Rule: Q[3, 6, 41]

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)
163.70576817691822711 + 6.1386029628459942449e-1153j 1.73e-494, 1.73e-494j
137.25171168108557505 + 3.0892742062690209984e-1149j 1.08e-491, 1.08e-491j
127.25983333016726591 - 1.3654859253033425211e-1145j 9.71e-491, 9.71e-491j
118.39856736337667253 - 7.8917759310545334801e-1146j 5.98e-490, 5.98e-490j
148.92604333292058754 + 3.5062094971803502531e-1153j 6.14e-493, 6.14e-493j
50.995703650155781653 - 5.0670160916925887153e-1150j 3.98e-487, 3.98e-487j
37.06803774572865041 - 1.263090043886397305e-1161j 7.48e-488, 7.48e-488j
19.489990377765696814 + 6.7724064105054836743e-1178j 4.1e-490, 4.1e-490j
110.37992111230039823 + 1.9034231081887141706e-1176j 2.86e-489, 2.86e-489j
31.161378362991358447 - 1.5601006032747019095e-1197j 2.01e-488, 2.01e-488j
3.0116676633841944792 + 5.0882292184351071281e-1225j 6.71e-500, 6.71e-500j
23.54719157727562468 - 8.6255506429823088308e-1224j 2.11e-489, 2.11e-489j
78.420304195311031422 - 6.8188828131398008907e-1256j 2.41e-487, 2.41e-487j
11.238002918682145245 + 7.0919307582551686255e-1284j 2.46e-493, 2.46e-493j
28.454858638018066749 - 2.9272654242753351805e-1293j 1.06e-488, 1.06e-488j
7.1571780963097337607 - 8.1839787688450324027e-1318j 2.33e-495, 2.33e-495j
12.829387593764969814 + 4.0090132237167521822e-1317j 1.51e-492, 1.51e-492j
63.574542760882187436 - 3.9778162524460217322e-1345j 5.51e-487, 5.51e-487j
17.837562636834985847 - 1.8856056129729730063e-1373j 1.53e-490, 1.53e-490j
40.275540566246339918 - 6.1068290456888737068e-1382j 1.29e-487, 1.29e-487j
5.6761128976338315004 + 6.742783333398822254e-1412j 2.08e-496, 2.08e-496j
25.913465774183642815 - 3.5375250456172193637e-1403j 4.44e-489, 4.44e-489j
68.24483059235169895 - 7.79784834796540668e-1418j 4.59e-487, 4.59e-487j
6.2899450829374791969 + 2.3435016617406795345e-1442j 8.03e-496, 8.03e-496j
96.230339419030212565 - 1.0185233564558802305e-1433j 3e-488, 3e-488j
43.660528364198898309 - 6.4095071565870961182e-1450j 2.04e-487, 2.04e-487j
2.2942803602790417198 + 2.2265606249617365384e-1481j 5.56e-501, 5.56e-501j
14.501292642300796639 + 5.8825433616601017452e-1471j 8.2e-492, 8.2e-492j
16.199176121951090198 - 3.9530650853249191915e-1470j 4.12e-491, 4.12e-491j
89.900896917568547007 + 3.6320299010798431926e-1466j 6.79e-488, 6.79e-488j
0.20592891009617054562 - 3.6688880615207330766e-1500j 1.82e-507, 1.82e-507j
21.386110825520344838 - 1.1254498925445468574e-1479j 9.17e-490, 9.17e-490j
1.6909753443312066252 + 7.6856324963929879127e-1504j 6.42e-502, 6.42e-502j
34.031588713616204177 + 1.3340923024613685302e-1489j 4.07e-488, 4.07e-488j
54.965902411554794749 - 1.2170451999513991452e-1522j 4.8e-487, 4.8e-487j
4.7497053381688388761 - 2.1046866266485652591e-1561j 1.28e-497, 1.28e-497j
73.185248195531981902 + 4.2777816135338648522e-1553j 3.46e-487, 3.46e-487j
0.71223966644492667954 + 7.0471186957932754515e-1597j 1.32e-504, 1.32e-504j
3.8343455071274751198 - 1.1124227726400573326e-1589j 9.43e-499, 9.43e-499j
47.230836315705455068 - 6.8014908021487290933e-1578j 2.98e-487, 2.98e-487j
0.077311092319026922809 + 7.3537340898288988886e-1626j 8.15e-509, 8.15e-509j
83.979850448354222371 - 6.6780723713946877618e-1603j 1.46e-487, 1.46e-487j
1.2627083649697538623 - 4.2070267894456461795e-1636j 1.26e-502, 1.26e-502j
1.0480692470897750704 + 1.3066021305260680838e-1637j 3.42e-503, 3.42e-503j
59.153969191215018806 - 1.3046361374285325409e-1620j 5.35e-487, 5.35e-487j
103.02924029726093676 - 9.7759635687955215711e-1633j 1.01e-488, 1.01e-488j
9.7500082014447782041 - 4.0038599952388212968e-1643j 4.44e-494, 4.44e-494j
8.3792074722440796233 + 7.7437563654290820878e-1644j 9.46e-495, 9.46e-495j
0.41577455678347908331 - 1.0629908010940917454e-1655j 4.63e-506, 4.63e-506j
0.013993151608491287585 + 1.3498263003541168921e-1658j 2.78e-510, 2.78e-510j

