Rule: Q[1, 3, 60]

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.

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)
210.7757201597874654 + 1.5552441985918086044e-2513j 1.15e-998, 1.15e-998j
227.35894752014795586 + 1.8846345928273001289e-2518j 1.55e-1000, 1.55e-1000j
186.20649100356740732 - 1.1192670393932610226e-2507j 4.26e-996, 4.26e-996j
176.05169903646661623 + 8.5807871662125149643e-2510j 3.94e-995, 3.94e-995j
85.892067846161293611 + 4.5010097475127046317e-2525j 6.79e-990, 6.79e-990j
11.530443342072311915 + 1.0882777022557350319e-2560j 1.82e-1001, 1.82e-1001j
197.57944640938005942 + 1.369051936685203211e-2548j 3.23e-997, 3.23e-997j
81.448033083100351033 - 5.7067104927736594175e-2550j 6.63e-990, 6.63e-990j
17.692238306276929176 + 6.1379759226220205649e-2574j 2.33e-998, 2.33e-998j
158.25969771904024956 - 2.3165552130972628644e-2565j 1.55e-993, 1.55e-993j
129.1584617043190884 + 6.1253930542051200642e-2579j 2.03e-991, 2.03e-991j
54.771273025227816109 + 1.9317348115810123138e-2591j 6.39e-991, 6.39e-991j
42.494015615417947848 + 1.6653763758413984403e-2602j 2.63e-992, 2.63e-992j
65.323318941812474583 - 1.2452098797445937339e-2612j 2.71e-990, 2.71e-990j
5.7766549012239696368 + 1.4691570438291309998e-2658j 7.58e-1006, 7.58e-1006j
4.8815190434135835591 - 2.1955260703164078023e-2659j 9.44e-1007, 9.44e-1007j
23.267271963637416138 + 7.1583546405334477602e-2647j 2.12e-996, 2.12e-996j
12.938372921524315065 - 5.9357944027908901879e-2653j 1.24e-1000, 1.24e-1000j
166.79976168729874477 + 7.9091581244306032792e-2642j 2.96e-994, 2.96e-994j
29.704418019624644281 - 2.5195557665728200038e-2666j 1.23e-994, 1.23e-994j
16.018134792089208616 - 1.4932296468826471607e-2682j 4.41e-999, 4.41e-999j
37.055002065033130751 - 6.2296169155170174494e-2673j 3.64e-993, 3.64e-993j
95.338835355125762598 + 1.4478847023612853947e-2738j 5.64e-990, 5.64e-990j
135.8128823919047039 - 2.9493512095955593211e-2838j 8.17e-992, 8.17e-992j
100.36454566401880459 - 3.2259811754176888214e-2913j 4.28e-990, 4.28e-990j
1 + 6.9269364285532140394e-2986j 6.53e-1014, 6.53e-1014j
34.499645187307536692 + 2.4632462548929462246e-2962j 1.35e-993, 1.35e-993j
58.15326194485639421 + 5.9598141269575843852e-3001j 1.08e-990, 1.08e-990j
10.20914861133068909 + 2.9961765062414036207e-3062j 2.69e-1002, 2.69e-1002j
105.60992085199799262 - 1.9891889055167554289e-3105j 2.73e-990, 2.73e-990j
73.070978406075038797 - 1.385903511654584989e-3222j 5.41e-990, 5.41e-990j
7.8232631436879996743 - 7.8514544023675954705e-3284j 5.15e-1004, 5.15e-1004j
2.3193935741149708798 + 1.1151515606404929671e-3292j 3.68e-1010, 3.68e-1010j
122.84083677134154111 - 3.201141998185932418e-3329j 4.89e-991, 4.89e-991j
21.315352724058560953 - 2.7633246115356400707e-3378j 5.13e-997, 5.13e-997j
116.82736588051170957 - 3.8307005536696401623e-3393j 9.57e-991, 9.57e-991j
8.9736463332023372571 + 9.5790745702709604001e-3437j 4.1e-1003, 4.1e-1003j
4.0757166343200668382 + 8.2393922771907653829e-3442j 1.31e-1007, 1.31e-1007j
25.314897166937965325 + 7.0660870643062379162e-3429j 9.39e-996, 9.39e-996j
111.09120197690872647 - 1.5116109494660499862e-3422j 1.73e-990, 1.73e-990j
2.7883138437554260945 - 1.4108202573769406622e-3451j 2.53e-1009, 2.53e-1009j
61.668932494646222969 + 1.6443462356715847577e-3431j 1.7e-990, 1.7e-990j
0.38485818474670956007 + 5.2639883242198196003e-3465j 1e-1016, 1e-1016j
32.050240278591766975 - 5.5795653987755416045e-3442j 4.35e-994, 4.35e-994j
48.390379062695325895 + 1.9503183699759103373e-3438j 1.43e-991, 1.43e-991j
19.45751146766909431 - 5.7659874542048068738e-3455j 1.05e-997, 1.05e-997j
150.30457806332050164 - 4.0602002173357882578e-3447j 7.18e-993, 7.18e-993j
6.757583189418260011 - 1.2857371500249502652e-3474j 6.29e-1005, 6.29e-1005j
0.65733225281898801781 - 1.118101365188386705e-3483j 3.16e-1015, 3.16e-1015j
0.0024250677112708865824 + 7.2648019751548726682e-3490j 9.9e-1022, 9.9e-1022j
1.861013236347602836 - 3.0106592324690424629e-3480j 2.76e-1011, 2.76e-1011j
90.518754058714674544 + 4.9768754534730874724e-3457j 6.28e-990, 6.28e-990j
45.383435510529064135 - 1.9733988114789416039e-3469j 6.46e-992, 6.46e-992j
0.18449965117564237439 + 4.4665204267887214323e-3496j 3.64e-1018, 3.64e-1018j
1.4071378512414880322 - 5.0128813404137102936e-3490j 1.66e-1012, 1.66e-1012j
14.433909000306801864 - 1.3760814652651490045e-3477j 7.18e-1000, 7.18e-1000j
142.84452325724100659 - 1.0585141303935158001e-3468j 2.74e-992, 2.74e-992j
69.121961518543824013 + 1.0849422008573220966e-3466j 3.91e-990, 3.91e-990j
0.056897625001077184683 - 2.6648351505019446071e-3506j 9.52e-1020, 9.52e-1020j
3.369839231310923141 + 2.3219686526393290366e-3495j 1.61e-1008, 1.61e-1008j
27.459982535533175003 + 4.4130678432490765535e-3481j 3.91e-995, 3.91e-995j
51.518376921733708233 + 1.2178375925075997669e-3475j 3.14e-991, 3.14e-991j
77.177151995064351921 + 2.509535778939692633e-3487j 6.14e-990, 6.14e-990j
39.718869863701026001 - 1.2062186314601072743e-3504j 1.04e-992, 1.04e-992j

