Rule: Q[3, 71]

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)
267.99474103422644415 - 3.3494539437278962115e-2215j 1.48e-997, 1.48e-997j
236.41734331501196989 + 4.0125153610371878293e-2209j 4.4e-994, 4.4e-994j
250.43435998216312695 - 1.1688086510591319211e-2224j 1.45e-995, 1.45e-995j
213.45603857738748055 - 1.4151555592079119423e-2257j 1.06e-991, 1.06e-991j
79.903777742682799931 - 1.3604022585899388033e-2297j 3.42e-985, 3.42e-985j
15.765341495963898458 - 3.9504509069001531503e-2349j 5.64e-997, 5.64e-997j
65.483272650469172687 + 1.8535706053935995347e-2336j 5.68e-986, 5.68e-986j
44.464990198097897067 - 1.364239316994211167e-2359j 2.26e-988, 2.26e-988j
203.546936583524485 + 1.4258032673964023051e-2390j 9.16e-991, 9.16e-991j
87.86511346259806008 - 2.711544475251424e-2440j 6.04e-985, 6.04e-985j
32.325238794271823651 + 4.7389460103067279024e-2474j 6.72e-991, 6.72e-991j
41.856489593402158837 - 7.0363296879595258843e-2468j 8.02e-989, 8.02e-989j
105.49574008403729071 - 1.2063044303411250839e-2491j 6.82e-985, 6.82e-985j
76.11742756921186526 + 3.0275539893025404989e-2542j 2.48e-985, 2.48e-985j
96.379345952257667995 + 3.050019302736055255e-2584j 7.48e-985, 7.48e-985j
47.167462243915843457 - 6.6014423946348978722e-2613j 5.84e-988, 5.84e-988j
28.078613143898987761 + 1.9846853788282369599e-2626j 4.43e-992, 4.43e-992j
72.454560861412865174 + 1.2006532428686600827e-2648j 1.63e-985, 1.63e-985j
120.4356152571612791 - 3.2040874908779677363e-2685j 3.28e-985, 3.28e-985j
194.3754715734824658 + 1.9766944358698686536e-2713j 6.14e-990, 6.14e-990j
22.326637039330301691 - 1.1562054729566461363e-2741j 4.5e-994, 4.5e-994j
131.35658042890218929 - 2.1928590440541845969e-2731j 1.4e-985, 1.4e-985j
18.890831245995290069 + 8.3095385495833553719e-2753j 1.88e-995, 1.88e-995j
156.02943010448035636 - 7.0935345030844569381e-2742j 6.09e-987, 6.09e-987j
185.80882438852850482 + 1.0427116178516318199e-2749j 3.4e-989, 3.4e-989j
224.30272969589642048 + 1.547608336898446194e-2756j 8.79e-993, 8.79e-993j
12.944279422765047752 - 1.3463428941961772712e-2778j 1.44e-998, 1.44e-998j
162.91116856075466218 - 8.0861901233473275919e-2764j 2.06e-987, 2.06e-987j
110.29810484224277636 - 1.5286596357553547739e-2783j 6.09e-985, 6.09e-985j
34.576035422712085109 + 2.2447647033003269412e-2811j 2.49e-990, 2.49e-990j
125.79195971130128723 - 1.431058086133493534e-2804j 2.29e-985, 2.29e-985j
14.317058909218619569 + 6.2057344863075011312e-2840j 9.57e-998, 9.57e-998j
10.423707861844832154 + 7.3397414095224047034e-2843j 2.93e-1000, 2.93e-1000j
62.167622997895617033 + 3.5684144888368975648e-2827j 3.18e-986, 3.18e-986j
83.818055690078254145 + 3.9758789933268184646e-2854j 4.86e-985, 4.86e-985j
137.14415663216516853 + 1.194917989909366623e-2885j 7.09e-986, 7.09e-986j
2.8338656959412632292 - 4.9435496930284729009e-2949j 1.51e-1008, 1.51e-1008j
2.2942803602790417198 - 1.3547623481290540558e-2949j 1.06e-1009, 1.06e-1009j
