Rule: Q[2, 4, 53]

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)
175.21462178116884355 - 3.9255417629741721414e-2719j 4.31e-999, 4.31e-999j
203.86788771463309476 - 5.6493386145354570145e-2727j 3.09e-1002, 3.09e-1002j
187.89608259251523674 - 5.0944965069318536409e-2728j 1.82e-1000, 1.82e-1000j
164.3078876930824716 - 1.1930845753923467018e-2768j 5.15e-998, 5.15e-998j
137.6109440938872833 + 2.4625926846112353151e-2859j 1.17e-995, 1.17e-995j
93.01265620423128885 + 9.7025899475033928075e-2948j 4.18e-993, 4.18e-993j
44.234908480945332723 - 1.8882810899377857614e-2988j 2.72e-994, 2.72e-994j
25.622323487264852391 + 4.8665381294458252507e-3030j 2.38e-997, 2.38e-997j
82.98506788905861126 - 1.090881277417290236e-3108j 7.12e-993, 7.12e-993j
122.96132018335487073 + 2.1210530117185122828e-3209j 1.38e-994, 1.38e-994j
14.05833627068033742 + 4.9940938259304771619e-3259j 4.16e-1001, 4.16e-1001j
6.5912401281057108452 - 3.9935924687814378875e-3271j 6.12e-1004, 6.12e-1004j
104.05318457786583686 - 2.7871909808288429046e-3280j 1.6e-993, 1.6e-993j
87.881879705603584965 - 2.8037844890550546659e-3320j 6e-993, 6e-993j
11.010451524894569593 + 1.6857345649198328193e-3341j 1.41e-1002, 1.41e-1002j
15.72837193831587311 + 9.3518405386022445684e-3340j 2.08e-1000, 2.08e-1000j
47.402207252572476634 + 2.1186795033844419904e-3331j 5.3e-994, 5.3e-994j
38.300929903856938589 + 2.6666560406645229531e-3337j 5.13e-995, 5.13e-995j
32.873654993471281805 + 7.9538760591996319842e-3339j 7.31e-996, 7.31e-996j
154.58892551912629736 + 4.6478687326686475768e-3337j 3.86e-997, 3.86e-997j
5.1733699010243677936 - 1.9389281454012474215e-3364j 9.15e-1007, 9.15e-1007j
98.39582918241567905 - 1.1256132113028793365e-3349j 2.75e-993, 2.75e-993j
41.202616543887146159 + 1.9220336246130507521e-3362j 1.17e-994, 1.17e-994j
4.2407788646313611891 - 1.3408497594781478614e-3376j 5.18e-1008, 5.18e-1008j
145.75174900481094695 - 6.0409919696553520576e-3361j 2.53e-996, 2.53e-996j
73.832409823495825223 - 1.6291642475372471376e-3364j 7.94e-993, 7.94e-993j
2.0438318360945004245 + 5.9463922334216061989e-3409j 1.63e-1011, 1.63e-1011j
8.3226315504534469957 - 1.7546052786466698852e-3401j 5.31e-1004, 5.31e-1004j
130.04323897886679568 - 1.3094601933018517391e-3391j 4.6e-995, 4.6e-995j
69.551075717058884665 + 1.7307815623294055137e-3424j 6.92e-993, 6.92e-993j
6.4305806617660342325 + 1.1955884989323888869e-3466j 3.12e-1004, 3.12e-1004j
21.347791098059002164 + 1.0540731817044929418e-3461j 1.69e-998, 1.69e-998j
2.6828720421353367779 + 2.5382008494829008639e-3473j 2.43e-1010, 2.43e-1010j
12.486507079040894342 - 1.7083432686191885985e-3464j 7.85e-1002, 7.85e-1002j
6.9239565457104964806 + 1.8373493049435242887e-3466j 4.19e-1004, 4.19e-1004j
116.30042668824174322 - 1.4514084580317338014e-3455j 3.55e-994, 3.55e-994j
57.765069540554594845 - 7.5420272189588225021e-3463j 3.13e-993, 3.13e-993j
1.4962504791434361144 - 3.2010582006719666847e-3488j 1.27e-1012, 1.27e-1012j
1.0406748406401594478 + 8.4067904856791514334e-3489j 1.51e-1013, 1.51e-1013j
9.6262397044997838737 - 5.6579027247368688633e-3479j 2.65e-1003, 2.65e-1003j
17.498647553764944174 + 4.8354169909808742829e-3475j 9.53e-1000, 9.53e-1000j
35.525833300045040426 - 4.1756777208019744885e-3470j 2.09e-995, 2.09e-995j
3.4142135623730950488 + 1.0351760391431197928e-3484j 3.45e-1009, 3.45e-1009j
0.66928049756728044934 + 1.8096224087655317496e-3489j 5.19e-1014, 5.19e-1014j
54.161671954104974574 + 2.9741730266816731361e-3468j 1.91e-993, 1.91e-993j
27.924867528792308437 - 3.6242021418879631126e-3479j 7.8e-997, 7.8e-997j
50.70935069894734308 + 2.0547213611674004565e-3474j 1.09e-993, 1.09e-993j
0.5857864376269049512 - 4.4762555799466860796e-3513j 3.39e-1014, 3.39e-1014j
0.47193845768537280597 - 8.600621391054869592e-3514j 5.33e-1015, 5.33e-1015j
23.430773884794543467 - 2.7745654063545101619e-3493j 6.51e-998, 6.51e-998j
61.526091310294717553 + 1.9474045661995973786e-3502j 4.2e-993, 4.2e-993j
110.01080995492003274 - 1.9341458237649546146e-3567j 7.94e-994, 7.94e-994j
65.452035801340535467 - 4.1687186090919222254e-3636j 5.57e-993, 5.57e-993j
0.28163726483522308367 + 1.5866862557709734663e-3697j 8.66e-1017, 8.66e-1017j
19.371119417055191707 + 2.5471321830358375306e-3674j 4.6e-999, 4.6e-999j
0.023677849122602471897 + 8.5644285168435224305e-3718j 1.57e-1020, 1.57e-1020j
78.306451808781001307 + 2.0108073840339619966e-3694j 8.22e-993, 8.22e-993j
0.12211744905067718704 - 8.7934137467132561885e-3743j 1.39e-1018, 1.39e-1018j
30.341029910027634462 - 5.6034776300813801325e-3718j 2.49e-996, 2.49e-996j

