Rule: Q[3, 76]

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)
287.39451326596817508 + 1.1554759880275683528e-2442j 3.44e-996, 3.44e-996j
194.63863932367787787 - 2.158195849723771603e-2428j 9.39e-987, 9.39e-987j
255.02453007313717611 + 3.9298391814655316759e-2443j 1.44e-992, 1.44e-992j
221.23627708911844613 - 1.1480384752702537949e-2433j 4.17e-989, 4.17e-989j
211.78845326909135316 - 4.8640244862778433012e-2439j 3.23e-988, 3.23e-988j
19.1376154313301953 + 2.3015987562310615644e-2459j 3.52e-994, 3.52e-994j
231.43342787867983739 + 3.2085171152826588638e-2447j 4.2e-990, 4.2e-990j
124.56033971336938372 - 5.5631555324532205274e-2459j 1.09e-982, 1.09e-982j
51.768007030233161816 + 2.3921907991760575121e-2477j 1.47e-985, 1.47e-985j
242.58384304622856965 - 1.3453121201696325418e-2483j 3.14e-991, 3.14e-991j
12.013059270522230744 - 1.5601853502439984597e-2489j 4.02e-998, 4.02e-998j
20.774067296758406067 + 4.0909093258488053653e-2485j 1.86e-993, 1.86e-993j
46.352029258021952375 - 2.3265949905374385655e-2477j 2.19e-986, 2.19e-986j
202.95452104317453776 - 1.5232339193200617095e-2478j 1.82e-987, 1.82e-987j
66.93518549330764673 + 1.5376915176792601632e-2473j 7.34e-984, 7.34e-984j
17.572738373120573754 - 3.7474380555552273066e-2487j 6.18e-995, 6.18e-995j
13.299584749655126527 + 4.9951360007460528018e-2489j 2.78e-997, 2.78e-997j
30.060952661666322334 - 1.5720118465088140039e-2481j 4.17e-990, 4.17e-990j
49.015551417981003461 + 2.2201827394501437141e-2477j 5.95e-986, 5.95e-986j
179.29338540106523948 + 3.9877923651104570353e-2474j 1.51e-985, 1.51e-985j
100.99068581789594202 - 1.931112124530703014e-2472j 1.92e-982, 1.92e-982j
4.9526630159914734967 - 2.4963285309427162885e-2504j 2.08e-1004, 2.08e-1004j
158.82791024983227121 + 8.1633998292986370825e-2481j 3.37e-984, 3.37e-984j
92.575997582395937841 + 6.7561133793524351002e-2495j 1.41e-982, 1.41e-982j
152.56389848171562363 + 9.513589293244942849e-2520j 7.65e-984, 7.65e-984j
28.053100038960636602 + 6.8489592665579716671e-2565j 9.91e-991, 9.91e-991j
63.706977383733553285 - 1.5506557008454590388e-2561j 3.99e-984, 3.99e-984j
10.794002284765298059 + 7.3051881791549666463e-2634j 5.98e-999, 5.98e-999j
96.71698390530101896 + 4.1930444937712353198e-2620j 1.73e-982, 1.73e-982j
2.8582611182371468867 + 5.6631158878630450836e-2693j 3.31e-1008, 3.31e-1008j
41.284788174774940164 + 4.6499829063232082389e-2667j 2.36e-987, 2.36e-987j
269.40299256914203525 + 2.24408113190256691e-2740j 4.01e-994, 4.01e-994j
6.3770865254709583925 + 5.1030938139844245869e-2816j 3e-1001, 3e-1001j
140.74455085562499936 + 3.4975078782706559958e-2897j 3e-983, 3e-983j
129.76603772161198311 - 5.8062936182067540171e-3011j 7.55e-983, 7.55e-983j
119.52971261929210121 + 6.3880075289701027576e-3087j 1.34e-982, 1.34e-982j
36.553320548917075251 + 3.0022978916902047126e-3125j 2.03e-988, 2.03e-988j
0.66831828292564744315 - 4.6931133512671215314e-3165j 1.08e-1014, 1.08e-1014j
186.76977358926510346 - 4.8742916701842123746e-3133j 4.08e-986, 4.08e-986j
14.654504407490982351 - 1.9368642927783881815e-3176j 1.63e-996, 1.63e-996j
