Rule: Q[1, 3, 5, 46]

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)
183.33623738100694141 + 1.2806573924263273735e-335j 9.65e-334, 9.65e-334j
119.88097681738540757 - 7.8648093554557244265e-341j 3.78e-338, 3.78e-338j
136.05381663514138944 - 1.0529099108220097094e-351j 2.2e-349, 2.2e-349j
167.96487067164745241 + 1.4596468474172009203e-357j 1.25e-355, 1.25e-355j
30.578124993449022575 + 4.0130762452831287858e-364j 5.15e-362, 5.15e-362j
145.34262564866992411 + 6.9161764528576876533e-369j 9.88e-367, 9.88e-367j
99.698197224998410219 - 1.074461840799617677e-387j 2.22e-385, 2.22e-385j
105.99063916632999247 - 3.8795164765468731101e-402j 4.38e-400, 4.38e-400j
17.205481464219114565 - 1.3222754120007703046e-428j 1.23e-425, 1.23e-425j
39.022838755063656467 + 4.4132234731015724016e-412j 3.16e-410, 3.16e-410j
19.12622188851013496 - 5.6912649895097627302e-430j 7.48e-428, 7.48e-428j
52.369273231043377732 + 2.9430056791129449374e-406j 1.65e-404, 1.65e-404j
48.791072831660686442 - 1.2331450179769018431e-410j 7.2e-409, 7.2e-409j
21.168662747002224991 - 3.2182263232679613109e-432j 1.32e-429, 1.32e-429j
33.254456472402474838 - 6.3374938876580393109e-418j 3.57e-416, 3.57e-416j
64.18164900202704622 + 9.449588334873028812e-424j 5.25e-422, 5.25e-422j
88.172680401835850725 - 1.9484344102980700026e-447j 1.87e-445, 1.87e-445j
9.0720472619082311575 + 8.625925414134769554e-498j 3.06e-493, 3.06e-493j
155.78991231363996131 - 1.3979151713878028114e-461j 1.02e-459, 1.02e-459j
77.840075349147599526 - 3.2004545839263545734e-476j 3.64e-474, 3.64e-474j
3.369839231310923141 + 1.3725867188500762435e-525j 6.27e-497, 6.27e-497j
15.411049476442019863 - 1.1846100903739203054e-516j 2.65e-490, 2.65e-490j
10.383765186968690506 + 8.1177901908101891528e-524j 2.69e-492, 2.69e-492j
82.870618605941653011 + 3.1442123807402396713e-497j 7.14e-485, 7.14e-485j
68.512185703150611706 - 1.6931947973344514677e-509j 1.23e-484, 1.23e-484j
13.768277024647049067 + 4.1396259453243915469e-551j 1e-490, 1e-490j
60.055078244391735277 - 8.9642636613612874711e-516j 1.01e-484, 1.01e-484j
3.4849364779110753601 - 7.8376066930438513549e-559j 1.3e-496, 1.3e-496j
25.620749295219499964 - 7.9280903508346000205e-535j 7.85e-488, 7.85e-488j
12.438835636362665227 + 2.323511409058634566e-556j 4.84e-491, 4.84e-491j
28.034765910296604955 + 4.7050818994497901769e-532j 2.11e-487, 2.11e-487j
11.57041287682063097 + 6.0096099971464685525e-553j 1.93e-491, 1.93e-491j
5.6127759611126063262 + 4.9472884288301142927e-561j 7.3e-496, 7.3e-496j
36.067843042784605636 - 2.1456136243030644103e-527j 2.94e-486, 2.94e-486j
56.120978625122273656 - 1.4847501091729874774e-524j 8.49e-485, 8.49e-485j
45.378493366288486293 - 1.3032892903494388776e-530j 2.41e-485, 2.41e-485j
3.7068293223182415456 + 4.6610445046502572491e-565j 9.17e-497, 9.17e-497j
0.61955665428714360774 + 2.8093761995986171943e-593j 2.65e-505, 2.65e-505j
42.124509859521303346 - 4.4035569257245486253e-534j 1.32e-485, 1.32e-485j
7.8232631436879996743 + 4.5667109225451298005e-565j 3.72e-494, 3.72e-494j
112.69726101033114398 - 7.6371788156181554659e-550j 2.42e-486, 2.42e-486j
23.332915101402519044 - 1.679587293279804742e-575j 2.77e-488, 2.77e-488j
1 - 2.3308657184955103666e-613j 8.5e-504, 8.5e-504j
1.4616079057440004201 - 2.3467267375853298942e-604j 2.22e-502, 2.22e-502j
0.052485028214125533477 - 3.1344123368283287018e-611j 1.07e-507, 1.07e-507j
127.62659449065028868 + 7.1974668289405994134e-588j 1.8e-487, 1.8e-487j
93.77160070915924935 - 2.6472792253063576102e-630j 2.79e-485, 2.79e-485j
2.5881521468595084418 - 3.3479552683444593574e-675j 1.86e-499, 1.86e-499j
1.9946843180543350135 - 4.5109438682162861144e-678j 6.71e-501, 6.71e-501j
0.056897625001077184683 + 2.7383636692002584029e-686j 1.41e-507, 1.41e-507j
4.6593170713888545915 + 5.4252924500713164854e-669j 1.27e-496, 1.27e-496j
6.6676149816610979114 - 1.1061590532923473416e-668j 4.63e-495, 4.63e-495j
73.059894904032803624 - 3.1438311184061266839e-662j 1.09e-484, 1.09e-484j
0.097980875760985309374 + 8.2322384093146161232e-716j 6.5e-508, 6.5e-508j
0.3244017905872709546 - 3.8609685249357509664e-717j 1.03e-506, 1.03e-506j