Weights

Weight (ball center) Error (ball radius)
9.3724447791655309587e-76 + 1.8930357422900983866e-2794j 6.45e-184, 8.29e-933j
5.4578488281159154008e-88 - 6.6677436270622593513e-2802j 3.25e-188, 4.18e-937j
3.478109912579616748e-81 + 4.6788992772800673347e-2798j 5.89e-186, 7.56e-935j
4.493448918372848699e-71 - 8.6995875672434538035e-2793j 3.76e-183, 4.84e-932j
1.350493362741314757e-59 + 2.1751867069120295144e-2787j 4.15e-180, 5.33e-929j
2.1163027143714111968e-40 - 1.0785287198851576856e-2777j 1.84e-172, 2.37e-921j
1.9065523237382345728e-19 - 1.439829381487150095e-2766j 2.51e-157, 3.22e-906j
1.6745464673235754402e-11 + 5.3948893543034281037e-2762j 7.99e-146, 1.03e-894j
4.3646583071366346355e-36 - 1.8556270436692790276e-2775j 1.61e-170, 2.07e-919j
2.7228967405120621397e-53 + 2.9654604469368252902e-2784j 3.9e-179, 5.01e-928j
1.2711936912804375205e-06 + 8.9717419474131973533e-2759j 2.5e-136, 3.21e-885j
-0.008092498616472918502 + 1.3883252817756139016e-2754j 1.9e-121, 2.44e-870j
3.7489369269936479136e-45 - 3.9249878447499019229e-2780j 1.03e-175, 1.32e-924j
3.4143327698555945007e-38 + 1.4935782836233306413e-2776j 8.58e-172, 1.1e-920j
2.3622472479116372126e-05 + 9.4860445497165248596e-2758j 1.72e-133, 2.2e-882j
2.539452766973806524e-07 - 2.773539667582231477e-2759j 4.38e-140, 5.63e-889j
8.3857495342720867606e-21 + 2.5690008076061101497e-2767j 1.2e-161, 1.55e-910j
6.5931352370681026076e-17 - 3.7881552086830270745e-2765j 5.35e-158, 6.87e-907j
1.3701413341205548897e-14 - 8.0063919674075191159e-2764j 1.69e-155, 2.16e-904j
6.7383212888287768555e-67 + 6.5808870446904407099e-2791j 3.56e-186, 4.57e-935j
0.0056475200781813904263 + 1.4613026748378259214e-2755j 1.16e-127, 1.49e-876j
1.0206647882015151057e-42 + 6.9301056327822890539e-2779j 7.72e-176, 9.92e-925j
3.7856853844946814475e-18 + 7.6000039010948377737e-2766j 1.79e-160, 2.31e-909j
0.012615785270056555919 - 1.8686921143362868053e-2755j 9.84e-128, 1.26e-876j
4.2502946536075381878e-63 - 4.2521919169010562428e-2789j 5.44e-185, 6.99e-934j
3.7675002290587459466e-32 - 2.1265525701147965087e-2773j 1.8e-172, 2.31e-921j
0.076849003761136554043 + 9.5376929746415204306e-2755j 5.15e-123, 6.62e-872j
0.00030960417381433274716 + 1.3804265656340527205e-2756j 2.82e-140, 3.62e-889j
2.4378240996226824067e-56 - 8.8918889104445958251e-2786j 9.72e-183, 1.25e-931j
