Rule: Q[3, 69]

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)
260.14001631298665055 + 9.3616157368737164969e-2205j 3.64e-998, 3.64e-998j
242.75776115882745077 + 1.2514044829900028007e-2202j 3.72e-996, 3.72e-996j
216.91048065619168654 + 4.405081819178518799e-2196j 1.96e-993, 1.96e-993j
228.89018767291903763 - 1.6663286736056505444e-2199j 1.12e-994, 1.12e-994j
22.887099477267767295 + 7.1477754895208639747e-2203j 1.94e-994, 1.94e-994j
60.806641011842323971 - 1.476370866305018851e-2195j 3.74e-987, 3.74e-987j
187.34281271293521105 + 6.6784363092968180587e-2201j 1.28e-990, 1.28e-990j
24.782846121289009757 - 2.9969615968040056962e-2240j 8.24e-994, 8.24e-994j
196.39974011991470531 + 1.4110441826639635525e-2233j 1.95e-991, 1.95e-991j
17.688825648105346675 - 4.5841853102297759823e-2273j 1.42e-996, 1.42e-996j
13.202997536658440873 + 3.5183463370065138333e-2273j 6.34e-999, 6.34e-999j
74.846061538600637593 + 1.1989370978809433961e-2275j 2.61e-986, 2.61e-986j
35.539777177932222908 + 7.7903100356183262218e-2303j 7.64e-991, 7.64e-991j
40.466911996871361642 + 2.2026895985735969263e-2327j 7.84e-990, 7.84e-990j
64.138878658875661182 + 3.5981897503668298607e-2394j 6.81e-987, 6.81e-987j
21.073576871607199663 + 5.3116201081335488152e-2436j 3.95e-995, 3.95e-995j
14.620592988792086894 + 1.9860847541998924434e-2439j 4e-998, 4e-998j
30.975794143920698125 + 1.6595624831597484929e-2463j 5.66e-992, 5.66e-992j
114.52188531273391361 - 1.3465410575011790141e-2528j 4.16e-986, 4.16e-986j
48.571546083355668973 - 6.4352785721438924387e-2590j 1.54e-988, 1.54e-988j
104.57584996278782182 - 3.6375298188196256321e-2641j 6.26e-986, 6.26e-986j
163.4298425737417801 + 9.3782163791538441927e-2701j 1.09e-988, 1.09e-988j
178.8870024244574822 + 1.5578141661739941811e-2754j 6.7e-990, 6.7e-990j
99.868753334342898313 - 3.6077661408917086571e-2793j 7.11e-986, 7.11e-986j
143.05648404540305844 - 3.7686232289016903425e-2821j 2.4e-987, 2.4e-987j
206.18952599896683606 - 1.9728861311807802933e-2840j 2.25e-992, 2.25e-992j
3.256889401807762021 - 1.245778281474087776e-2871j 9.11e-1008, 9.11e-1008j
54.476325907548252996 - 9.2789848793618816763e-2849j 8.37e-988, 8.37e-988j
37.957071214326948916 + 1.4335868829433650216e-2866j 2.45e-990, 2.45e-990j
156.30627303329258853 - 7.0594129971829180034e-2862j 3.48e-988, 3.48e-988j
57.586848064382311786 + 6.9286247661732420668e-2884j 1.81e-987, 1.81e-987j
1.8244937080495580804 - 1.4541590602222341507e-2934j 7.76e-1011, 7.76e-1011j
2.2942803602790417198 + 1.0615293988881813355e-2932j 1.3e-1009, 1.3e-1009j
90.942322360282281175 + 1.8420564432713303685e-2908j 6.96e-986, 6.96e-986j
109.45693731041393402 + 1.2075025234798660533e-2930j 5.19e-986, 5.19e-986j
125.24953516041382993 + 6.9137594950204074465e-2943j 1.82e-986, 1.82e-986j
33.213241926537400431 - 9.8389708402618360986e-2965j 2.05e-991, 2.05e-991j