Weights

Weight (ball center) Error (ball radius)
4.1848211705567850115e-91 - 2.8793803760668696863e-2591j 1.08e-175, 5.71e-923j
3.5546978508744629796e-98 + 6.6083688605006049433e-2595j 5.68e-178, 3.01e-925j
1.4479789143155730882e-80 - 7.9524785865227409957e-2586j 4.74e-173, 2.51e-920j
3.3641794394711307143e-76 + 1.4619336604805790837e-2583j 5.47e-172, 2.9e-919j
2.2594349683076957519e-37 - 5.2631925786597235162e-2562j 5.6e-156, 2.97e-903j
1.3407658372685042267e-05 + 2.3074876789612809685e-2546j 7.66e-107, 4.06e-854j
1.8909518860545089761e-85 + 2.3880191966878713339e-2588j 8.7e-175, 4.61e-922j
1.8477932963215755905e-35 + 2.241880727154084457e-2561j 5.79e-155, 3.06e-902j
3.5624738660116927957e-08 + 6.5642874584634507644e-2548j 6.76e-120, 3.58e-867j
1.5278941838073805306e-68 + 1.4555558896795816204e-2579j 1.36e-170, 7.2e-918j
5.2332163702821468178e-56 + 6.1214031051487682385e-2573j 1.39e-166, 7.35e-914j
5.4180890381257029558e-24 - 3.1540499151086103926e-2556j 5.05e-148, 2.68e-895j
9.9343724804820398199e-19 - 1.4218753338368218937e-2553j 5.79e-143, 3.07e-890j
1.590863532235708618e-28 + 1.981981765399519818e-2558j 8.77e-152, 4.64e-899j
0.0029079628103863864466 - 1.0616479965386528652e-2544j 1.88e-101, 9.95e-849j
0.006458359861849449173 + 2.2068494943305611869e-2544j 4.1e-98, 2.17e-845j
1.5706215740898318839e-10 - 3.104963664229101633e-2549j 6.24e-131, 3.3e-878j
3.4895658344617429777e-06 - 9.9609638753137975681e-2547j 2.08e-118, 1.1e-865j
3.2191691916864808017e-72 - 1.7439491701202900301e-2581j 8.41e-173, 4.45e-920j
2.8858621321829746456e-13 + 1.0202464084902896636e-2550j 1.16e-136, 6.14e-884j
1.8002065802271798494e-07 - 1.6830052849437358189e-2547j 9.26e-124, 4.91e-871j
2.1072657726278180131e-16 - 2.2652356603971129134e-2552j 3.15e-141, 1.67e-888j
1.9359690183924816633e-41 + 8.5160621402557929277e-2565j 9.45e-162, 5e-909j
7.111905649139929622e-59 - 1.8133427926130507812e-2574j 5.13e-170, 2.71e-917j
1.3261903363026713678e-43 - 4.258406780840766556e-2566j 2.11e-163, 1.12e-910j
0.13847721977490434151 - 2.0585119758021239597e-2543j 2.98e-110, 1.58e-857j
2.6018167225323145746e-15 + 8.4316487317295931051e-2552j 7.09e-143, 3.76e-890j
1.9139484025705080476e-25 + 6.0753719250640686395e-2557j 6.63e-153, 3.51e-900j
4.7081013329777100162e-05 - 5.1887851232148078418e-2546j 1.69e-124, 8.97e-872j
7.3011696136502691512e-46 + 2.1479415995670095954e-2567j 4.28e-165, 2.27e-912j
7.4232605912595596638e-32 + 5.8004805251050017867e-2560j 4.18e-158, 2.21e-905j
0.00044354348196925232576 - 2.4299037189930382735e-2545j 2.37e-124, 1.26e-871j
