Rule: Q[1, 3, 5, 45]

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)
163.78869593628627479 + 9.9877333090702791332e-348j 5.43e-346, 5.43e-346j
179.04418591546769412 - 1.2910603640782556893e-352j 9.26e-351, 9.26e-351j
116.13272243951243463 + 2.2028688143787260951e-331j 1.2e-329, 1.2e-329j
141.3535940183662595 - 2.5057144985188581684e-340j 2.16e-338, 2.16e-338j
132.14843367038235963 - 1.0452312810734102813e-336j 6.23e-335, 6.23e-335j
23.440923140376980586 - 1.3420224371159861701e-354j 7.27e-353, 7.27e-353j
6.6362266832251170834 - 4.2491303236060960953e-372j 5.24e-370, 5.24e-370j
123.80112287902889415 + 2.0241482303835901916e-335j 3.17e-333, 3.17e-333j
46.037758740141007208 - 1.088706425734708521e-340j 5.97e-338, 5.97e-338j
109.02421709935283088 - 9.3342917037574274513e-338j 5.1e-336, 5.1e-336j
49.545440602901497302 + 1.5555635534536809519e-346j 1.66e-344, 1.66e-344j
12.627051119829555935 + 1.060747929022117732e-376j 6.12e-375, 6.12e-375j
42.696003955130012499 - 1.3474461121733613382e-347j 9.23e-346, 9.23e-346j
79.556875045655223294 + 1.9743632697711906249e-352j 2.31e-350, 2.31e-350j
28.254480545935110312 + 1.1222029740683083217e-373j 6.62e-372, 6.62e-372j
2.6307576306098249721 - 6.7303850207240721466e-401j 4.98e-397, 4.98e-397j
7.8232631436879996743 + 1.2703441001892270435e-398j 8.49e-397, 8.49e-397j
1.4704610360411319012 + 4.263991484943747895e-402j 2.35e-400, 2.35e-400j
151.71175086169499745 + 7.5780136251735517329e-368j 8.68e-366, 8.68e-366j
25.783290141602299402 - 4.2309142511747416232e-377j 5.79e-375, 5.79e-375j
69.886223653640129711 - 2.9479844677765682691e-370j 3.11e-367, 3.11e-367j
5.5640841709325606716 - 4.0141672608753146797e-411j 3.1e-409, 3.1e-409j
57.090948363822723921 + 1.6184289170985414933e-383j 1.19e-381, 1.19e-381j
39.513179389628640997 + 3.8638537466231536891e-394j 6.4e-392, 6.4e-392j
65.408341656563157599 - 1.9159777229622820831e-408j 5.65e-406, 5.65e-406j
2.0206302391446468612 + 2.2822223851598336263e-458j 3.22e-456, 3.22e-456j
3.4849364779110753601 - 2.9166034159350737134e-455j 1.63e-453, 1.63e-453j
10.561208835011173744 - 1.5569579316060172162e-447j 1.49e-445, 1.49e-445j
17.143202004675389513 - 1.5038445414015505844e-439j 8.89e-438, 8.89e-438j
74.596474004452028563 - 1.4108043321531029968e-428j 1e-426, 1e-426j
53.226891747571343983 - 9.2820693580672779968e-448j 5.98e-446, 5.98e-446j
36.483011260354263294 - 9.2807341281479209366e-465j 1.38e-462, 1.38e-462j
13.271271652158229649 - 6.7077729402388454001e-489j 1.9e-486, 1.9e-486j
3.7068293223182415456 + 5.4659312003135479938e-507j 7.7e-497, 7.7e-497j
1 - 4.3137729030699205419e-535j 8.12e-504, 8.12e-504j
61.147624336460287528 - 4.7071274465024671839e-483j 2.6e-481, 2.6e-481j
0.095437162418107254506 - 1.8392474524642109735e-561j 5.91e-508, 5.91e-508j
0.056897625001077184683 + 4.3866666082068411319e-563j 1.39e-507, 1.39e-507j
12.438835636362665227 - 1.1949231059850798123e-515j 3.3e-490, 3.3e-490j
30.858560896829208783 + 6.3755272263196271067e-507j 2.35e-487, 2.35e-487j
96.171365785685705074 + 4.0171860098619614069e-536j 4.88e-486, 4.88e-486j
33.599846039089938084 - 3.3054806634691535963e-562j 5.97e-487, 5.97e-487j
9.1268771271146616526 + 1.2693892535536862401e-586j 1.77e-493, 1.77e-493j
0.3215208031274231831 - 2.2836512516591969937e-629j 8.57e-507, 8.57e-507j
19.12622188851013496 - 3.3882692973915702577e-574j 1.59e-489, 1.59e-489j
102.39128330448243918 + 6.9568129845730548335e-594j 2.1e-486, 2.1e-486j
21.223369064710692261 - 1.2611778213747053861e-624j 4.92e-489, 4.92e-489j
0.052485028214125533477 + 4.9893291550183572403e-670j 9.38e-508, 9.38e-508j
0.61656865206089706011 + 7.8059780567534366475e-670j 2.76e-505, 2.76e-505j
3.369839231310923141 - 1.9985503344668398012e-646j 5.13e-497, 5.13e-497j
90.316406421283926522 + 7.5392099879358348863e-637j 8.98e-486, 8.98e-486j
84.78845566741355583 - 1.0810144027130961052e-658j 1.5e-485, 1.5e-485j
15.258489384453228571 - 1.1092584396266615978e-695j 2.06e-490, 2.06e-490j
4.6100534724383758491 - 2.7216169659335344504e-707j 1.01e-496, 1.01e-496j

