Rule: Q[2, 4, 41]

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)
143.11743221205631456 + 2.3697785616174064086e-528j 3.19e-238, 3.19e-238j
157.71276310106448296 - 4.1756863268445419596e-530j 8.42e-240, 8.42e-240j
121.7492774210547912 - 8.0249444171637828856e-524j 4.27e-236, 4.27e-236j
113.02129620687311077 - 7.6537923505462587679e-529j 2.28e-235, 2.28e-235j
131.5991709136781263 - 9.529913321354649689e-535j 4.69e-237, 4.69e-237j
22.70265911901995236 + 7.448614225332800047e-538j 1.07e-235, 1.07e-235j
8.0058004061442226095 + 5.9253987565881854841e-547j 2.16e-240, 2.16e-240j
63.808338256031329948 - 1.1955292162998446058e-539j 8.19e-233, 8.19e-233j
43.341345664749719713 + 1.0110859577542803003e-547j 3.06e-233, 3.06e-233j
16.162387863787984609 + 1.1307936929963332301e-561j 2.65e-237, 2.65e-237j
6.9239565457104964806 + 4.7671674079391827497e-565j 7.07e-241, 7.07e-241j
50.859608100042752685 + 1.4708797759847384968e-556j 6.48e-233, 6.48e-233j
68.637177138527093717 - 8.7085825575123978725e-570j 6.76e-233, 6.76e-233j
5.2705496502648679928 - 2.5697922926486065038e-588j 2.21e-242, 2.21e-242j
46.998168448773793013 - 1.5012610237382299582e-580j 4.89e-233, 4.89e-233j
2.6339247438226597874 + 2.8234101091817628756e-596j 1.55e-245, 1.55e-245j
36.599134188027491246 + 1.6267729022607588114e-582j 9.32e-234, 9.32e-234j
3.4142135623730950488 + 4.2107600294907552912e-595j 1.65e-244, 1.65e-244j
97.902334701387860027 + 5.6181762440055670798e-583j 3.42e-234, 3.42e-234j
25.169618228864713488 + 2.014302429150545747e-593j 3.04e-235, 3.04e-235j
30.560652267508323034 + 8.4709631485533388867e-591j 1.97e-234, 1.97e-234j
14.257611292774809513 - 2.5747741051692625119e-597j 6.13e-238, 6.13e-238j
12.486507079040894342 - 3.6539758949589156747e-598j 1.61e-238, 1.61e-238j
73.759655248106128852 - 3.4151434470318810494e-591j 5.2e-233, 5.2e-233j
91.223225338099172622 - 5.0794274596852492391e-603j 8.3e-234, 8.3e-234j
10.848737889203577852 + 2.2351802999029205888e-616j 3.45e-239, 3.45e-239j
1.9789585476694683523 - 1.0351083738534529585e-623j 1.52e-246, 1.52e-246j
1.460519758252481865 - 3.7554353601835502843e-624j 1.93e-247, 1.93e-247j
33.495763763307734029 - 2.1142595094344336392e-609j 4.16e-234, 4.16e-234j
105.12998708707043613 - 5.8156472096350787248e-617j 9.94e-235, 9.94e-235j
54.93827427809295698 + 7.9864559062302119063e-640j 7.18e-233, 7.18e-233j
0.47193845768537280597 + 6.0837241080123307669e-673j 1.68e-249, 1.68e-249j
6.1688112359606135024 + 1.1923813598504025175e-664j 1.93e-241, 1.93e-241j
27.787218523131135997 + 9.8038750355468664987e-656j 8.69e-235, 8.69e-235j
39.878190922816343425 - 4.7714012872004028593e-680j 1.7e-233, 1.7e-233j
9.3482735672435383509 - 3.6585475478394234005e-706j 7.61e-240, 7.61e-240j
79.205390304848549891 + 9.766314255495240629e-708j 3.54e-233, 3.54e-233j
0.5857864376269049512 + 2.1858184600494247397e-752j 8.45e-249, 8.45e-249j
0.53665973581612225993 - 5.475197835737248418e-753j 9.08e-249, 9.08e-249j
59.248803051357162478 + 4.5620950802869663954e-736j 8.67e-233, 8.67e-233j
0.03159956604758855999 - 3.0170055130603106333e-776j 1.1e-254, 1.1e-254j
1.0406748406401594478 - 5.7037069847274525493e-771j 1.9e-248, 1.9e-248j
0.16765652080881102342 - 9.7655867590655731698e-775j 1.24e-252, 1.24e-252j
4.3040968121346327729 - 4.928945842875298149e-766j 1.89e-243, 1.89e-243j
18.202811891370346838 + 1.6511971776253212879e-760j 9.89e-237, 9.89e-237j
85.011083759591952572 + 1.8825369569178440874e-754j 1.89e-233, 1.89e-233j
20.381739303108432924 + 9.4100362713633768223e-763j 3.28e-236, 3.28e-236j

