Rule: Q[3, 6, 42]

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.

Warning: This rule has negative weights!

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)
167.75156569486468495 + 1.9184891501019427279e-2357j 8.49e-1005, 8.49e-1005j
106.50070435800786357 - 1.7553256949474327623e-2369j 7.15e-999, 7.15e-999j
152.84984385464746675 + 6.1233208276927683477e-2381j 3.87e-1003, 3.87e-1003j
141.07216647863447109 + 2.6924363208420801679e-2398j 6.17e-1002, 6.17e-1002j
122.03647764783165325 + 9.2061846161786823597e-2435j 3.78e-1000, 3.78e-1000j
76.2691877761548946 - 2.4456458335511770554e-2466j 2.93e-997, 2.93e-997j
12.809839019063956534 + 4.8565818304929000313e-2491j 6.4e-1003, 6.4e-1003j
14.501292642300796639 + 2.3105632560069923167e-2491j 3.25e-1002, 3.25e-1002j
19.774871246636789841 - 1.4702212527790077032e-2488j 3.71e-1000, 3.71e-1000j
9.7500082014447782041 - 1.6237819365171184336e-2492j 1.9e-1004, 1.9e-1004j
18.083542492243885514 - 4.4196078772519700735e-2489j 8.9e-1001, 8.9e-1001j
71.253358324291062275 - 8.7234771788387255162e-2485j 4.11e-997, 4.11e-997j
36.352989728675634079 + 4.7233053476668317376e-2490j 5.98e-998, 5.98e-998j
21.386110825520344838 + 4.7288956981536685083e-2502j 9.21e-1000, 9.21e-1000j
25.538271056557542933 + 2.3287289746951750997e-2500j 3.71e-999, 3.71e-999j
11.223239673769254675 + 4.3827030953119541368e-2507j 1e-1003, 1e-1003j
42.753756550109039136 + 6.421877958477573862e-2500j 1.64e-997, 1.64e-997j
130.98618036961407807 + 1.7159683520124071701e-2515j 6.33e-1001, 6.33e-1001j
3.8343455071274751198 + 1.7797027139509012993e-2549j 3.15e-1009, 3.15e-1009j
46.215768862541425592 + 1.2578236861424812633e-2548j 2.58e-997, 2.58e-997j
4.7286928238183570047 - 6.1948868318058842089e-2592j 4.72e-1008, 4.72e-1008j
1.2627083649697538623 - 1.1549013882309226606e-2598j 1.53e-1012, 1.53e-1012j
7.2011776197746125765 - 5.2097522260126974061e-2591j 8.88e-1006, 8.88e-1006j
99.621972724905940433 + 4.3207546138383639466e-2616j 2.04e-998, 2.04e-998j
81.580036682263024221 - 3.1608962030163587702e-2694j 2.05e-997, 2.05e-997j
0.19331389355392371257 + 2.8575375372423046358e-2746j 3.81e-1018, 3.81e-1018j
33.402500324222473871 - 2.1654360359258910077e-2762j 3.22e-998, 3.22e-998j
8.3993284715919155634 + 1.2109356805797428121e-2801j 3.85e-1005, 3.85e-1005j
49.862433376931048148 + 4.8286031209188616703e-2839j 3.54e-997, 3.54e-997j
23.302146698768611425 - 2.5727594928212744977e-2903j 1.78e-999, 1.78e-999j
30.614054057819239194 - 3.1401484205103368754e-2972j 1.69e-998, 1.69e-998j
2.2942803602790417198 - 2.4174883125803651536e-3006j 1.71e-1011, 1.71e-1011j
0.41577455678347908331 + 1.9334844987643525541e-3021j 9.75e-1017, 9.75e-1017j
57.748822956788951787 - 3.5730188765119821511e-3017j 4.81e-997, 4.81e-997j
5.605787386329110327 + 1.4202533590509922093e-3055j 5.67e-1007, 5.67e-1007j
66.507865175696967625 + 1.4768359225252590798e-3044j 4.68e-997, 4.68e-997j
27.988918437907975807 + 4.1143069015879454343e-3057j 8.6e-999, 8.6e-999j
1.6659389830205541848 + 7.4889971556945649921e-3071j 2.49e-1012, 2.49e-1012j
39.468380144400484344 + 3.6319045543401752638e-3055j 1.06e-997, 1.06e-997j
113.93323591053413435 + 1.117199215092397929e-3077j 1.92e-999, 1.92e-999j
93.214206125791335278 + 5.133851699668779091e-3136j 5.22e-998, 5.22e-998j
87.21595895252248468 - 1.1795408876083009481e-3216j 1.11e-997, 1.11e-997j
1.1912433960891918819 + 3.0115930173762704259e-3275j 9.16e-1013, 9.16e-1013j
3.0171793610999622105 + 3.2121493803899254763e-3264j 2.16e-1010, 2.16e-1010j
0.73971832779489493166 + 3.2120300447588392828e-3280j 3.62e-1015, 3.62e-1015j
53.703146322746247938 + 2.4775033711237272021e-3288j 4.6e-997, 4.6e-997j
16.27841739968505949 + 4.5233356651917351682e-3322j 1.84e-1001, 1.84e-1001j
6.2899450829374791969 - 7.0457101243843878784e-3332j 2.61e-1006, 2.61e-1006j
0.068378627123824838559 - 7.8493780621978331335e-3350j 1.41e-1019, 1.41e-1019j
0.013993151608491287585 + 5.0448978205159732572e-3350j 6.11e-1021, 6.11e-1021j
62.012137113995062971 + 1.5940281428278892087e-3336j 5.35e-997, 5.35e-997j