Weights

Weight (ball center) Error (ball radius)
9.7821134169205375112e-71 + 7.640407082581959444e-390j 1.66e-193, 8e-275j
3.1517054678748532775e-77 - 2.6622684490849492342e-393j 1.11e-195, 5.34e-277j
2.7026460795991947839e-50 - 8.8968704021827703369e-379j 8.17e-187, 3.92e-268j
3.9672538370938151089e-61 + 1.1038727519534006358e-384j 4.45e-191, 2.14e-272j
3.5493448773641447132e-57 - 1.5273329986197511843e-382j 8.11e-190, 3.9e-271j
1.5049929079204448206e-10 + 2.9546958340355610444e-355j 1.7e-157, 8.18e-239j
0.0014822737265926718651 - 1.0537869376972667492e-349j 3.81e-132, 1.83e-213j
1.3679986477033743369e-53 + 1.3761731426575000285e-380j 1.18e-188, 5.65e-270j
3.4715546073947169008e-20 + 2.2599494509926608001e-360j 6.53e-172, 3.14e-253j
3.0734880423124295569e-47 + 4.3347697404488940933e-377j 3.13e-187, 1.5e-268j
1.0918620488037986255e-21 + 1.3746443707429528419e-361j 1.3e-173, 6.25e-255j
-2.6389361193339113368e-05 + 4.0736359470111398655e-350j 4.25e-150, 2.04e-231j
9.3483906272096171066e-19 - 8.2604836049695078971e-360j 5.01e-171, 2.41e-252j
1.4315003989299581791e-34 - 6.6375367982480884884e-370j 1.57e-183, 7.54e-265j
1.3600204737629763849e-12 + 1.3416658019389599943e-356j 3.41e-165, 1.64e-246j
0.04544116605252168994 - 7.2524612447756956489e-348j 7.79e-128, 3.75e-209j
0.0004981861457430797404 + 3.7137103740369283091e-350j 1.16e-144, 5.58e-226j
0.11773358117388140667 - 3.8368868941382589812e-348j 5.37e-120, 2.58e-201j
1.4361044758822242067e-65 - 4.4728994228600619068e-387j 2.13e-195, 1.02e-276j
1.5267770264217342761e-11 - 6.312422397036237586e-356j 7.48e-164, 3.6e-245j
2.0452095623247057861e-30 - 1.9421050059217087666e-367j 1.19e-181, 5.7e-263j
0.0038861126349741167277 + 3.4929541391284269776e-349j 1.13e-143, 5.44e-225j
6.3570631350816222849e-25 + 5.6225320621625594387e-364j 2.93e-178, 1.41e-259j
2.1467256268077200903e-17 + 2.8941142843272633668e-359j 2.26e-172, 1.09e-253j
1.7127607683082031625e-28 + 2.9118659477160266468e-366j 6.66e-181, 3.2e-262j
0.077531288480126069423 + 4.6711434933257129751e-348j 4.14e-136, 1.99e-217j
-0.073537937978057840385 - 1.0008436667944807306e-346j 1.05e-142, 5.06e-224j