Weights

Weight (ball center) Error (ball radius)
1.4017324683555955182e-70 - 5.4573718740922536598e-1200j 2.28e-201, 1.23e-443j
2.6418350688181568533e-59 - 6.4745262525611603263e-1194j 7.07e-198, 3.82e-440j
5.0493862420051695185e-55 + 1.3921043504150924553e-1191j 1.21e-196, 6.55e-439j
3.1962743656115911182e-51 - 1.7009302900589939108e-1189j 1.04e-195, 5.64e-438j
2.6972755836060365329e-64 + 1.2936989542750153387e-1196j 3.59e-200, 1.94e-442j
2.7546360236634632435e-22 + 8.2647084655984011445e-1172j 3.84e-182, 2.08e-424j
2.4880164406372039337e-16 + 4.5422365884009424841e-1169j 1.5e-176, 8.08e-419j
6.0059116385011782623e-09 - 5.4644416566953804799e-1164j 8.02e-166, 4.33e-408j
8.8496474305136278939e-48 + 1.3688143172988819832e-1187j 2.25e-195, 1.21e-437j
8.1678401427208447668e-14 + 1.4620146719227497686e-1167j 5.25e-174, 2.84e-416j
0.037946710574501194734 + 4.1904691273401902187e-1159j 6.17e-137, 3.33e-379j
1.3485151202415199026e-10 - 2.4172282649841298803e-1165j 8.68e-170, 4.69e-412j
4.7231152015128144725e-34 - 9.4931197729397129335e-1180j 3.22e-191, 1.74e-433j
2.0301548062261779375e-05 + 8.0850278257392617503e-1162j 6.26e-160, 3.38e-402j
1.1515641488310859342e-12 - 8.134510744803513341e-1167j 5.81e-173, 3.14e-415j
0.00086739686872126741123 - 3.7718867974008076292e-1160j 2.29e-154, 1.24e-396j
4.3888913701685287183e-06 - 2.823339005463075043e-1162j 3.97e-162, 2.14e-404j
1.1148197033764159348e-27 + 8.0945801356646511834e-1176j 3.55e-188, 1.92e-430j
2.8766817770597186468e-08 + 1.7136513477092194125e-1163j 3.24e-167, 1.75e-409j
1.0627166575100129801e-17 - 8.0069352726128339991e-1170j 6.79e-180, 3.67e-422j
0.0028194445128817453605 - 1.6260800510395789078e-1159j 3.14e-155, 1.7e-397j
1.3685566852727193418e-11 + 4.4666461520493558428e-1166j 1.89e-172, 1.02e-414j
1.1041716014314185619e-29 - 4.2723133234772530076e-1177j 8.93e-190, 4.82e-432j
0.0010635373387643168713 + 1.179400612173915811e-1159j 4.56e-158, 2.46e-400j
1.0570687505314647365e-41 + 3.5351864803603724559e-1184j 1.23e-196, 6.63e-439j
3.7982333443310320204e-19 + 1.4852578198835447648e-1170j 3.77e-182, 2.04e-424j
0.066809863287511658808 - 8.8147540803742802922e-1159j 1.18e-152, 6.39e-395j
8.5532660864474749499e-07 + 1.0665822183616797057e-1162j 2.46e-168, 1.33e-410j
1.5492563728841409643e-07 - 4.3216084769673202412e-1163j 2.28e-169, 1.23e-411j
5.5339372134973658037e-39 - 1.261894588347910098e-1182j 8.04e-196, 4.35e-438j
0.1360472062779194013 - 3.5317672801478402532e-1158j 5.2e-157, 2.81e-399j
1.0512854559652728326e-09 + 1.252226028740074539e-1164j 8.73e-173, 4.72e-415j
0.099266148010673567615 + 2.3766107739136719457e-1158j 2.79e-157, 1.51e-399j
4.9032687356049822367e-15 - 2.5903807747077867244e-1168j 5.93e-179, 3.21e-421j
5.4820117207343384633e-24 + 3.4966032490216602154e-1173j 1.62e-187, 8.74e-430j
0.0082203529384452967418 + 1.6762176113843734169e-1159j 4.6e-166, 2.49e-408j
8.3597355027278314604e-32 + 2.1172810795583673355e-1178j 1.63e-192, 8.78e-435j
0.16465605891904628589 - 5.0960069287141273929e-1158j 2e-163, 1.08e-405j
0.018862211276938871648 - 2.3791808720914890111e-1159j 9.71e-167, 5.25e-409j
1.1274365726685604354e-20 - 3.4111057605733140055e-1171j 2.71e-185, 1.46e-427j
0.086022600100256537913 + 2.5732971763605647101e-1158j 8.97e-166, 4.85e-408j
1.9338720463278079807e-36 + 3.741882715975679137e-1181j 1.9e-195, 1.03e-437j
0.07649704949647876306 - 7.0008161541603026517e-1158j 1.16e-167, 6.26e-410j
0.097383096962462791115 + 8.1912917304067118686e-1158j 1.45e-167, 7.83e-410j
8.7780113362935483711e-26 - 1.5363083011519939603e-1174j 2.53e-189, 1.37e-431j
1.2696978784773014477e-44 - 7.94366840869815474e-1186j 5.26e-200, 2.84e-442j
8.3465842727526516726e-05 - 2.5179845629907908474e-1161j 9.12e-176, 4.93e-418j
0.00029985550793031562233 + 8.8285314187240976934e-1161j 3.66e-175, 1.98e-417j
0.16736130720941750945 + 4.0378767131111211705e-1158j 1.75e-172, 9.47e-415j
0.035767958209854236891 - 9.4228727575852744901e-1159j 5.73e-173, 3.06e-415j

Download

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