Rule: Q[1, 3, 61]

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)
214.80745541343883303 + 2.2368092932450195412e-2256j 2.35e-998, 2.35e-998j
170.53627025160832498 + 1.8115128374709748375e-2251j 7.21e-994, 7.21e-994j
201.52816050616236129 + 7.7467096609790224737e-2258j 6.37e-997, 6.37e-997j
190.08004976653144291 + 2.5297276001832077752e-2263j 9.83e-996, 9.83e-996j
231.48933143700157455 + 2.4309808358355311269e-2272j 3.11e-1000, 3.11e-1000j
7.8232631436879996743 + 2.301703640979586806e-2293j 7.08e-1004, 7.08e-1004j
98.428952743135826983 + 1.2138810803877677745e-2297j 1.73e-989, 1.73e-989j
84.371258347129093538 - 1.1817926281235137388e-2368j 2.11e-989, 2.11e-989j
93.553161299858901873 - 3.5163755664206352786e-2452j 1.94e-989, 1.94e-989j
64.313249060559339394 + 1.085566793866475873e-2522j 6.52e-990, 6.52e-990j
23.070829087177636415 + 1.729634944335443558e-2551j 3.29e-996, 3.29e-996j
31.709037332402431615 + 1.9049174095087680262e-2569j 7.38e-994, 7.38e-994j
14.363438802971504805 + 2.927165917325411841e-2611j 1.02e-999, 1.02e-999j
103.51053348560546004 - 6.9936814223003114921e-2711j 1.22e-989, 1.22e-989j
60.741285844887430867 - 4.1102789481104086801e-2859j 4.26e-990, 4.26e-990j
126.21344914822250415 + 1.1937220637822244431e-2954j 1.34e-990, 1.34e-990j
34.115434960461895208 + 4.8457354265201147628e-2994j 2.49e-993, 2.49e-993j
120.14266851783271323 - 9.5743467975066013003e-3023j 3.05e-990, 3.05e-990j
179.85502532479651945 + 1.891677347336431566e-3056j 1.04e-994, 1.04e-994j
10.187451581166825975 - 1.1123733370836129798e-3083j 4.28e-1002, 4.28e-1002j
17.57826699087458341 - 4.1542133717954166471e-3080j 3.36e-998, 3.36e-998j
4.0879198016405352761 + 4.1781807660313640726e-3090j 1.24e-1007, 1.24e-1007j
39.239589690306125836 + 2.1214660155933296483e-3071j 2.04e-992, 2.04e-992j
114.34969812292964084 - 1.4766029301221161712e-3083j 5.22e-990, 5.22e-990j
25.086149257961332041 - 7.7796474118865406906e-3114j 1.4e-995, 1.4e-995j
8.9638850683781212002 - 4.1829901034014506496e-3122j 5.72e-1003, 5.72e-1003j
12.886332141703801472 + 1.4047212135807847083e-3120j 1.8e-1000, 1.8e-1000j
68.023704285577949899 + 5.4933101135486333503e-3107j 1.06e-989, 1.06e-989j
5.7892523456053042649 + 6.5348825072547894894e-3142j 1.11e-1005, 1.11e-1005j
132.58901151043097415 - 4.9441087037697528703e-3126j 6.12e-991, 6.12e-991j
71.87823069578385232 + 3.1954654766222965937e-3135j 1.46e-989, 1.46e-989j
4.8962169176666545658 + 2.2770338932581512412e-3154j 1.07e-1006, 1.07e-1006j
47.743302551559642754 + 1.6814670789174028037e-3138j 3.2e-991, 3.2e-991j
27.196401374060735964 + 5.4579839612488716852e-3142j 5.88e-995, 5.88e-995j
50.807806657469228331 - 9.1955097120907166189e-3139j 6.47e-991, 6.47e-991j
53.992993191895816634 + 1.3766077753539324595e-3137j 1.28e-990, 1.28e-990j
11.494654621297973379 - 4.3959010955625431026e-3149j 2.87e-1001, 2.87e-1001j
1.3972225753803087208 - 5.1128861900915735512e-3160j 1.78e-1012, 1.78e-1012j
15.927032148667996068 - 3.5070372064025812812e-3146j 6.04e-999, 6.04e-999j
88.870863134305425303 - 9.9141774827884142257e-3136j 2.27e-989, 2.27e-989j
161.93190221942891854 + 1.7494457438277314681e-3151j 4.06e-993, 4.06e-993j
0.056897625001077184683 + 1.2343596093417709043e-3195j 1.19e-1019, 1.19e-1019j
3.369839231310923141 - 1.7733504350045527062e-3183j 1.48e-1008, 1.48e-1008j
2.2581944863606346108 + 7.301027974751627387e-3186j 2.41e-1010, 2.41e-1010j
44.795913740132745053 + 1.2032342004535219788e-3166j 1.38e-991, 1.38e-991j
6.7651008943136125347 - 6.7574950046568763257e-3180j 8.8e-1005, 8.8e-1005j
57.30274252250950054 + 4.5741343607286943521e-3164j 2.36e-990, 2.36e-990j
21.148764443482709944 - 4.890535664178334563e-3181j 8.1e-997, 8.1e-997j
0.65983144550216817308 + 4.9890281678935384469e-3199j 2.88e-1015, 2.88e-1015j
1 + 3.0100434597419977593e-3197j 8.61e-1014, 8.61e-1014j
139.3021476294809658 + 1.1198845832767003894e-3172j 2.18e-991, 2.18e-991j
153.91439978502569023 + 5.8464242258443438479e-3197j 1.83e-992, 1.83e-992j
108.81200875868128792 + 3.3123259610597933875e-3214j 8.9e-990, 8.9e-990j
75.882986890164036888 + 6.7626175611853713814e-3222j 1.79e-989, 1.79e-989j
0.0019677590828496266051 - 6.2017136601157158775e-3261j 7.11e-1022, 7.11e-1022j
0.38707439279303175613 + 7.9529630382546999991e-3257j 1.1e-1016, 1.1e-1016j
146.39346748035735202 - 4.4591100624851484187e-3229j 6.79e-992, 6.79e-992j
19.318394527630822778 - 5.9648730036230155415e-3244j 1.63e-997, 1.63e-997j
41.962353940346194764 + 5.0364176168094709847e-3238j 5.95e-992, 5.95e-992j
1.8249634487698213027 - 7.2549356645096331565e-3258j 2.63e-1011, 2.63e-1011j
36.624815977156183468 + 2.1836910071780045515e-3240j 7.29e-993, 7.29e-993j
29.40338594113518229 - 7.2416499101608672836e-3241j 2.11e-994, 2.11e-994j
2.7556462644454607855 - 8.426499662422707883e-3256j 1.84e-1009, 1.84e-1009j
80.044797589351298884 + 9.8943150224376891852e-3235j 2.23e-989, 2.23e-989j
0.18557452325303085947 + 2.5508756211109965135e-3275j 4.07e-1018, 4.07e-1018j