3.9246911880125272947e-05 + 7.5656992842270843956e-351j 1.86e-156, 8.95e-238j
6.9219264084314455981e-08 - 3.4317596556894573419e-353j 3.26e-163, 1.57e-244j
1.937761948072290436e-32 + 1.1931859948389530944e-368j 1.1e-183, 5.3e-265j
2.8862438537126847868e-23 - 7.9311868861590833781e-363j 1.54e-177, 7.4e-259j
4.2296105349733044608e-16 - 1.2725932622480620415e-358j 3.61e-173, 1.73e-254j
5.5344541296258220515e-06 - 6.2157032572084637827e-351j 4.32e-162, 2.07e-243j
0.036281483134552509995 + 3.0935944545497826342e-347j 1.85e-150, 8.91e-232j
0.15728321606067321024 + 3.7042917753065914696e-348j 1.94e-144, 9.31e-226j
1.1552311812519088424e-26 - 4.1072297740623546048e-365j 3.1e-180, 1.49e-261j
0.34608289460305912651 - 3.4242124726777068824e-347j 7.22e-145, 3.47e-226j
-1.7717397651274953793 + 2.1485449676176467899e-346j 6.83e-145, 3.28e-226j
3.1023512288288920171e-05 - 3.7582715133279103399e-350j 4.05e-161, 1.94e-242j
1.059554851372317608e-13 - 2.8304777927431362882e-357j 5.77e-172, 2.77e-253j
1.0319330948695970079e-41 + 5.3383242795229435413e-374j 2.59e-191, 1.24e-272j
7.1894666956982075524e-15 + 5.9570131084636379559e-358j 3.05e-173, 1.47e-254j
0.00014832818033810597023 - 1.5056811532191890567e-350j 7.47e-163, 3.59e-244j
0.18251802184104971441 + 5.2730145638158732017e-348j 2.05e-154, 9.86e-236j
1.0068052272614663407e-08 + 6.6804137961118223105e-354j 3.57e-169, 1.72e-250j
2.1846862578642687313e-44 - 1.6794353896924821425e-375j 1.23e-192, 5.93e-274j
1.3078738830592782153e-09 - 1.3885839302614081805e-354j 1.09e-170, 5.24e-252j
1.6106300258274584724 - 1.8370302530839674869e-346j 2.25e-156, 1.08e-237j
0.1830439475166097419 - 4.0626519160107221091e-348j 4.15e-159, 2e-240j
0.073764985443860163452 + 7.49609185486404996e-347j 1.26e-160, 6.04e-242j
3.3952807945081604992e-39 - 1.4287884284688288065e-372j 1.76e-190, 8.46e-272j
8.0766876120860489129e-37 + 3.2897991622363407863e-371j 3.67e-189, 1.76e-270j
4.3708306311580235499e-07 + 2.1242946326018414243e-352j 5.45e-170, 2.63e-251j
0.0089022589215144118966 - 1.488977218639381041e-348j 1.54e-165, 7.31e-247j

Download

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