276e-7632j 5.48e-1996, 5.48e-1996j
21.126325047279132443 - 7.4020186183314595542e-7654j 6.4e-2011, 6.4e-2011j
31.315997731748091876 + 1.365820420309558316e-7650j 1.41e-2006, 1.41e-2006j
111.69252411492975502 - 3.5501126022527974531e-7638j 1.26e-1995, 1.26e-1995j
1.6293059199236552525 + 8.5281742019249232548e-7702j 9.99e-2031, 9.99e-2031j
39.333634374144967378 - 3.6592604503930259533e-7676j 4.66e-2004, 4.66e-2004j
128.76682243835169656 + 1.1629428305340241684e-7665j 2.13e-1995, 2.13e-1995j
1.3137924939849685003 - 1.537957494247567715e-7748j 7.89e-2032, 7.89e-2032j
2.3432094002181817945 - 1.0411081774450169553e-7744j 6.35e-2029, 6.35e-2029j
41.497466265533012324 + 5.7491480673565906106e-7711j 1.84e-2003, 1.84e-2003j
186.64155252779222406 - 2.3321348742555770858e-7710j 3.26e-1997, 3.26e-1997j
4.6359332858372246184 + 8.0410527206087447928e-7786j 7.39e-2025, 7.39e-2025j
22.676131840131440405 + 5.1269321599524164967e-7771j 3.57e-2010, 3.57e-2010j
0.28988861380303484764 + 5.7596197669383965309e-7799j 2.11e-2037, 2.11e-2037j
0.056897625001077184683 + 1.9499981415387157155e-7800j 2.72e-2040, 2.72e-2040j
124.32975136638467191 + 8.6726975040307737007e-7754j 1.99e-1995, 1.99e-1995j
152.83108334437056839 - 3.776885340095900625e-7799j 8.48e-1996, 8.48e-1996j
2.8232520098685572178 + 5.5997190995730921407e-7875j 6.39e-2028, 6.39e-2028j
120.00749762668925206 + 3.7444641814643365948e-7841j 1.78e-1995, 1.78e-1995j
6.1212813136103333861 - 7.0685004737940198954e-7900j 8.48e-2023, 8.48e-2023j
16.823902700822268187 + 7.2412551049672749501e-7891j 2.08e-2013, 2.08e-2013j
1 + 1.2450937318568754934e-7910j 3.36e-2033, 3.36e-2033j
9.7425175451747513675 - 1.9809397853061712942e-7896j 7.43e-2019, 7.43e-2019j
72.847415546791729062 + 4.8658106731597141176e-7872j 5.25e-1998, 5.25e-1998j
0.47994174263413944232 + 1.4382889880019851307e-7946j 6.51e-2036, 6.51e-2036j
11.880766717394457692 + 1.8594355926523539824e-7928j 6.07e-2017, 6.07e-2017j
115.79626274975633684 + 1.9133177739014872182e-7905j 1.61e-1995, 1.61e-1995j
3.369839231310923141 + 5.9420431664595586772e-7984j 6.32e-2027, 6.32e-2027j
252.59840508637707816 + 1.6036545441120044091e-7951j 4.53e-2002, 4.53e-2002j
0.71798092110102556981 - 1.4755928025093517988e-8020j 1.5e-2034, 1.5e-2034j
0.14903758114399597611 - 2.8899810974523452562e-8025j 7.68e-2039, 7.68e-2039j
66.891141251866302602 + 2.6664958470605337399e-7980j 9.43e-1999, 9.43e-1999j
158.05692092491798312 + 3.5467311931677511564e-7983j 6.16e-1996, 6.16e-1996j
24.284590789856582663 + 2.8318724307614109448e-8021j 2.13e-2009, 2.13e-2009j
15.503916920715091853 + 3.7047248259345579622e-8027j 2.83e-2014, 2.83e-2014j