Weights

Weight (ball center) Error (ball radius)
7.4708799084596786006e-93 + 7.0061735633180407821e-2336j 1.41e-165, 1.08e-912j
7.730203566209287344e-74 - 7.1220214322533207801e-2325j 9.17e-160, 7.02e-907j
3.6691924130861225899e-87 - 7.704094167766315892e-2333j 3.7e-164, 2.83e-911j
3.0298806456702204476e-82 + 3.8257031923947612457e-2330j 8.42e-163, 6.45e-910j
5.7477723884919495772e-100 - 1.2642464080407379023e-2339j 7.83e-169, 6e-916j
0.00044007771548475571949 - 5.1727185638111042417e-2290j 7.34e-85, 5.62e-832j
8.9078475581115974957e-43 + 1.4676675484572596784e-2310j 1.2e-148, 9.22e-896j
1.006045895751280585e-36 - 1.6301767913382215104e-2307j 1.49e-145, 1.14e-892j
1.1208442808878254972e-40 - 1.6594831192000129702e-2309j 1.2e-147, 9.21e-895j
4.268259706171809922e-28 + 4.0184350782149439028e-2303j 2.39e-140, 1.83e-887j
1.8818484398351028733e-10 - 8.0882656497070113988e-2294j 1.16e-117, 8.92e-865j
3.9907418447641680455e-14 - 8.0492881539923393105e-2296j 4.53e-125, 3.47e-872j
8.788781605710857014e-07 + 1.006163805156361273e-2291j 1.85e-107, 1.42e-854j
5.7680739989317695493e-45 - 1.1813147688725143821e-2311j 7e-151, 5.36e-898j
1.4622250682253967202e-26 - 2.4684718479917922986e-2302j 8.19e-140, 6.27e-887j
9.5469215687631916006e-55 - 1.7233375932997269684e-2316j 2.43e-157, 1.86e-904j
3.7527431421906834708e-15 + 2.2684652082383372105e-2296j 2.14e-129, 1.64e-876j
3.9408937576254597028e-52 + 3.3084831102965483673e-2315j 4.91e-156, 3.76e-903j
7.5539795225720295358e-78 - 1.3739993152405337779e-2327j 1.44e-166, 1.11e-913j
4.7623836668200268629e-05 - 1.1716912328894681351e-2290j 1.95e-108, 1.49e-855j
3.9368091394366178e-08 + 1.6426143574959360058e-2292j 1.28e-118, 9.81e-866j
0.012825287735267455248 - 8.1648891946867156939e-2289j 1.78e-93, 1.36e-840j
2.4249374468122044654e-17 + 1.5580024893291817331e-2297j 2.65e-134, 2.03e-881j
1.2345782062358166065e-49 - 5.6430382278721619964e-2314j 5.3e-155, 4.06e-902j
2.6279498196294515951e-11 + 2.7291065393945098996e-2294j 9.99e-126, 7.65e-873j
0.00015123391962436766116 + 2.4948289190223359683e-2290j 1.71e-108, 1.31e-855j
3.632068912056211955e-06 - 2.3582394236244393799e-2291j 1.93e-114, 1.48e-861j
1.0847919452015392374e-29 - 6.1273830785268569383e-2304j 4.12e-145, 3.16e-892j
0.0028601432473728061659 - 2.0905651415395988945e-2289j 4.7e-105, 3.6e-852j
1.7091870426676461967e-57 + 7.9270271678641295578e-2318j 3.07e-160, 2.35e-907j
2.3873423859174973396e-31 + 8.7291262428503972853e-2305j 1.57e-146, 1.21e-893j
0.0063623735031583645117 + 4.1300581980239771342e-2289j 1.57e-105, 1.2e-852j