8.2934960154722071914 - 5.5462817580861760225e-2976j 2.29e-1002, 2.29e-1002j
3.8716139681852821621 + 8.5209147650271247408e-2981j 6.09e-1007, 6.09e-1007j
82.617703007581251525 + 2.8021190342657626599e-2959j 5.09e-986, 5.09e-986j
149.52643407507246007 - 4.0658909041848698698e-2968j 9.37e-988, 9.37e-988j
9.4077908425518306951 + 7.5545877090974124074e-2993j 1.77e-1001, 1.77e-1001j
4.5931623093415053711 + 3.7851642956086714734e-2997j 4.68e-1006, 4.68e-1006j
10.597187672565697213 + 3.7049838832381622994e-2992j 1.31e-1000, 1.31e-1000j
11.86207750456933464 - 7.9330904570393769601e-2991j 9.91e-1000, 9.91e-1000j
43.07121335957676944 + 2.5956262442845475057e-2980j 2.38e-989, 2.38e-989j
78.665457704118951172 - 2.5485287525545246272e-2976j 3.84e-986, 3.84e-986j
1.3850658793784211811 - 1.8385709850599988974e-3019j 4.21e-1012, 4.21e-1012j
0.99931729609036389063 + 1.3216941529737400785e-3020j 1.78e-1013, 1.78e-1013j
5.4019643703915269511 - 3.3766486187707413573e-3012j 3.87e-1005, 3.87e-1005j
86.708062564045204076 - 1.4570357103376292781e-2992j 6.33e-986, 6.33e-986j
45.77202538505655172 + 2.4219050369565720183e-3005j 6.17e-989, 6.17e-989j
170.93905643234592858 + 3.0504774462025312701e-3002j 3.2e-989, 3.2e-989j
19.341164559968458218 + 1.7479874365974643327e-3028j 7.64e-996, 7.64e-996j
16.115597912331128843 - 1.7205833757090709127e-3029j 2.53e-997, 2.53e-997j
51.472134561286164337 + 9.8080876275411703678e-3019j 3.96e-988, 3.96e-988j
136.86858907968988608 + 5.4872286103089993215e-3019j 5.19e-987, 5.19e-987j
95.326863848217024393 + 3.2091894177779559056e-3045j 7.19e-986, 7.19e-986j
71.154707561784378132 - 2.5910708480815273592e-3083j 1.87e-986, 1.87e-986j
0.41577455678347908331 - 1.5090483360120311987e-3163j 3.23e-1016, 3.23e-1016j
6.2899450829374791969 - 9.066451206579306588e-3141j 3.3e-1004, 3.3e-1004j
119.78185164626331707 + 4.8000126103865344739e-3132j 2.72e-986, 2.72e-986j
130.93949904634088342 + 6.9099362676067069575e-3168j 1.03e-986, 1.03e-986j
28.825870951430784754 + 1.0085195528383692373e-3185j 1.54e-992, 1.54e-992j
0.67537560419759826503 - 9.4855489713773896295e-3209j 7.93e-1015, 7.93e-1015j
2.7575417343620055721 + 1.2651744610939476753e-3202j 1.35e-1008, 1.35e-1008j
0.08848592946754548595 - 1.2942761551305586267e-3212j 4.76e-1019, 4.76e-1019j
67.586993919943200255 - 2.3800959837261727993e-3178j 1.13e-986, 1.13e-986j
0.016620103480974776803 + 5.8821495021730477723e-3220j 1.15e-1020, 1.15e-1020j
7.254136993549744535 - 2.1156994141014068815e-3201j 2.82e-1003, 2.82e-1003j
0.22063693103840436827 + 1.5542745314413759589e-3214j 1.29e-1017, 1.29e-1017j
26.762010619523319788 + 1.657873721947541044e-3190j 3.82e-993, 3.82e-993j

Weights

Weight (ball center) Error (ball radius)
2.1578867709896316346e-112 - 7.8792723195987667345e-2267j 1.09e-153, 2.64e-900j