6.2899450829374791969 + 1.2247626880373881659e-2943j 9.73e-1004, 9.73e-1004j
17.289702157165058033 + 9.8509457383810499971e-2937j 3.26e-996, 3.26e-996j
177.75298699763671162 + 1.5162329190400657508e-2924j 1.66e-988, 1.66e-988j
30.159893665405483928 + 3.0805063256193519431e-2957j 1.77e-991, 1.77e-991j
9.2757364596719658257 + 1.7163426602361067804e-2972j 4.52e-1001, 4.52e-1001j
1.8022713916862594778 - 3.1816954812025526127e-2983j 6.05e-1011, 6.05e-1011j
5.4547965421823246572 - 4.4222618652423573541e-2976j 1.32e-1004, 1.32e-1004j
143.17166761280957582 - 6.9263076376066698398e-2956j 3.55e-986, 3.55e-986j
52.862781232845751528 + 1.0691757837540307608e-2967j 3.46e-987, 3.46e-987j
49.965983642501192426 - 7.9062824223023281847e-2973j 1.4e-987, 1.4e-987j
0.41577455678347908331 + 3.967152603273867697e-3022j 3.94e-1016, 3.94e-1016j
20.569517231906694484 + 5.2203295515393880877e-2999j 1.03e-994, 1.03e-994j
92.050264327231699685 - 3.0359724707150062034e-2988j 6.87e-985, 6.87e-985j
149.45894760183422836 + 2.8044239716178647961e-3013j 1.48e-986, 1.48e-986j
58.960937885439195831 + 1.2641628796112074395e-3035j 1.62e-986, 1.62e-986j
100.85879557508525545 + 8.3989808568504014193e-3070j 7.33e-985, 7.33e-985j
3.4123932001098265521 - 9.9525575123182551581e-3138j 1.7e-1007, 1.7e-1007j
11.646573346239446188 + 1.3491040886613662236e-3129j 2.09e-999, 2.09e-999j
0.67055960023696946215 + 3.7832440639929208479e-3145j 8.86e-1015, 8.86e-1015j
68.911095518839622862 - 2.8131457880067924078e-3115j 1.03e-985, 1.03e-985j
8.203153483992120308 - 2.5923941480291850999e-3159j 5.7e-1002, 5.7e-1002j
1.3651700394671394559 + 1.753328367857677022e-3169j 3.58e-1012, 3.58e-1012j
4.703711476786871891 - 3.2809406175845316149e-3163j 1.37e-1005, 1.37e-1005j
0.090111673092255388873 + 8.1738208066890384666e-3177j 5.34e-1019, 5.34e-1019j
0.9872452110440930957 - 8.5788753670664970557e-3172j 1.66e-1013, 1.66e-1013j
7.2071489013980744828 + 2.7195139443871496221e-3160j 7.59e-1003, 7.59e-1003j
4.0297825424606312198 - 1.2655835904118533178e-3164j 1.67e-1006, 1.67e-1006j
36.913767026603781226 - 1.370250357423491546e-3143j 8e-990, 8e-990j
115.27474631259201435 + 8.1436939573451095274e-3145j 4.76e-985, 4.76e-985j
0.017045630206938375165 + 3.8975065157317125359e-3247j 1.28e-1020, 1.28e-1020j
39.340019776657580132 + 1.194951963168234011e-3169j 2.56e-989, 2.56e-989j
26.080101738694663124 + 2.1749021580661613422e-3173j 1.01e-992, 1.01e-992j
0.22260439098712135782 + 1.1875776985618306122e-3198j 1.56e-1017, 1.56e-1017j
55.86024397429040366 - 2.4661015744335748841e-3165j 7.89e-987, 7.89e-987j
24.163151137447555647 + 9.2898472223163533089e-3192j 2.31e-993, 2.31e-993j
170.13827211442501237 - 2.6107670076864874696e-3183j 6.47e-988, 6.47e-988j

Weights

Weight (ball center) Error (ball radius)
8.4542515620579098998e-116 + 5.3779750114399958354e-2319j 2.12e-158, 6.39e-902j