2.6086529800451855256e-30 + 1.9849838077445387374e-2772j 6.18e-172, 7.94e-921j
0.0080220839425521210654 - 1.0898764317055676641e-2754j 6.13e-138, 7.88e-887j
1.08680980297542413e-09 + 7.2269536538304851524e-2761j 1.65e-155, 2.11e-904j
0.046826266914941465246 - 5.0130221433485592235e-2755j 1.59e-131, 2.04e-880j
5.754581653821225376e-06 - 2.8919420352595310535e-2758j 1.57e-147, 2.01e-896j
0.0028761235415316054607 - 3.7927467199720398766e-2755j 1.38e-139, 1.77e-888j
2.0050874730734883198e-50 - 8.2342659902680246511e-2783j 5.67e-181, 7.29e-930j
3.012464180256994907e-25 - 9.8942849581338343002e-2770j 3.16e-170, 4.06e-919j
0.11238480590344187396 - 2.0782967523634938365e-2754j 1.36e-132, 1.75e-881j
0.14451095509630766678 + 5.8917116766658617019e-2754j 2.04e-131, 2.62e-880j
8.8448753917041961436e-05 - 3.304513404419061377e-2757j 3.55e-146, 4.56e-895j
4.5788343905689850014e-08 + 8.4392306216006976001e-2760j 5.16e-154, 6.63e-903j
1.0110782822513120777e-15 + 1.7875983088265464198e-2764j 7.38e-163, 9.49e-912j
0.025604031137022451065 + 2.9036905431172026368e-2755j 5.09e-141, 6.54e-890j
0.20134200342538239835 - 5.6485681628550566253e-2753j 1.78e-136, 2.28e-885j
1.0599092566980301325e-23 + 6.7550265371667742132e-2769j 1.6e-169, 2.05e-918j
1.7583015136839569394e-12 - 1.3872334287525853191e-2762j 1.52e-161, 1.96e-910j
3.2060563982088280271e-22 - 4.3049036945341444354e-2768j 1.77e-168, 2.27e-917j
-0.086090660838818633563 + 9.0980309883738039412e-2753j 9.44e-142, 1.21e-890j
0.14608408359699392035 - 4.750192516712922254e-2753j 3.24e-142, 4.16e-891j
1.425357054673334319e-10 - 2.0127173664103661884e-2761j 3.55e-160, 4.56e-909j
7.3137117106191758874e-27 + 1.3482070850618571786e-2770j 2.49e-172, 3.2e-921j
1.0221301653626409143e-47 + 1.9379292603839847036e-2781j 2.52e-183, 3.23e-932j
1.5059138182904215868e-28 - 1.7026880207538924234e-2771j 1.21e-173, 1.56e-922j
0.1332413084738789818 + 1.1009383898454754299e-2753j 1.13e-151, 1.45e-900j
7.4385242931087952817e-09 - 2.50687200993268662e-2760j 1.79e-161, 2.3e-910j
0.059098665024301620328 + 6.3001192113556581645e-2755j 5.09e-154, 6.56e-903j
4.4901080385456184923e-34 + 2.0831885130617160307e-2774j 8.66e-177, 1.11e-925j
0.11865151369383379735 - 3.07801284465865369e-2754j 1.43e-154, 1.91e-903j
1.6460396209062597345e-13 + 3.4121184108239560457e-2763j 5.16e-165, 6.62e-914j

Download

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