6.9451893027064972208 + 3.0569345652431279979e-8033j 8.4e-2022, 8.4e-2022j
192.91742389361318574 + 5.3694149490104304543e-8006j 1.41e-1997, 1.41e-1997j
103.79466439910615715 - 2.0404236502197390107e-8021j 7.83e-1996, 7.83e-1996j
0.010091997876027062321 - 1.2634345264500539082e-8079j 5.11e-2042, 5.11e-2042j

Weights

Weight (ball center) Error (ball radius)
2.093492847506383005e-144 + 3.734776583339467308e-6165j 1.3e-365, 5.77e-1866j
9.3092158390131932796e-138 - 9.2231305650692337919e-6162j 7.21e-364, 3.21e-1864j
1.1626997401735446449e-152 - 2.3216728496001996436e-6169j 1.13e-368, 5.02e-1869j
5.6085404525480820719e-132 + 8.2998727874393762366e-6159j 1.47e-362, 6.54e-1863j
2.3197431917562037923e-73 + 2.3663640533903396487e-6127j 1.29e-341, 5.75e-1842j
2.5807200549642710863e-06 + 1.7631997178955155135e-6094j 2.27e-243, 1.01e-1743j
3.4076152779616838278e-64 + 9.8599707897967638321e-6124j 9.81e-337, 4.37e-1837j
5.5567466251912401459e-42 + 5.9976195007711033625e-6113j 9.44e-322, 4.21e-1822j
5.5262793460213475611e-60 + 9.3119366630038747548e-6122j 2.02e-334, 9e-1835j
9.0965595695901205897e-12 - 1.6581314498138698333e-6097j 7.82e-274, 3.48e-1774j
1.4027622382713359655e-30 + 3.1631536807632570693e-6107j 1.53e-310, 6.82e-1811j
1.3955031414494965943e-16 - 4.7414012413568028072e-6100j 9.44e-288, 4.21e-1788j
2.0092710228687824588e-92 + 2.36422524687809266e-6138j 2.59e-352, 1.15e-1852j
1.3969190879249711086e-24 - 3.5392490220745004287e-6104j 1.28e-303, 5.72e-1804j
8.900730591825401115e-127 - 3.8150822139374993314e-6156j 4.57e-364, 2.04e-1864j
3.3444530792701616371e-102 - 1.7851280586195860305e-6143j 1.37e-356, 6.09e-1857j
3.2692246507982993897e-33 + 1.4825411380356875319e-6108j 6.77e-316, 3.01e-1816j
1.6514507027799922422e-86 + 3.3643598301895111076e-6135j 2.5e-350, 1.11e-1850j
7.2128704623765925204e-15 - 3.7481968955996780367e-6099j 1.25e-289, 5.57e-1790j
1.3983472080130249829e-34 - 3.0328933026714716832e-6109j 1.05e-317, 4.66e-1818j
2.324654897370908852e-21 + 1.5863606448446054643e-6102j 2.28e-302, 1.02e-1802j
2.2771536554107379486e-78 - 1.1667091472446030222e-6130j 4.77e-347, 2.12e-1847j
6.9648031106645811618e-27 - 2.3716404510956799538e-6105j 1.12e-310, 4.97e-1811j
1.4970771436085638559e-95 - 5.3257699988072075485e-6140j 7.37e-355, 3.28e-1855j
7.9426448206034381207e-76 + 4.6023804018717439637e-6129j 9.99e-346, 4.45e-1846j
2.3987982022563172187e-20 - 5.2801655266507012641e-6102j 3.37e-303, 1.5e-1803j
2.3135297307469963657e-19 + 1.7026314781793495055e-6101j 4.66e-302, 2.08e-1802j
4.4038300996032032223e-28 + 5.8283404499546654608e-6106j 2.66e-313, 1.18e-1813j
1.9912734241774654106e-37 - 1.1294703646971132566e-6110j 5.81e-324, 2.59e-1824j