2.7317524924313096741e-102 - 5.5276277965490926896e-2311j 8.15e-155, 2.45e-898j
2.6529780177505726264e-108 - 7.2691851951484042607e-2315j 1.57e-156, 4.74e-900j
2.0492957589692929885e-92 - 4.5865298107783711869e-2307j 2.14e-152, 6.45e-896j
7.6496082183547929309e-35 - 1.1282011074174963228e-2278j 6.39e-125, 1.92e-868j
2.1148567313702601338e-07 + 2.5881232358086518098e-2264j 3.64e-78, 1.1e-821j
1.2267556264475701993e-28 - 1.6117564596776837339e-2275j 1.91e-119, 5.75e-863j
1.2977453347731320378e-19 + 7.0539819708583121885e-2271j 6.84e-109, 2.06e-852j
3.7935405593424824017e-88 + 4.5748404509521266152e-2305j 5.73e-152, 1.72e-895j
2.8513769148055406143e-38 - 2.0787586303165654008e-2280j 2.71e-128, 8.17e-872j
2.0197292891017466493e-14 - 3.713251179722147216e-2268j 1.09e-101, 3.28e-845j
1.700458087642708854e-18 - 2.689782323162442789e-2270j 5.46e-108, 1.64e-851j
7.2038420231398487809e-46 - 3.1020483507259777493e-2284j 9.12e-135, 2.75e-878j
3.2630156689183698913e-33 + 7.568714459377554736e-2278j 1.58e-124, 4.77e-868j
6.1198987370518562819e-42 - 2.9349498795738587473e-2282j 5.33e-132, 1.6e-875j
9.0112693927533055937e-21 - 1.7690969962463490205e-2271j 2.92e-113, 8.81e-857j
1.303697621264252446e-12 - 3.4239009386745345721e-2267j 3.17e-102, 9.54e-846j
1.2302395471653433067e-31 - 4.7843483524239718552e-2277j 1.21e-123, 3.65e-867j
2.6072507760848793588e-52 + 1.8378116988430066101e-2287j 2.18e-140, 6.58e-884j
3.3945895208823799704e-84 - 3.5459734869367431635e-2303j 9.25e-155, 2.79e-898j
3.6151658563374322107e-10 + 7.2273417607026905068e-2266j 2.75e-101, 8.29e-845j
5.0864080251197718729e-57 + 8.1966842219147150829e-2290j 7.07e-144, 2.13e-887j
1.0247048168321611977e-08 + 4.6217414279676168902e-2265j 4.72e-99, 1.42e-842j
1.1606800864181457975e-67 + 4.2903741879510464474e-2295j 1.08e-149, 3.25e-893j
1.671950967994060135e-80 + 2.1643999008593427472e-2301j 1.75e-154, 5.27e-898j
4.4037459241566371165e-97 + 3.8319522255616920667e-2309j 3.03e-160, 9.14e-904j
3.190894458758368091e-06 + 1.2813126368852752538e-2263j 3.99e-98, 1.2e-841j
1.2492606150092729031e-70 - 1.4729457381016360168e-2296j 3.04e-151, 9.15e-895j
6.1272801181505572836e-48 + 2.8364761158123808716e-2285j 1.45e-140, 4.37e-884j
2.2101087223098100781e-15 + 1.1525545975206699048e-2268j 1.89e-117, 5.68e-861j
1.2773086661962768266e-54 - 1.2896355364399571535e-2288j 4.56e-144, 1.37e-887j
8.5415521053790666971e-07 - 5.844074837245952696e-2264j 1.21e-103, 3.65e-847j
3.5231180164170902042e-05 + 5.6745762654436464182e-2263j 4.85e-100, 1.46e-843j
3.2677510455391557352e-27 + 8.6201397354192530201e-2275j 2.4e-129, 7.23e-873j
1.5781368199068974994e-36 + 1.581190963554725442e-2279j 3.03e-134, 9.13e-878j
1.622678392226935449e-59 - 4.6876355028970582553e-2291j 2.09e-147, 6.28e-891j
0.032936169125448016329 - 5.4568169989159685272e-2261j 2.08e-86, 6.27e-830j
0.052159633205815445267 + 5.7663030699813630982e-2261j 1.95e-83, 5.88e-827j