114.66512397789520704 - 1.1808678991924430665e-3159j 1.72e-982, 1.72e-982j
57.547415608551266344 + 1.1118924275901179776e-3173j 8.05e-985, 8.05e-985j
22.48293501812838123 - 2.61354081699795519e-3182j 9.9e-993, 9.9e-993j
7.519117180732351068 - 1.166895980820215782e-3190j 2.3e-1001, 2.3e-1001j
26.121495613902614655 + 1.1225362793927244922e-3180j 2.32e-991, 2.32e-991j
70.265813994488932743 - 1.0103595299104912857e-3172j 1.34e-983, 1.34e-983j
172.16642196329178765 - 4.4631653252611310925e-3175j 4.97e-985, 4.97e-985j
6.2899450829374791969 - 4.2528940476163431379e-3191j 2.83e-1001, 2.83e-1001j
1.3567821977643596675 - 7.1399166865137502211e-3202j 5e-1012, 5e-1012j
43.775664332970429241 - 1.6910050935840743343e-3176j 6.97e-987, 6.97e-987j
38.877832192212004798 - 1.8036840676602252783e-3177j 7e-988, 7e-988j
3.4871124009015314618 + 8.6693245119027057466e-3197j 5.1e-1007, 5.1e-1007j
2.2942803602790417198 - 1.1399881400091527233e-3199j 1.87e-1009, 1.87e-1009j
80.901740492002366051 + 2.3060634086847106997e-3171j 5.76e-983, 5.76e-983j
16.078629250509380918 - 7.4619632097629938948e-3196j 1.16e-995, 1.16e-995j
73.701704785359291351 - 1.2707307170133043617e-3181j 2.22e-983, 2.22e-983j
88.562765388812816505 - 7.0434832535417223456e-3207j 1.15e-982, 1.15e-982j
24.265101195649113396 - 7.0877284041232007878e-3250j 4.61e-992, 4.61e-992j
109.95848854840458678 + 1.0301077811124619186e-3238j 1.89e-982, 1.89e-982j
0.98176228516941646055 + 2.4202354801439193769e-3288j 2.6e-1013, 2.6e-1013j
165.35412547670942142 - 8.7851634557562947978e-3257j 1.41e-984, 1.41e-984j
105.40253316012575228 + 1.7552612851393651558e-3281j 1.98e-982, 1.98e-982j
146.54187950079307155 + 3.7690183715110328592e-3315j 1.59e-983, 1.59e-983j
60.578543422321180298 + 4.4370470843035353488e-3335j 1.66e-984, 1.66e-984j
1.7940546821248365299 - 1.4744829131337852205e-3386j 9.79e-1011, 9.79e-1011j
0.41577455678347908331 + 8.2693182816513887633e-3392j 4.94e-1016, 4.94e-1016j
8.552109835711035019 - 2.7021073505276396279e-3376j 1.23e-1000, 1.23e-1000j
135.1569526396875543 - 2.3307035064713855861e-3358j 4.98e-983, 4.98e-983j
32.146152465498257841 - 6.0910433565919005637e-3391j 1.6e-989, 1.6e-989j
84.672739737927333063 - 7.3136775064031508027e-3383j 8.36e-983, 8.36e-983j
0.22346810139748672272 + 1.7159501013490132507e-3433j 1.73e-1017, 1.73e-1017j
9.6411487658801893659 + 6.9079876036882288981e-3415j 9.72e-1000, 9.72e-1000j
54.611288794018634459 + 2.4504231741719206775e-3398j 3.64e-985, 3.64e-985j
77.245915189320659152 + 1.0994939862351387527e-3402j 3.82e-983, 3.82e-983j
0.090787851200191752521 + 4.5435083651971862893e-3452j 6.24e-1019, 6.24e-1019j
5.8801180394374506196 - 3.4985958555333509618e-3435j 1.88e-1002, 1.88e-1002j
4.1829747608167631693 + 7.0301366199619219969e-3439j 9.53e-1006, 9.53e-1006j
34.309863695110354999 - 1.6819239925493344297e-3422j 5.85e-989, 5.85e-989j
0.017215275811635983146 + 2.8516666383811019188e-3453j 1.29e-1020, 1.29e-1020j

Weights

Weight (ball center) Error (ball radius)
3.2517997017556277526e-124 - 6.6275072939268763355e-2529j 4.36e-139, 6.66e-881j