Weights

Weight (ball center) Error (ball radius)
8.8697406763031586282e-62 - 2.3598386211361831043e-577j 1.99e-76, 1.05e-191j
5.5480527111609414771e-68 + 1.2986438204291057281e-580j 1.36e-78, 7.19e-194j
1.2303830198486325563e-52 - 1.6170954485221007039e-572j 5.08e-74, 2.67e-189j
6.810739233115542254e-49 + 1.5981189506386056334e-570j 3.97e-73, 2.09e-188j
7.4256816740852249626e-57 + 9.3612154701501632863e-575j 2.02e-75, 1.06e-190j
3.3063051657252681439e-10 - 1.5538831796803737856e-547j 2.29e-47, 1.21e-162j
0.00041469207477695245588 - 9.9000342198572372947e-544j 1.05e-29, 5.52e-145j
9.1119247989464285406e-28 + 5.6929458308292384883e-559j 3.3e-65, 1.74e-180j
5.3497529423254495972e-19 - 7.7294830702012230166e-554j 3.7e-59, 1.95e-174j
1.8867387058147333924e-07 + 2.5833531369344502654e-546j 1.07e-43, 5.65e-159j
0.00086312910097437311742 + 3.422579760016717187e-543j 2.02e-30, 1.06e-145j
3.2396807541979368202e-22 - 9.0571707617321419956e-556j 4.8e-62, 2.53e-177j
7.7217358825897898116e-30 - 3.8698265814776543664e-560j 2.54e-67, 1.34e-182j
0.0050152090121428428575 + 7.5743354463134810095e-543j 5.92e-30, 3.12e-145j
1.4581984263517318835e-20 + 8.7071324774965471166e-555j 8.82e-61, 4.65e-176j
0.051708269742896448962 - 3.1231048541130230261e-542j 3.64e-23, 1.92e-138j
4.0641982503175796844e-16 - 5.0264537885978243396e-552j 3.84e-58, 2.02e-173j
0.027571232603177202238 + 1.6779377170610486987e-542j 2.69e-27, 1.42e-142j
2.1026238546501268075e-42 + 4.886524419453685867e-567j 1.65e-74, 8.67e-190j
2.9789132487073400684e-11 - 2.2120327682453324627e-548j 1.16e-53, 6.13e-169j
1.5241079145153119155e-13 - 2.847654035508938799e-550j 2.52e-56, 1.33e-171j
1.1810670514406214722e-06 - 7.6185286413985218685e-546j 1.94e-47, 1.02e-162j
6.438711421614245883e-06 + 2.3568734902251772102e-545j 3.22e-46, 1.7e-161j
4.8877812639968871732e-32 + 2.2932077693737925384e-561j 2.8e-70, 1.47e-185j
1.5514695022805898556e-39 - 1.7495246606547063718e-565j 2.25e-74, 1.18e-189j
3.0511941477354079739e-05 - 7.617127738329548585e-545j 3.27e-47, 1.72e-162j
0.081138548367445876265 + 6.3092426195355753358e-542j 2.66e-34, 1.4e-149j
0.10571235975663607476 - 1.2162080134547764436e-541j 8.49e-33, 4.47e-148j
8.5645597140437765407e-15 + 3.7992454904342759669e-551j 3.82e-59, 2.01e-174j
1.658827154465999037e-45 - 1.0415869069431893792e-568j 7.64e-77, 4.02e-192j
5.7946678071558285659e-24 + 8.6097116191994460347e-557j 3.42e-66, 1.8e-181j
0.80716026988944154823 - 2.0595286952104483474e-540j 8.03e-39, 4.23e-154j
0.0016142528759091904021 - 6.0825456913115303533e-543j 5.58e-46, 2.94e-161j
2.3049345247652111e-12 + 2.2432756266835166236e-549j 2.59e-58, 1.36e-173j
1.6169696004966661425e-17 + 6.4074404216994231971e-553j 5.63e-62, 2.97e-177j
0.00012438613832598986085 + 2.6201773078191691006e-544j 8.72e-51, 4.59e-166j
2.2448467346239084152e-34 - 1.1656565232508056657e-562j 6.71e-73, 3.53e-188j
1.0371880859685570952 - 3.3076334632727923245e-540j 4.78e-44, 2.52e-159j
-1.5143337222845251403 + 5.1926876716077046571e-540j 7.92e-44, 4.17e-159j
8.2255572461619199907e-26 - 7.4021162838373144456e-558j 8.58e-68, 4.52e-183j
0.078646603989620161933 - 1.1261619878616569855e-542j 1.1e-46, 5.79e-162j
0.14151939221150293321 + 2.0701516863213422956e-541j 1.12e-46, 5.92e-162j
0.16295095875077918451 + 5.7844925134787095312e-542j 2.62e-46, 1.38e-161j
0.012667981655077179153 - 1.0272008633768354903e-542j 3.85e-50, 2.03e-165j
2.6225586215670147502e-08 - 9.5660206442636113877e-547j 8.78e-58, 4.62e-173j
7.2163800083673675537e-37 + 4.9840719575282469515e-564j 1.08e-74, 5.72e-190j
3.1649688989621489687e-09 + 4.5415447441854664959e-547j 1.48e-58, 7.8e-174j

Download

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