Weights

Weight (ball center) Error (ball radius)
4.3421404162771667071e-79 - 3.6765804402436092858e-408j 3.12e-188, 1.03e-276j
6.4328623061264280249e-52 + 2.7022621950687306643e-392j 9.63e-179, 3.18e-267j
7.212675005353144828e-59 - 6.2481695715748272119e-397j 9.85e-182, 3.26e-270j
1.5140811471535540165e-72 + 1.2923474825991469441e-404j 5.34e-187, 1.77e-275j
1.3696098565757713941e-13 + 2.8365932203738698595e-372j 2.56e-152, 8.48e-241j
7.4114374875031721397e-63 + 3.0741244002666229302e-399j 1.66e-183, 5.49e-272j
3.0699091775148563679e-43 - 1.1663800989009786979e-388j 6.4e-177, 2.11e-265j
6.0412204967543992537e-46 + 5.8462065940040395012e-390j 7.27e-178, 2.4e-266j
6.2669134330454512129e-08 + 3.4618574953910981556e-368j 2.19e-144, 7.23e-233j
3.417216828168700749e-17 - 1.6338988024708404071e-374j 2.51e-160, 8.3e-249j
9.7869066934963975934e-09 - 7.3435621372935105342e-369j 8.25e-147, 2.73e-235j
6.6102363211850135413e-23 - 7.5620715065822075029e-378j 1.2e-166, 3.96e-255j
2.2576056286509152489e-21 + 5.6879228360505541537e-377j 3.12e-165, 1.03e-253j
1.3472121132918043565e-09 + 1.5809041130121668396e-369j 2.13e-150, 7.05e-239j
9.9124126519078662852e-15 - 5.3394085742565940194e-373j 3.29e-158, 1.09e-246j
5.6525644435894786786e-28 + 1.1309746761176981988e-380j 1.01e-171, 3.35e-260j
2.774329831414009133e-38 - 3.704128673134938044e-386j 5e-178, 1.65e-266j
0.000148080721185547823 + 2.3950658098718282347e-365j 1.04e-142, 3.45e-231j
2.4529142873839468266e-67 - 9.4553211488809820181e-402j 2.55e-190, 8.44e-279j
7.6713175626506250323e-34 - 7.7890612561138210562e-384j 2.61e-176, 8.64e-265j
0.093885391612348805757 - 7.5252148260530477739e-362j 4.14e-132, 1.37e-220j
3.5016183822123726401e-07 - 1.7170107493260977614e-367j 2.05e-151, 6.77e-240j
4.057962503083225388e-05 - 1.3379562706858836463e-365j 5.88e-147, 1.94e-235j
5.2796439539882062752e-36 + 5.659336725781997796e-385j 2.45e-177, 8.11e-266j
7.8091169942637483762e-30 - 1.0957493242164513289e-381j 1.79e-174, 5.92e-263j
1.6144239261303593645e-06 + 9.473228478989404367e-367j 1.94e-152, 6.41e-241j
3.3385605009644016746e-26 - 1.0710831101546068644e-379j 1.78e-172, 5.9e-261j