4.6381314146932828806e-62 - 9.7063100764607810851e-6123j 4.72e-341, 2.1e-1841j
5.7269671698925937074e-71 - 1.3769969011263352288e-6126j 1.79e-345, 7.99e-1846j
1.0357006698877388567e-15 + 1.3529051860558946746e-6099j 7.36e-300, 3.28e-1800j
0.0035212419569808485828 + 1.936922568648853891e-6092j 9.21e-256, 4.1e-1756j
4.3445225935908168447e-09 - 4.7323972613244399317e-6096j 3.3e-288, 1.47e-1788j
1.0229302609153953671e-25 + 9.320139403489451544e-6105j 2.65e-312, 1.18e-1812j
5.7941229463781295856e-58 - 8.6196660153025157975e-6121j 6.69e-340, 2.98e-1840j
0.00015120273409695469427 + 2.1202908250589088343e-6093j 1.12e-271, 4.99e-1772j
5.5051867331781917381e-36 + 5.9691952284017436735e-6110j 1.66e-323, 7.41e-1824j
2.0615386102502316675e-89 - 9.3588516889940224492e-6137j 2.73e-355, 1.22e-1855j
2.2157380254321907691e-05 + 6.3711357858818950831e-6094j 1.38e-278, 6.17e-1779j
1.7511297107806467454e-08 + 1.0247929747355093647e-6095j 3.94e-290, 1.75e-1790j
6.6047794024706239859e-39 + 2.0531431642674109858e-6111j 4.26e-327, 1.9e-1827j
2.898101767401331902e-13 - 2.6378160674244125758e-6098j 1.62e-300, 7.21e-1801j
0.011893093396638204291 + 5.625066589673614214e-6092j 8.67e-261, 3.86e-1761j
1.4366393277923081821e-117 - 2.0333535302161005747e-6151j 1.49e-369, 6.62e-1870j
9.3868565766461306996e-106 + 2.5542586372879673586e-6145j 9.53e-365, 4.24e-1865j
2.1036079643213464126e-22 - 4.6150369695411910945e-6103j 1.18e-314, 5.24e-1815j
2.0768319070649827571e-113 + 2.821119798396291575e-6149j 2.92e-368, 1.3e-1868j
5.2685944216310118288e-122 + 1.0690003146817575569e-6153j 1.67e-371, 7.43e-1872j
6.6980205293325366208e-47 - 2.1762002226879344533e-6115j 3.35e-339, 1.49e-1839j
0.049573032079819262181 + 5.3202618504967025754e-6091j 7.82e-263, 3.49e-1763j
8.079160977360587869e-07 - 8.9711153432160327976e-6095j 7.47e-297, 3.33e-1797j
1.7757663553553239355e-23 + 1.2994280757056760797e-6103j 3.51e-318, 1.57e-1818j
2.0047899922450844779e-40 - 3.5828481287949230723e-6112j 3.08e-333, 1.37e-1833j
0.00036236233493937702995 - 3.7632125990246778384e-6093j 9.43e-290, 4.2e-1790j
1.6740850238026849951e-12 + 6.7061390777979977459e-6098j 3.83e-309, 1.71e-1809j
8.3174192869640983132e-99 + 1.0512579517905481791e-6141j 3.87e-363, 1.72e-1863j
1.4031688845120195775e-43 - 9.623840697378159456e-6114j 1.29e-336, 5.73e-1837j
1.0162093223937540229e-09 + 2.1301176981515950646e-6096j 2.14e-307, 9.55e-1808j
4.7167536747195886432e-14 + 1.0086824874130979304e-6098j 4.94e-312, 2.2e-1812j
1.259291328290182401e-48 + 3.0627362680731978717e-6116j 3.52e-341, 1.57e-1841j
0.060264945019803488574 - 6.4441670970189743114e-6091j 4.09e-278, 1.82e-1778j
1.7631528107812000421e-17 + 1.6127058370166645492e-6100j 1.05e-316, 4.67e-1817j