5.6635400913554705178e-105 + 4.6961237293021181183e-2263j 1.02e-151, 2.48e-898j
7.0675517944163654741e-94 + 2.1280879984037216761e-2257j 4.24e-149, 1.03e-895j
5.0197252122066282397e-99 - 5.0333189654606180638e-2260j 1.96e-150, 4.75e-897j
2.1304549276793506871e-10 - 8.5480965406065500178e-2213j 4.73e-87, 1.15e-833j
1.2802193620752149034e-26 + 8.6889281561469458472e-2222j 2.19e-115, 5.33e-862j
3.797297616531177528e-81 - 6.862865449905300093e-2251j 2.68e-146, 6.51e-893j
3.3429685782151207882e-11 - 2.8400132418558582689e-2213j 4.74e-91, 1.15e-837j
4.7607135682601703252e-85 + 6.902946046246839729e-2253j 2.66e-147, 6.47e-894j
3.3525489237926420857e-08 + 5.2123464003395567204e-2212j 7.75e-83, 1.88e-829j
2.5446035295379634507e-06 - 3.592035218711760322e-2211j 9.88e-76, 2.4e-822j
1.1730951327074968073e-32 - 1.6497113524575263658e-2225j 4.76e-123, 1.16e-869j
8.7159997147043015513e-16 + 1.1552529537419450599e-2216j 9.31e-103, 2.26e-849j
6.8097344254221546279e-18 + 5.0086004462943291537e-2218j 1.68e-106, 4.09e-853j
4.7313489947052290261e-28 + 1.2129335106384831186e-2222j 8.71e-119, 2.12e-865j
1.2488743184301222802e-09 + 2.2791300863587928334e-2212j 2.35e-89, 5.72e-836j
6.509828228643297699e-07 + 1.8584813543399995926e-2211j 1.24e-81, 3.02e-828j
7.7358499194771066172e-14 + 2.2464007478354314736e-2215j 1.18e-99, 2.86e-846j
9.4725549157388723376e-50 + 1.1338507698058256341e-2234j 3.27e-137, 7.94e-884j
2.293172178266134619e-21 - 3.1352126966916526805e-2221j 5.58e-113, 1.36e-859j
1.8359104128253698445e-45 + 2.0235916134868935469e-2232j 9.75e-135, 2.37e-881j
7.7117943121319675173e-71 + 1.340927631239069056e-2245j 2.52e-147, 6.14e-894j
1.6733097770803862414e-77 + 5.064012730347854007e-2249j 2.99e-149, 7.27e-896j
1.9610372052822023855e-43 - 2.3866980924917571881e-2231j 9e-135, 2.19e-881j
4.7032562809363123945e-62 - 4.5489508263621294475e-2241j 8.2e-145, 1.99e-891j
2.8989902477330751942e-89 - 4.8274259509719164489e-2255j 1.51e-153, 3.68e-900j
0.021288451487540866639 - 2.0098998869523967328e-2208j 9.71e-70, 2.36e-816j
6.7067386034608397501e-24 + 4.3196424533176159164e-2221j 4.09e-121, 9.94e-868j
8.0716727342906304348e-17 - 2.4898498846914264032e-2217j 4.67e-113, 1.14e-859j
9.0938965247720569679e-68 - 5.114737313250358573e-2244j 6.49e-147, 1.58e-893j
3.0951035384038631727e-25 - 2.4375741362710073965e-2221j 2.12e-122, 5.16e-869j
0.074283373199479697227 + 2.5199540495526355321e-2208j 5.48e-67, 1.33e-813j
0.04748565588720163612 - 2.9230721457184698508e-2208j 9.73e-71, 2.36e-817j
1.3758005424199566096e-39 - 2.6622178111693067447e-2229j 1.35e-134, 3.29e-881j
1.4451859148832594281e-47 - 1.5820596373559983018e-2233j 2.17e-138, 5.28e-885j
2.24469884547031165e-54 + 4.3726304297451756708e-2237j 8.33e-143, 2.02e-889j
8.5888513075743788426e-15 - 5.1414650000373451468e-2216j 5.01e-115, 1.22e-861j