-0.098888084285896304023 + 1.0098792586860621904e-361j 1.85e-139, 6.11e-228j
1.7546852724390656498e-11 + 7.0925683131260567299e-371j 5.31e-161, 1.75e-249j
4.0719706974401801968e-06 - 4.635735071344012569e-366j 1.44e-152, 4.76e-241j
1.6549249662127731451e-12 - 1.4445257315624379006e-371j 3.57e-162, 1.18e-250j
9.0368777536150971037e-06 + 9.1825163196784663859e-366j 2.79e-152, 9.23e-241j
0.0036634553041724402104 - 3.983032647820504596e-364j 6.65e-149, 2.2e-237j
6.2494003733653850477e-16 + 9.5855521423346818686e-374j 4.88e-166, 1.61e-254j
1.6272345024736410069e-24 + 9.3517611804695565753e-379j 5.97e-173, 1.97e-261j
6.5327894260342326325e-20 - 3.9962064197911968087e-376j 3.02e-170, 9.99e-259j
0.044226324719493758398 - 3.1270802208218253105e-362j 3e-150, 9.91e-239j
0.18193570718190253954 + 4.7678945623385079724e-363j 2.27e-150, 7.5e-239j
1.6126967587269171723e-18 + 2.6332354352658914448e-375j 3.01e-169, 9.96e-258j
0.00048207504498613203026 - 5.312770122883002129e-365j 4.12e-156, 1.36e-244j
7.8910214151858454029e-49 - 3.1766028950629267477e-391j 6.6e-189, 2.18e-277j
1.6372068119701028628e-10 - 3.3818779976086941239e-370j 3.05e-164, 1.01e-252j
0.1552973011485631394 - 4.4519157628962307719e-363j 7.46e-153, 2.46e-241j
0.11580732324076840127 + 4.6417255492335097465e-363j 7.02e-154, 2.32e-242j
1.5403014287468943193 + 1.9489859288306504263e-361j 2.44e-153, 8.07e-242j
3.0126566213110055569e-55 + 1.0944584514698375391e-394j 2.64e-192, 8.72e-281j
1.0857100109779997304e-40 + 2.1824509112858866719e-387j 1.04e-184, 3.44e-273j
0.047060463843027433667 + 7.3548007985994882315e-363j 1.32e-157, 4.38e-246j
0.076774781112079259304 - 5.4125839267069540827e-363j 1.84e-157, 6.08e-246j
-1.6770917472625910123 - 2.2646881620967305735e-361j 4.54e-156, 1.5e-244j
0.0085913029292565067636 + 1.4648234700536790285e-363j 2.03e-159, 6.7e-248j
0.0014061193456628910925 + 1.3569045897745968674e-364j 8.22e-161, 2.72e-249j
8.689371230163969169e-32 + 9.6927547853452338754e-383j 2.68e-180, 8.86e-269j
0.32368454494723039356 + 3.506561629956193138e-362j 2.09e-158, 7e-247j
0.1826598046053463788 - 6.0252946314071527607e-363j 3.07e-159, 1.01e-247j

Download

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