2.3825285183585226945e-84 - 1.2912756931208153123e-2508j 2.08e-126, 3.17e-868j
2.3267446003974999108e-110 - 7.2012737507737256654e-2522j 1.82e-135, 2.78e-877j
8.115839116687795927e-96 + 1.8152478429876824814e-2514j 4.6e-131, 7.03e-873j
9.583972052288689984e-92 - 2.1639794706756994074e-2512j 7.23e-130, 1.1e-871j
7.8145206095856881443e-09 - 1.0333740260356630043e-2467j 2.99e-58, 4.57e-800j
3.2835749662738106296e-100 - 1.0496356998530635776e-2516j 6.22e-133, 9.49e-875j
4.1030873249005162028e-54 + 4.4776702855617142175e-2493j 2.98e-117, 4.55e-859j
9.2090957411042854751e-23 - 1.7582899492541678697e-2476j 1.6e-91, 2.45e-833j
5.2024275718845975031e-105 + 3.7830937759073642992e-2519j 8.04e-135, 1.23e-876j
7.5965095404451923565e-06 + 1.6998787525598641662e-2466j 3.99e-49, 6.09e-791j
1.589672209436872428e-09 - 4.4188736209915521808e-2468j 1.38e-64, 2.11e-806j
1.9400541865824365537e-20 - 3.4642285794330562267e-2475j 9.73e-89, 1.48e-830j
6.1732501550091336335e-88 + 1.9015495543354925474e-2510j 1.75e-129, 2.68e-871j
2.7935382533109762023e-29 + 4.9838262247062868242e-2480j 2.23e-100, 3.41e-842j
3.5708096787966685753e-08 + 2.7819579209670590764e-2467j 9.87e-62, 1.51e-803j
2.2122237888618469157e-06 - 9.2360830852280007256e-2467j 7.29e-55, 1.11e-796j
1.8016542770465631423e-13 + 4.3712048266356783071e-2471j 5.81e-78, 8.86e-820j
1.3977013418886544966e-21 + 7.9526182569766353752e-2476j 1.33e-90, 2.03e-832j
9.9291901620327409659e-78 - 3.1437439960116293751e-2505j 2.97e-128, 4.53e-870j
5.9975654970975388273e-44 - 8.6880672270036654591e-2488j 4.79e-114, 7.31e-856j
0.0057460394955317683681 + 9.919445138670311364e-2465j 2.94e-38, 4.49e-780j
6.7222656523899387079e-69 + 1.0627454190694811873e-2500j 4.08e-126, 6.23e-868j
2.5411084718596110558e-40 - 6.9103527370102662441e-2486j 2.39e-112, 3.64e-854j
3.3923669061086616595e-66 - 2.6056931664388547382e-2499j 2.23e-125, 3.41e-867j
1.2913994273698778649e-12 - 1.5617038304087581919e-2470j 2.31e-82, 3.53e-824j
6.8320472448361873731e-28 - 2.7892742366373926833e-2479j 8.42e-103, 1.29e-844j
2.4333090891745236001e-05 - 3.2588928146696103774e-2466j 2.88e-62, 4.39e-804j
4.17125198916449994e-42 + 8.0017196026443484205e-2487j 1.8e-113, 2.74e-855j
0.034202149078089764624 - 7.0692274290096443532e-2465j 1.95e-38, 2.98e-780j
2.8785465441839393098e-18 - 5.9172624510747605745e-2474j 7.89e-93, 1.2e-834j
1.5724499383674620766e-116 + 5.2763081623633525343e-2525j 9.62e-145, 1.47e-886j
0.0077276095544570353966 - 1.4139508298225325769e-2463j 1.18e-56, 1.8e-798j
4.2711154324263125687e-61 - 1.1028798438831278935e-2496j 2.46e-124, 3.75e-866j
2.329785460580613934e-56 - 3.0809484800141500941e-2494j 2.58e-122, 3.94e-864j
6.0698206868433854528e-52 - 5.9706154678377679261e-2492j 1.19e-120, 1.82e-862j
3.0461056742276874153e-16 - 8.9175170219056041993e-2473j 1.5e-95, 2.28e-837j
0.14499648434375868555 + 4.9515246378935011469e-2465j 3.49e-52, 5.33e-794j
5.907568897585965014e-81 + 7.024459287732873889e-2507j 8.24e-133, 1.26e-874j
6.0041870326286253017e-07 + 5.2970662995878007903e-2467j 7.42e-79, 1.13e-820j
