Rule: Q[1, 3, 5, 25]

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)
104.86071154350137623 - 9.0055555121523520005e-520j 8.77e-244, 8.77e-244j
66.760100400067542086 + 5.7655926673612701729e-515j 2.46e-240, 2.46e-240j
74.041999284489145052 - 5.4479666840687830279e-522j 7.21e-241, 7.21e-241j
92.215465201347364682 + 8.8146663036447485962e-528j 1.82e-242, 1.82e-242j
19.12622188851013496 + 9.985731951935497945e-529j 2.21e-240, 2.21e-240j
54.388423490279430558 + 1.3639037816915299122e-539j 1.22e-239, 1.22e-239j
82.363407909130806243 + 5.1684383286027413451e-559j 1.45e-241, 1.45e-241j
9.3036874811094767039 - 2.9762039598964863638e-568j 2.09e-242, 2.09e-242j
31.655986368018127534 + 7.2074072043780881749e-582j 1.85e-239, 1.85e-239j
12.438835636362665227 + 1.5531009470989496088e-598j 2.06e-241, 2.06e-241j
2.2856664706479856404 - 5.4349049946709724803e-614j 2.72e-247, 2.72e-247j
21.871423421846397262 + 1.0138017979177424071e-612j 4.38e-240, 4.38e-240j
35.48461231271917377 + 2.5744379892474125064e-633j 2.5e-239, 2.5e-239j
24.867120295596153768 - 1.1428450985743021904e-649j 7.75e-240, 7.75e-240j
1.5779071740282311217 - 8.2877422127371622838e-674j 1.2e-248, 1.2e-248j
6.3982620099148830011 - 3.2137216342506600233e-669j 7.66e-244, 7.66e-244j
3.369839231310923141 + 6.0964121404566618724e-670j 1.55e-244, 1.55e-244j
16.628521091005119979 - 1.313978900116390915e-665j 1.13e-240, 1.13e-240j
60.260880813835029306 - 4.0211677637522206442e-695j 5.74e-240, 5.74e-240j
39.634935609404805604 + 2.9538062424803914966e-721j 2.56e-239, 2.56e-239j
7.8232631436879996743 - 2.6792567650855316828e-741j 4.09e-243, 4.09e-243j
0.052485028214125533477 - 1.4683966290533948605e-750j 3.35e-253, 3.35e-253j
0.22075232991031398274 - 2.959837635267175548e-750j 7.56e-253, 7.56e-253j
49.039013035534013607 + 9.2357370703466343262e-736j 1.8e-239, 1.8e-239j
14.388566804482337835 + 5.874971871850478642e-747j 5.05e-241, 5.05e-241j
3.4849364779110753601 + 3.7576058712068498214e-751j 3.02e-244, 3.02e-244j
1 + 3.8287976236584814965e-757j 4.65e-250, 4.65e-250j
10.793495011408879483 + 5.9347436466954820708e-748j 7.2e-242, 7.2e-242j
44.139267445523565299 + 3.7969918481944704459e-745j 2.48e-239, 2.48e-239j
0.056897625001077184683 + 1.9821872135176567018e-765j 5.44e-253, 5.44e-253j
5.0844843304161481192 + 8.2041726636358039909e-758j 1.55e-244, 1.55e-244j
3.7068293223182415456 - 1.653369646745392549e-757j 1.65e-244, 1.65e-244j
0.54463492940080284291 + 3.7297207888243834104e-764j 2.02e-251, 2.02e-251j
28.123530031180136758 + 1.8530000459092281126e-751j 1.34e-239, 1.34e-239j

Weights

Weight (ball center) Error (ball radius)
4.3449710100733941336e-45 + 1.6611655092099371601e-553j 3.67e-101, 1.6e-218j
6.9612405990872799093e-29 - 2.2267951261764666819e-543j 3.91e-95, 1.7e-212j
5.4083109334866573202e-32 - 1.0541223616079775902e-545j 1.22e-96, 5.28e-214j
9.7523155722290085254e-40 - 1.8480201541934520912e-550j 3.79e-100, 1.65e-217j
1.2947332456113492811e-08 + 1.8637437522939716737e-532j 2.29e-82, 9.97e-200j
1.3407174109314533905e-23 - 3.041745295832619791e-541j 2.66e-94, 1.16e-211j
1.5238231986456472773e-35 + 5.6300656150097179537e-548j 1.57e-98, 6.83e-216j
0.00013493322454593774539 - 4.2923090013078856197e-529j 4.73e-76, 2.06e-193j
6.5681984175063445277e-14 + 6.2140065277015678705e-536j 2.94e-89, 1.28e-206j
7.0954372029412582041e-06 - 3.6409107737088003249e-530j 9.89e-80, 4.3e-197j
0.080119159209341765001 + 1.0998198372395332164e-526j 2.05e-64, 8.93e-182j
9.1018034114139602223e-10 - 2.8047675571953358987e-533j 2.1e-85, 9.12e-203j
1.5474827959781107117e-15 - 6.7420801176004446921e-537j 4.95e-91, 2.15e-208j
4.9549926593214368024e-11 + 3.9609302567261153247e-534j 3.75e-87, 1.63e-204j
0.13180718967062283232 - 1.0674620670650193169e-526j 5.41e-66, 2.35e-183j
0.0022864485179298301034 - 3.6550260988614224387e-528j 4.12e-77, 1.79e-194j
0.24175362330311216148 - 1.5388626814151544881e-525j 2.1e-72, 9.11e-190j
1.4238550865600939339e-07 - 1.1739385692116275612e-531j 6.11e-84, 2.65e-201j
4.1589065437529823283e-26 + 2.2007274593424176976e-542j 2.68e-97, 1.17e-214j
2.6447134808422313696e-17 + 6.5547167157827357516e-538j 3.33e-93, 1.45e-210j
0.00058703728193737519845 + 1.1939613346233696837e-528j 1.83e-81, 7.97e-199j
0.41528618706296152607 + 2.3933736746260778492e-525j 1.14e-73, 4.94e-191j
0.20518879846498552382 + 2.0995659892725090697e-526j 1.02e-73, 4.43e-191j
2.5787292544309657572e-21 + 4.3538599240082149915e-540j 8.89e-96, 3.87e-213j
1.1852132878601143201e-06 + 6.9675061224154558506e-531j 2.2e-85, 9.56e-203j
-0.29227320325512964835 + 2.1150918573486759025e-525j 4.36e-79, 1.9e-196j
0.19046703295049892718 + 1.1536754128193647304e-526j 1.35e-77, 5.88e-195j
3.1369238461459952964e-05 + 1.4342959186465117171e-529j 5.44e-84, 2.36e-201j
3.1777777069751862739e-19 - 5.6666875022140048014e-539j 6.83e-95, 2.97e-212j
-0.31505050366162843904 - 2.5280195343562129556e-525j 2.76e-77, 1.2e-194j
0.0077828610272202501529 + 1.4174015771029003581e-527j 2.21e-82, 9.61e-200j
0.10495875043158943596 - 6.4551231418707172403e-526j 1.31e-80, 5.69e-198j
0.22691187958834911742 - 1.3602761522645737509e-526j 9.61e-81, 4.2e-198j
2.0725075243486243596e-12 - 5.1846768168572913679e-535j 9.69e-91, 4.21e-208j

Download

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