0.00026935512246153485563 - 4.7026388295670203876e-2210j 2.51e-98, 6.1e-845j
0.014006660115822025588 + 1.1004788247502008919e-2208j 2.21e-87, 5.37e-834j
5.2948661739857051173e-36 - 2.3022595971066977787e-2227j 1.9e-133, 4.61e-880j
7.6267650668882971615e-65 + 1.6463581916354135466e-2242j 7.22e-147, 1.76e-893j
9.4541792182167167406e-05 + 2.5081344275019752321e-2210j 5.1e-101, 1.24e-847j
0.0077650667779873855098 - 5.7225501489447525964e-2209j 6.53e-93, 1.59e-839j
3.0659648744261308182e-05 - 1.3245339920589154904e-2210j 1.13e-102, 2.75e-849j
9.1885036164808160966e-06 + 6.9249104137823597722e-2211j 5.27e-104, 1.28e-850j
5.2241602124911555327e-19 - 8.9511459903099561168e-2219j 7.9e-122, 1.92e-868j
2.6632685477405118337e-34 + 1.9832193244400450367e-2226j 1.83e-133, 4.46e-880j
0.10381081194548288356 - 2.1478788641583184264e-2208j 4.53e-88, 1.1e-834j
0.13089197227120995553 + 1.8526519695981945936e-2208j 4.46e-88, 1.08e-834j
0.0038277195528684897282 + 3.0256656318338440849e-2209j 7.38e-100, 1.79e-846j
9.1705578488634592315e-38 + 2.5472106488887628803e-2228j 1.85e-135, 4.5e-882j
3.6371483477821087562e-20 + 1.2321456183223409195e-2219j 7.8e-124, 1.9e-870j
4.4632313813701149834e-74 - 2.9049490189681521675e-2247j 2.37e-153, 5.77e-900j
6.7405134074986537033e-09 - 3.0414286084224134741e-2212j 1.62e-114, 3.94e-861j
1.5378106972947533683e-07 - 9.6947356307856291896e-2212j 9.13e-113, 2.22e-859j
1.306307043539359668e-22 - 7.0276332055166674475e-2221j 3.23e-126, 7.85e-873j
2.1919826522364531356e-59 + 1.0942184484635614191e-2239j 6.25e-148, 1.52e-894j
1.7766269659876080668e-41 + 2.6102888854917853927e-2230j 1.08e-138, 2.63e-885j
4.5464241822700087637e-31 + 1.3559661309641179616e-2224j 9.36e-134, 2.27e-880j
0.14994356054387248406 + 1.2701485788475706089e-2208j 2.55e-108, 6.21e-855j
0.0017182775138289799647 - 1.6233586093781919361e-2209j 8.08e-114, 1.96e-860j
5.1132189747525179032e-52 - 7.4027730761301791922e-2236j 8.99e-145, 2.18e-891j
7.8997409258680146837e-57 - 2.3187253497954376491e-2238j 3.34e-147, 8.12e-894j
6.3778893817689044226e-13 - 9.9304684187484507043e-2215j 4.75e-125, 1.15e-871j
0.14859007547019410658 - 1.5749757762918918632e-2208j 5e-115, 1.21e-861j
0.029363771200209474528 + 2.8411061894370379701e-2208j 1.01e-115, 2.45e-862j
0.092895549645254438685 + 5.2476019363738530097e-2209j 1.45e-116, 3.49e-863j
1.5570786074628620664e-29 - 1.1585765200389404793e-2223j 5.93e-134, 1.44e-880j
0.04206259853666980786 - 1.6169827578107395349e-2209j 3.23e-117, 7.75e-864j
0.0007085589217693437707 + 8.7502568405256826573e-2210j 2.99e-119, 7.22e-866j
0.13095076072928513777 - 9.1641962976932469942e-2209j 3.43e-117, 8e-864j
4.8198725854447152529e-12 + 4.7046928059422948561e-2214j 1.38e-124, 3.36e-871j

Download

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