7.6101125949979633349e-50 + 7.3380500464626724975e-2491j 4.38e-120, 6.68e-862j
3.0350473709913263057e-25 - 7.6260603067447108357e-2478j 1.44e-105, 2.2e-847j
3.0038062584413348542e-10 + 8.4416509133011895338e-2469j 1e-87, 1.53e-829j
0.0005496477449662552079 + 3.7556382986759902977e-2465j 9.07e-73, 1.38e-814j
8.5687973391270950934e-12 + 5.6179277885009974007e-2470j 1.47e-90, 2.24e-832j
1.0309011526040497771e-30 - 8.4916055896523236833e-2481j 8.58e-111, 1.31e-852j
1.1802044288363462722e-74 + 1.182742432229091665e-2503j 6.7e-132, 1.02e-873j
-0.0079543990644983472957 + 1.7072956504955803006e-2463j 1.22e-72, 1.87e-814j
0.10454858417448886831 + 6.396441052439611282e-2465j 6.44e-58, 9.83e-800j
2.4669816031773122444e-19 + 1.456072831913934806e-2474j 1.53e-100, 2.33e-842j
3.0866976290843666647e-17 + 2.3303287903632713948e-2473j 8.37e-99, 1.28e-840j
0.020245024416204250959 + 7.2663887606295865238e-2465j 1.05e-70, 1.61e-812j
0.053639043086404652814 + 6.9519363020577992283e-2465j 6.14e-67, 9.37e-809j
2.7197036326744223341e-35 + 3.1027959298500543748e-2483j 2.46e-115, 3.75e-857j
1.517719907097944833e-07 - 3.360170949516068682e-2467j 1.25e-87, 1.91e-829j
3.4239092671109185733e-32 + 1.3772831890450031477e-2481j 6.19e-113, 9.45e-855j
1.3626240854904792023e-38 + 5.610618484431396042e-2485j 3.63e-117, 5.53e-859j
5.2681977917266463187e-11 - 2.085957257738845917e-2469j 4.44e-95, 6.78e-837j
8.1513544088655466546e-48 - 8.3469876155288788768e-2490j 2.69e-122, 4.11e-864j
0.12892442757320252971 - 5.800514560959898856e-2465j 2e-76, 3.05e-818j
1.0266229588349589102e-71 - 3.8061159431190733078e-2502j 8.3e-134, 1.27e-875j
7.5130556705017613455e-46 + 8.820366536111372809e-2489j 1.4e-121, 2.13e-863j
1.3459764140255061351e-63 + 5.6671530509825439911e-2498j 1.2e-130, 1.84e-872j
1.5119473338045932453e-26 + 1.4910776973981642061e-2478j 1.2e-112, 1.83e-854j
0.077925561409293636679 - 6.7601565244464817671e-2465j 4.2e-87, 6.41e-829j
0.14669135234291486903 - 3.8766777487365687387e-2465j 8.16e-86, 1.24e-827j
0.00020447360399705534164 - 1.4244896400259932956e-2465j 3.2e-95, 4.88e-837j
1.1001044641928512248e-58 + 1.9350057079033007785e-2495j 1.93e-128, 2.94e-870j
2.3243963461639526976e-14 - 1.2152003909001023436e-2471j 8.53e-106, 1.3e-847j
6.460668854744676723e-37 - 4.2930720760906816501e-2484j 1.22e-118, 1.86e-860j
0.12987662813078333851 + 2.6590217211894404979e-2465j 2.69e-93, 4.1e-835j
7.2822118318769354911e-05 + 6.5481169346594870518e-2466j 4.35e-99, 6.64e-841j
5.5388524664731831942e-24 + 3.7376157955936188647e-2477j 4.06e-112, 6.19e-854j
1.0203781182780642882e-33 - 2.1226757092546625601e-2482j 3.35e-117, 5.11e-859j
0.094104068968549249526 - 1.4404293407205277475e-2465j 3.88e-98, 5.9e-840j
0.0038839174296797611394 - 3.787264603687495739e-2464j 7.19e-99, 1.1e-840j
0.011146432199215016029 - 7.8565570042746646498e-2465j 2.26e-99, 3.44e-841j
2.7701507348814334742e-15 + 3.3268826087312235211e-2472j 1.35e-107, 2.05e-849j
0.043435193904308890127 + 4.2615538127260753831e-2466j 8.84e-100, 1.33e-841j

Download

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