Weights

Weight (ball center) Error (ball radius)
2.4719375540698074011e-72 - 2.6216155523615548196e-2429j 2.05e-198, 6.16e-950j
3.9902686084323348321e-46 + 3.7165539500977480036e-2415j 3.1e-189, 9.28e-941j
5.3770978978788033645e-66 + 1.0732780262987963834e-2426j 1.05e-196, 3.15e-948j
5.8432799947686505413e-61 - 4.1407642899082343674e-2424j 2.85e-195, 8.54e-947j
8.4948581859372316692e-53 - 1.3966926700728400562e-2419j 1.1e-192, 3.29e-944j
3.8838603362999613973e-33 - 2.486125531417292275e-2409j 7.52e-185, 2.26e-936j
4.4856938550403208863e-06 + 5.1989359805120725569e-2393j 5.29e-152, 1.59e-903j
8.7604114603723138176e-07 - 1.864543112743158212e-2393j 1.83e-154, 5.48e-906j
4.1195686081139508978e-09 + 1.3004708291096058851e-2394j 4.59e-161, 1.37e-912j
8.2433029514862708837e-05 + 4.7585482568301143637e-2392j 5.44e-149, 1.63e-900j
2.4909084906457017494e-08 - 3.0217189449070259384e-2394j 2.46e-159, 7.37e-911j
5.5361229698687990286e-31 + 3.356855802496883856e-2408j 8.91e-186, 2.67e-937j
4.9415285176719538547e-16 - 1.1198711814358198971e-2399j 2.22e-174, 6.65e-926j
8.8648327687790822004e-10 - 4.4247681296612738364e-2395j 1.18e-163, 3.53e-915j
1.908682920577355467e-11 - 1.6410887689326283094e-2396j 9.87e-168, 2.96e-919j
2.0455160208197449236e-05 - 1.5288985528452214635e-2392j 2.21e-154, 6.62e-906j
9.1248881575641718107e-19 - 2.3316039167135316282e-2401j 4.33e-178, 1.3e-929j
1.2277242420051335539e-56 + 9.1551210975766112753e-2422j 1.38e-198, 4.15e-950j
0.018611919710135894992 + 4.5941367030855467585e-2390j 3.36e-145, 1.01e-896j
3.0152852004018032774e-20 + 3.0849790004212983296e-2402j 6e-180, 1.8e-931j
0.0080960003143534939516 - 3.261135262068954432e-2390j 2.14e-148, 6.42e-900j
-0.081698923824675770244 + 4.0056707819575818595e-2388j 1.79e-134, 5.38e-886j
0.00081499493794763838996 + 6.0658846861522072675e-2391j 2.65e-153, 7.95e-905j
3.6003161148517637485e-43 - 3.8322511589998694411e-2414j 5.25e-194, 1.57e-945j
2.0326228768226706889e-35 + 1.6706844372114179255e-2410j 2.44e-190, 7.3e-942j
0.14209947722403077286 + 4.7399771351045455316e-2389j 3.73e-140, 1.12e-891j
8.938095648953384079e-15 + 7.2250731056600350955e-2399j 1.17e-175, 3.5e-927j
0.00028879951278454735176 - 1.6072453058050398536e-2391j 2.48e-158, 7.44e-910j
8.2817935403779980945e-22 - 3.8193344716235119466e-2403j 1.45e-182, 4.34e-934j
1.5927388919693004821e-10 + 9.504077655401874047e-2396j 2.18e-170, 6.54e-922j
1.3710625757521205432e-13 - 4.4997549360208440083e-2398j 7.57e-175, 2.27e-926j
0.06801322996211340983 + 1.6881204966959153653e-2389j 3.49e-153, 1.05e-904j
0.18000495589469362918 - 4.8702334429719733829e-2389j 1.43e-148, 4.29e-900j
3.4537057967491024366e-25 - 4.6845289280466231778e-2405j 4.36e-186, 1.31e-937j
0.0028732489065564487054 + 2.7794438122923348238e-2390j 2.13e-160, 6.39e-912j
6.0312278882178721568e-29 - 4.1131287685282984388e-2407j 2.32e-188, 6.96e-940j
1.7766283478448410171e-12 + 2.7365580119899290446e-2397j 1.27e-174, 3.8e-926j
0.11109482834259348787 - 5.8468163386785277143e-2389j 4.64e-158, 1.39e-909j
2.3129593846468041418e-17 + 1.6593777348541467491e-2400j 2.06e-179, 6.16e-931j
2.5610904672585930008e-49 + 1.934890103054907263e-2417j 1.57e-199, 4.7e-951j
2.0396943924595270582e-40 + 5.9884708607522808807e-2413j 1.15e-195, 3.45e-947j
7.7051005813695100397e-38 - 1.0274753429789936208e-2411j 2.21e-194, 6.62e-946j
0.22164357633663377166 - 3.9036075595453405962e-2388j 5.39e-165, 1.61e-916j
0.037735255334341969829 - 7.9270267816872139889e-2390j 3.69e-168, 1.1e-919j
0.17947031507663028996 + 6.176199193083097298e-2389j 5.06e-166, 1.51e-917j
1.873495372272700736e-23 + 4.398295932308336692e-2404j 7.65e-187, 2.29e-938j
1.5389971193176738184e-07 + 7.1667325087881420383e-2394j 1.19e-175, 3.49e-927j
0.0013122113702181048323 - 1.8042786755178578549e-2390j 1.22e-171, 3.57e-923j
0.07624456750090197853 - 4.1251052644297138006e-2389j 8.58e-170, 2.47e-921j
0.033287109480883562054 + 1.7309116948040543616e-2389j 3.76e-170, 1.08e-921j
5.1242923310298100218e-27 + 4.5891102070655675217e-2406j 5.16e-189, 1.55e-940j

Download

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