5.3714133098371522503e-56 + 7.6591954120709730729e-6120j 9.15e-346, 4.08e-1846j
0.086297129530515762453 + 5.6948032642954165226e-6091j 2.89e-280, 1.29e-1780j
0.042384890977753585414 - 3.1812818112911424323e-6091j 1.62e-286, 7.21e-1787j
2.0873057094830645707e-18 - 5.3213772740206304606e-6101j 3.74e-318, 1.67e-1818j
5.4089110528944174259e-81 + 3.5879136206126357727e-6132j 3.83e-358, 1.71e-1858j
0.0066749132408668347596 - 3.2951727025863939801e-6092j 2.52e-297, 1.12e-1797j
2.2401444108838964709e-10 - 9.3410831866633516287e-6097j 3.68e-313, 1.64e-1813j
0.12386350001577696527 + 2.5104698370261745748e-6091j 2.23e-286, 9.95e-1787j
0.064751331754484562339 + 1.2089685490981245867e-6091j 1.81e-286, 8.08e-1787j
4.4223231191901569211e-54 - 6.5159310525019458883e-6119j 2.54e-345, 1.13e-1845j
2.179094082948165871e-66 - 9.9665777419059938683e-6125j 7.08e-352, 3.16e-1852j
0.0306199433829511066 + 1.7362914867542850167e-6091j 1.35e-298, 6.02e-1799j
3.2466883843901747854e-52 + 5.3006038694612295538e-6118j 8.45e-345, 3.76e-1845j
0.0017495976327627965048 - 1.1337941730242260102e-6092j 5.44e-307, 2.42e-1807j
6.6567423117128594625e-08 - 2.1641504802654163312e-6095j 1.93e-315, 8.61e-1816j
0.1107936031465151633 - 4.5190932616072385706e-6091j 4.89e-298, 2.18e-1798j
5.9566738356281782343e-05 - 1.1735738089326346818e-6093j 3.88e-311, 1.73e-1811j
7.0469557015309039646e-32 - 6.9769279670363827191e-6108j 3.83e-333, 1.7e-1833j
0.13267617823792117487 - 3.0637062534677104295e-6091j 3.03e-300, 1.35e-1800j
7.7822791873482660263e-06 - 3.3881658444837961515e-6094j 2.02e-313, 9.02e-1814j
2.1335059407085264138e-50 - 4.1212815067498206177e-6117j 4.67e-344, 2.08e-1844j
0.019832530137005591885 - 9.7425573604256595227e-6092j 4.5e-308, 2.01e-1808j
1.7583173953117447142e-109 - 3.0051834321252332759e-6147j 4.34e-374, 1.93e-1874j
0.12733910851890682465 + 3.6835320442553239758e-6091j 4.81e-306, 2.14e-1806j
0.10015257965440892289 - 1.9193690234863496897e-6091j 7.94e-306, 3.54e-1806j
2.5825717810212627226e-29 - 1.3824722709991371786e-6106j 2.03e-332, 9.05e-1833j
1.2053112440071520816e-68 + 1.0539242848182459004e-6125j 4.61e-354, 2.05e-1854j
4.6519975032137009843e-11 + 3.989014054057755687e-6097j 1.86e-322, 8.31e-1823j
2.3872929185769764512e-07 + 4.4593472993319535028e-6095j 4.73e-320, 2.11e-1820j
0.0008197076448341079995 + 6.5747976101543648713e-6093j 3.21e-317, 1.43e-1817j
1.0517410767141120256e-83 - 1.1225260542356422143e-6133j 6.8e-362, 3.03e-1862j
3.220078474476975283e-45 + 1.4791819383005130507e-6114j 4.5e-342, 2e-1842j
0.026185885118673368295 - 4.0748760188045766386e-6092j 2.77e-317, 1.23e-1817j

Download

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