Rule: Q[2, 4, 7, 29]

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)
92.283519317089407572 + 1.236002735912426838e-507j 1.37e-238, 1.37e-238j
111.79038529301139324 + 3.0746512146386192476e-509j 1.65e-240, 1.65e-240j
77.303562083814461728 - 3.2799355124677795017e-504j 2e-237, 2e-237j
125.24073297411617889 + 3.6904098519004926534e-515j 6e-242, 6e-242j
84.392445707112576512 + 3.1193986324450257782e-507j 5.85e-238, 5.85e-238j
12.486507079040894342 + 1.2641350151489214183e-514j 1.13e-237, 1.13e-237j
7.7324712784297787773 - 2.4592486874718705001e-515j 1.96e-240, 1.96e-240j
54.403185569645969713 - 1.1160058790684119348e-509j 3.19e-236, 3.19e-236j
16.830324996744756898 - 2.2950892535425360791e-518j 1.18e-237, 1.18e-237j
24.16074380043342486 + 3.2601859186202949807e-520j 5.64e-236, 5.64e-236j
4.2350324715021175355 + 8.6685827292946317852e-541j 1.46e-243, 1.46e-243j
101.24505284952586629 - 1.9240401492147712841e-532j 1.92e-239, 1.92e-239j
30.394595499887096545 - 1.0575072595075436681e-541j 3.58e-236, 3.58e-236j
70.854007937281870639 + 6.1010646992390129583e-574j 5.94e-237, 5.94e-237j
6.9239565457104964806 - 1.555254271674483062e-596j 9.06e-241, 9.06e-241j
45.292899373594290417 + 6.2814107186200898123e-611j 5.17e-236, 5.17e-236j
6.2401301552317881834 - 2.2985900230978044151e-645j 2.45e-241, 2.45e-241j
41.187471851562286946 + 8.4755723840070285112e-640j 5.33e-236, 5.33e-236j
19.219158626264888268 - 1.2744791721100704819e-650j 4.97e-237, 4.97e-237j
5.1643048632572456383 - 1.3493457857215676999e-670j 1.61e-242, 1.61e-242j
0.10333586915048290461 + 1.908664967683749409e-684j 1.73e-253, 1.73e-253j
1.478078808681578306 + 5.0438751622608886404e-678j 1.14e-247, 1.14e-247j
59.470768341169205503 - 1.6665065957077151183e-664j 2.1e-236, 2.1e-236j
49.688779796770170462 + 7.7129677064061535496e-696j 4.34e-236, 4.34e-236j
33.757875780112680568 + 4.0018180361838260102e-714j 4.4e-236, 4.4e-236j
0.0045562447122039312376 - 2.2977390092933194964e-750j 7.22e-256, 7.22e-256j
1.0406748406401594478 + 9.698278501418827552e-745j 1.16e-248, 1.16e-248j
9.1914231833294223063 + 1.7984406367052629684e-733j 7.17e-240, 7.17e-240j
12.226319798133742805 + 6.2223354943365323871e-731j 1e-237, 1e-237j
37.349170892406136488 - 1.0473062293269432733e-730j 4.55e-236, 4.55e-236j
27.234714695023117534 + 1.7220966809919241169e-734j 3.31e-236, 3.31e-236j
0.36035513815924319922 - 3.9802964495780187698e-749j 8.6e-251, 8.6e-251j
10.879695872461670843 + 1.8220906340996224538e-737j 7.11e-239, 7.11e-239j
14.633380731314274859 - 8.0354533932449186329e-737j 4.79e-238, 4.79e-238j
0.5857864376269049512 - 1.4071636294554125056e-748j 1.1e-249, 1.1e-249j
22.500032886385026707 + 1.1335741113903848207e-732j 1.73e-235, 1.73e-235j
2.6492025349051043362 + 2.102713688216475406e-745j 1.23e-245, 1.23e-245j
0.47193845768537280597 + 1.3719690633565068377e-749j 5.57e-250, 5.57e-250j
1.9864608100954065734 + 1.7760449837088300029e-746j 1.01e-246, 1.01e-246j
22.123329173345185173 - 9.4066945358849110983e-734j 1.34e-235, 1.34e-235j
64.935363336863533222 + 4.3041427039683459618e-738j 1.23e-236, 1.23e-236j
3.4142135623730950488 + 2.3396691241517660171e-753j 1.42e-244, 1.42e-244j