5.5366365755309634534e-21 - 1.9104641135325242312e-2299j 1.16e-140, 8.91e-888j
3.3332375485555654529e-12 - 8.818413666590205153e-2295j 5.83e-131, 4.46e-878j
2.6865340734963712342e-22 + 3.9529738706047641186e-2300j 7.34e-142, 5.62e-889j
1.1550363148695180188e-23 - 7.7259567047478021957e-2301j 5.33e-143, 4.08e-890j
1.3741695105129175964e-05 + 5.341732056340528134e-2291j 5.75e-121, 4.4e-868j
0.10355384590995037318 + 5.1117185024847252815e-2288j 1.43e-102, 1.1e-849j
1.945590465797393036e-07 - 4.1418727682212688231e-2292j 2.64e-125, 2.02e-872j
1.1631011385550978779e-38 + 1.71605404134749615e-2308j 1.12e-152, 8.57e-900j
3.9138181491341059946e-70 + 1.2492577238325737391e-2323j 1.44e-169, 1.1e-916j
0.086899260096366101028 - 2.1901451804875261861e-2288j 1.04e-107, 7.95e-855j
0.023022757222576570828 + 1.6236097660884080725e-2288j 2.94e-114, 2.25e-861j
0.046941760211389212045 + 4.8797823010281982921e-2288j 8.56e-112, 6.55e-859j
1.0145465041733388532e-19 + 8.7368255862458890728e-2299j 1.32e-141, 1.01e-888j
0.0011729608596877436559 + 1.0486778798920010647e-2289j 1.8e-120, 1.38e-867j
4.3833306134053887181e-25 + 1.4236781233943443549e-2301j 9.64e-145, 7.38e-892j
1.2258387872691789808e-09 + 2.2981943782340112602e-2293j 1.2e-132, 9.22e-880j
0.15891993383788970141 + 3.9528220073702702884e-2288j 9.05e-114, 6.93e-861j
0.13661716248762697637 - 4.4759937841070634489e-2288j 5.12e-114, 3.92e-861j
2.1895762717612101737e-60 - 3.2075137239524909173e-2319j 1.16e-165, 8.85e-913j
1.1104223266561465255e-66 - 3.7102406007920839563e-2322j 4.68e-169, 3.58e-916j
3.0010698815534512951e-47 + 8.606875292196366513e-2313j 1.78e-159, 1.36e-906j
4.5218862116370216841e-33 - 1.1585982399686742567e-2305j 5.4e-153, 4.13e-900j
0.017002832441125828249 + 8.8499065592692417322e-2289j 9.04e-124, 6.92e-871j
0.16127685030361065122 - 3.4645570017325496161e-2288j 3e-124, 2.3e-871j
1.9285763533231991399e-63 + 1.145428496475186158e-2320j 1.19e-167, 9.11e-915j
7.2739418143558021471e-09 - 6.2677317535319992065e-2293j 5.31e-138, 4.07e-885j
1.6582990821139583279e-18 - 3.7868278179313537444e-2298j 1.73e-145, 1.33e-892j
0.069320501513405559109 - 5.5750913129130964155e-2288j 2.52e-131, 1.93e-878j
3.1810179751037345318e-16 - 6.0933554951127936272e-2297j 2.08e-144, 1.6e-891j
3.8336082521763258937e-13 + 2.7256541275362595719e-2295j 1.22e-142, 9.32e-890j
0.035304121676392388471 - 3.1178321858833099733e-2288j 1.42e-134, 1.08e-881j
7.3221500344487448499e-35 + 1.4283598383432154215e-2306j 1.51e-154, 1.15e-901j
0.13726277819508166781 + 2.9131698626955529025e-2288j 4.49e-134, 3.41e-881j

Download

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