0.0016262743353370561314 + 8.3248728784013786837e-2262j 3.21e-98, 9.67e-842j
4.8420746007719701377e-08 - 1.1113764723552050493e-2264j 4.22e-110, 1.27e-853j
4.9699815852933864366e-77 - 1.065031457010304261e-2299j 1.09e-155, 3.28e-899j
1.6931401119886811039e-13 + 1.1496798669101592507e-2267j 3e-119, 9.02e-863j
0.00010401142960727494339 - 1.1502798430635774968e-2262j 9.41e-105, 2.83e-848j
0.076772552499032334452 - 5.8410499263486337183e-2261j 2.37e-86, 7.14e-830j
0.0033909392644210598207 - 1.50601453647425882e-2261j 3e-99, 9.03e-843j
4.0783028568754911046e-62 + 2.3941121156661811027e-2292j 3.65e-149, 1.1e-892j
3.2458194335506230574e-23 - 9.6880078741421663342e-2273j 1.34e-129, 4.03e-873j
5.6817024184709005787e-22 + 4.238258555452055664e-2272j 2.16e-128, 6.52e-872j
0.14771344708461583342 - 3.8961318030467118359e-2261j 6.11e-94, 1.84e-837j
2.0032356777699202044e-09 - 1.85921164976411776e-2265j 1.35e-116, 4.05e-860j
4.4883794679375794844e-40 + 2.5570789580094959204e-2281j 4.89e-139, 1.47e-882j
7.9186642976300089484e-65 - 1.0825468877698728203e-2293j 1.81e-151, 5.45e-895j
7.8044671427562339949e-26 - 4.3750679915151387705e-2274j 2.71e-132, 8.17e-876j
7.1821683160421565382e-44 + 3.133670902817662846e-2283j 1.91e-141, 5.75e-885j
0.019661856670780839115 + 4.7979026522061836974e-2261j 3.75e-108, 1.13e-851j
1.1026051866805743029e-05 - 2.7319841358310628949e-2263j 4.35e-116, 1.31e-859j
0.14614190056425462937 + 4.7727720670789406095e-2261j 3.19e-104, 9.61e-848j
4.1162295874477718952e-30 + 2.8552841791843299972e-2276j 2.63e-134, 7.92e-878j
0.00028325280007211675148 + 2.2790448478866078654e-2262j 1.2e-114, 3.6e-858j
0.10417942742070560843 + 5.7181093019193860676e-2261j 1.35e-106, 4.06e-850j
0.0064345297130953425843 + 2.5247896193486486265e-2261j 4.45e-112, 1.34e-855j
0.09372690998903230265 - 1.559307131268055857e-2261j 7.78e-107, 2.34e-850j
0.12948364093949767602 - 5.3745675305978851532e-2261j 8.57e-107, 2.58e-850j
0.00070944928415363158516 - 4.4143204229633727495e-2262j 2.9e-114, 8.73e-858j
0.011405884161080043451 - 3.7421059978054632734e-2261j 1.49e-111, 4.49e-855j
2.2153644425862476975e-16 - 3.4347847625252723055e-2269j 1.36e-128, 4.1e-872j
4.3809101903368547993e-50 - 2.3859450097154723685e-2286j 2.2e-146, 6.62e-890j
0.043040694239403342998 + 4.7130583942588023791e-2262j 4.92e-113, 1.48e-856j
2.0311003586627838208e-17 + 9.8188141075582375507e-2270j 2.42e-129, 7.29e-873j
9.2313590198930521135e-12 + 9.8169293990401968584e-2267j 1.6e-126, 4.81e-870j
0.13017885240282262906 + 2.7826792450034883035e-2261j 4.14e-116, 1.25e-859j
1.6761378308666636472e-24 + 2.1103598399020992727e-2273j 1.09e-133, 3.28e-877j
6.0177946484169493581e-11 - 2.7122502412214009678e-2266j 3.74e-126, 1.13e-869j
9.5473879050662629302e-74 + 4.3202874390500285323e-2298j 2.7e-159, 8.15e-903j

Download

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