Weights

Weight (ball center) Error (ball radius)
6.9891158691955986566e-40 - 7.5794694312361860646e-542j 2.18e-83, 6.35e-199j
3.2815542715697440342e-48 - 6.4452943243705692147e-547j 3.83e-87, 1.12e-202j
1.8056870297240160426e-33 + 3.474686234394026728e-537j 4.19e-81, 1.22e-196j
6.4939717350870035824e-54 + 3.1347289656479988988e-550j 6.99e-90, 2.04e-205j
1.6647997299536652667e-36 + 1.4120714432832656422e-539j 2.23e-82, 6.49e-198j
1.2283985602752013975e-05 + 3.277074392460101907e-518j 2.6e-55, 7.58e-171j
0.00057079633930727363935 + 5.1338031590662236155e-517j 2.81e-48, 8.21e-164j
1.1529806135912183737e-23 + 3.228968799351662614e-532j 1.65e-77, 4.8e-193j
1.1212291265332710674e-07 + 9.5045087990020572876e-521j 1.43e-60, 4.16e-176j
1.0696002711948953093e-10 + 9.9472200181883066989e-523j 2.72e-66, 7.93e-182j
0.012433398744446077549 + 3.5057451663134007482e-516j 2.85e-43, 8.32e-159j
1.0318901295794793525e-43 + 3.136717911030304848e-544j 2.7e-86, 7.88e-202j
2.0535455923923720994e-13 + 2.0040383686506166139e-525j 2.62e-70, 7.64e-186j
1.0440524191133408138e-30 - 3.9652858632610716847e-536j 3.08e-81, 8.97e-197j
0.00034173969868483534685 - 1.4642241196793825462e-516j 1.47e-52, 4.28e-168j
9.0691594475187414428e-20 + 6.5054745609067695917e-530j 2.84e-76, 8.28e-192j
0.0021169579804935022279 + 1.8639600591120207679e-516j 8.06e-53, 2.35e-168j
5.1417647738212809254e-18 - 8.9925595540423847663e-529j 2.4e-75, 6.98e-191j
1.1274919910811409517e-08 - 1.8034554229152419741e-521j 1.35e-66, 3.92e-182j
0.0057803151970497223918 - 2.1668429705270162329e-516j 3.91e-53, 1.14e-168j
0.15006221069284343387 - 1.919229487359083671e-515j 7.8e-45, 2.27e-160j
0.10194803861920591675 + 2.9895675998350767499e-515j 7.79e-45, 2.27e-160j
7.8159462060104626578e-26 - 1.2356310350973933418e-533j 2.69e-80, 7.83e-196j
1.1979735612511194329e-21 - 4.5163033500862566211e-531j 9.78e-78, 2.85e-193j
7.5853739214695055186e-15 - 1.5254594995067436276e-526j 4.54e-74, 1.32e-189j
0.031480556653260613041 + 5.6493470176057703006e-516j 2.4e-48, 7e-164j
0.15548891744409668098 - 4.3136828393127454712e-515j 2.41e-49, 7.03e-165j
0.00016076191211917959642 - 8.3026087519963390886e-518j 4.23e-62, 1.23e-177j
-7.2933489238834235493e-06 - 4.6485902248015788344e-518j 4.08e-64, 1.19e-179j
2.2337057675253886607e-16 + 1.1858387452259719704e-527j 2.51e-75, 7.33e-191j
4.5677812052269750072e-12 - 3.0067791595572254804e-524j 1.74e-72, 5.07e-188j
0.33491554257644149282 + 1.4609237948354975722e-514j 3.7e-57, 1.08e-172j
3.4418822131940330078e-05 + 3.3395346619454340368e-518j 5.96e-65, 1.74e-180j
9.3359117997793460348e-07 - 7.5559359712298539611e-520j 1.47e-67, 4.29e-183j
0.3464707830849008464 + 1.9006137453531716183e-514j 3.43e-59, 1e-174j
-7.8870583432816593742e-10 - 1.6604859644765666827e-521j 2.39e-71, 6.96e-187j
0.051347299107888681545 + 9.4145314201439794111e-516j 8.64e-64, 2.52e-179j
-0.29986117037467695597 - 2.9766894365726433589e-514j 2.84e-60, 8.28e-176j
0.080579798558258248459 - 1.7681304095861056937e-515j 4.72e-63, 1.38e-178j
1.6152531103778702803e-09 + 1.9499756666985515926e-521j 2.7e-71, 7.87e-187j
3.57548634012108055e-28 + 6.872749657834894168e-535j 7.97e-86, 2.33e-201j
0.026123586379568847453 - 5.6219352653758560218e-516j 5.59e-65, 1.62e-180j

Download

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