0.04418263063251271956 + 2.5406926638253618554e-2543j 2.84e-110, 1.5e-857j
2.7575829676179631857e-53 - 1.7744528933739084712e-2571j 3.25e-169, 1.72e-916j
1.0535812812086880995e-09 + 8.9270542812637839922e-2549j 1.06e-139, 5.59e-887j
1.0745167882727039583e-50 + 4.5118929849494535465e-2570j 2.53e-168, 1.34e-915j
0.00015114018352194285664 + 1.1358837062371675883e-2545j 1.82e-129, 9.61e-877j
0.012881274709645183813 - 4.6428101902679559026e-2544j 2.84e-122, 1.51e-869j
2.1246230667327339183e-11 + 1.0370729740906352825e-2549j 3.03e-143, 1.61e-890j
3.1790901291154985607e-48 - 1.0277286136384014627e-2568j 3.32e-167, 1.76e-914j
0.031550747626666763334 - 1.867836469815395668e-2543j 5.67e-122, 3.01e-869j
5.9143773067239347739e-27 - 1.1192788433817067131e-2557j 3.89e-157, 2.06e-904j
0.16100866712912174964 - 1.7178667817286277018e-2543j 1.1e-119, 5.82e-867j
2.8871401726752904586e-14 - 2.9990106040296700662e-2551j 1.18e-147, 6.23e-895j
2.9581416473763252131e-21 - 7.3752685601622078893e-2555j 1.77e-154, 9.36e-902j
6.4225002817918157026e-09 - 2.4674437963363128095e-2548j 4.91e-142, 2.6e-889j
4.0714828212740826502e-65 - 9.1265705662320042212e-2578j 8.48e-177, 4.49e-924j
0.0011891891505108560531 + 5.1059839837319134676e-2545j 5.85e-135, 3.1e-882j
0.15965423926167066722 + 1.8951747673532458977e-2543j 1.72e-126, 9.1e-874j
0.017373244575520178934 + 4.5857078828290783626e-2544j 4.01e-127, 2.12e-874j
0.072284174182622204826 - 2.5353982418997822008e-2543j 7.91e-129, 4.19e-876j
2.3029397792540731572e-39 - 2.0505380213988225949e-2563j 2.58e-164, 1.36e-911j
5.7503667505164108683e-20 + 3.3173087477858602862e-2554j 2.43e-154, 1.29e-901j
0.13639901516806990799 + 1.4799084356421049425e-2543j 8.99e-130, 4.76e-877j
0.10656797180424695922 + 2.2649179119119178426e-2543j 1e-131, 5.3e-879j
8.2959609429779140098e-07 + 4.1644415594631422543e-2547j 2e-142, 1.06e-889j
6.6515619838928441702e-62 + 4.5049891987084325982e-2576j 1.73e-175, 9.15e-923j
3.7045364708774484048e-30 - 3.4064317741601615371e-2559j 1.98e-160, 1.05e-907j
0.086091855981244133448 - 1.1287743399672991019e-2543j 7.14e-135, 3.78e-882j
0.022313732529195385919 + 9.8434614795439747532e-2544j 2.18e-138, 1.15e-885j
2.6037756172460234542e-12 - 3.3228164245712296575e-2550j 1.29e-149, 6.82e-897j
1.3477635457436190679e-22 + 1.562289856676017957e-2555j 1.31e-156, 6.95e-904j
1.2714882560753719747e-33 - 1.0284896667839573131e-2560j 1.47e-162, 7.8e-910j
1.5301272585671411172e-17 + 5.8104383699816115156e-2553j 8.47e-154, 4.48e-901j

Download

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