Rule: Q[1, 5, 78]

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)
268.21106752529449168 + 2.2240006842153295252e-2510j 1.65e-991, 1.65e-991j
282.83261815733447535 - 4.6041123474392581197e-2512j 4.13e-993, 4.13e-993j
301.11437606287565327 - 4.1577685901028407205e-2515j 3.33e-995, 3.33e-995j
233.80650624957842372 - 4.5279792160458577601e-2502j 6.13e-988, 6.13e-988j
183.69769088990989769 + 3.628901456175666112e-2500j 1.03e-983, 1.03e-983j
56.280045646560676602 - 7.0842475718123276025e-2509j 1.37e-983, 1.37e-983j
224.17340012398141337 - 3.5703344128687972273e-2506j 4.94e-987, 4.94e-987j
48.084382677049632158 + 1.0580137584328095497e-2523j 8.36e-985, 8.36e-985j
198.63152666553060744 - 1.2959748963000842519e-2519j 7.87e-985, 7.87e-985j
24.172879378319928246 - 3.2232181231512406231e-2542j 4.43e-991, 4.43e-991j
20.78230448716007004 + 1.0609471939937660215e-2543j 1.77e-992, 1.77e-992j
78.595539644305500321 - 5.9012498371829415921e-2531j 1.54e-981, 1.54e-981j
115.08205060137064761 - 1.6228082646409493369e-2538j 1.02e-980, 1.02e-980j
89.6823222176736126 + 2.3158172248417554818e-2549j 5.46e-981, 5.46e-981j
75.114051226975597517 + 1.3782376366832507394e-2557j 9.52e-982, 9.52e-982j
68.454543614123638577 - 3.6519476906864413924e-2559j 2.77e-982, 2.77e-982j
9.9756688632458231076 + 5.5865473856375422569e-2594j 1.44e-998, 1.44e-998j
38.315788225512427034 + 2.0320733245356753997e-2576j 7.79e-987, 7.79e-987j
93.603203671669586243 - 1.0247381358756933965e-2574j 7.05e-981, 7.05e-981j
157.43846586924230387 - 6.5385988308965237463e-2620j 4.28e-982, 4.28e-982j
50.730893984315116534 + 1.5240351249681679996e-2648j 2.04e-984, 2.04e-984j
14.829781217182764814 - 2.5822683223129614238e-2690j 1.97e-995, 1.97e-995j
215.1603981888396116 + 2.8302796638523417727e-2679j 3.08e-986, 3.08e-986j
7.3248599988741952282 - 2.8272185538343434151e-2736j 1.3e-1000, 1.3e-1000j
134.8431161879579027 + 1.0362834209192265754e-2725j 3.9e-981, 3.9e-981j
255.55126747179445662 + 5.418061524348872715e-2747j 3.86e-990, 3.86e-990j
85.876448719480855187 + 7.7467624664311595107e-2770j 3.84e-981, 3.84e-981j
8.9529512477548957267 + 1.4199245891556196488e-2818j 2.73e-999, 2.73e-999j
151.48622345584978807 + 1.1103979164174511887e-2814j 8.43e-982, 8.43e-982j
29.791701401055175573 - 6.7528584366573311118e-2862j 3.98e-989, 3.98e-989j
124.64542164498174601 + 5.1428085226011458463e-2860j 8.07e-981, 8.07e-981j
101.80596000793064055 + 6.465966941884754958e-2909j 9.8e-981, 9.8e-981j
190.98848189019083972 - 1.066806662951749386e-2946j 2.9e-984, 2.9e-984j
71.734616208545698944 - 7.2007368404413318412e-2974j 5.82e-982, 5.82e-982j
5.8993231586621279741 + 2.3219201673637188618e-3029j 1.83e-1002, 1.83e-1002j
27.846613825016642824 - 1.1931212193102138026e-3008j 9.59e-990, 9.59e-990j
129.66098623405706678 - 2.9789935519219261265e-3013j 5.61e-981, 5.61e-981j
8.0490888769342364438 - 4.6915976800855345103e-3087j 5.85e-1000, 5.85e-1000j
110.52021663681080172 + 5.276469094791346415e-3066j 1.06e-980, 1.06e-980j
65.271322516258134406 + 6.2490425513112354059e-3128j 1.56e-982, 1.56e-982j
170.03834290451692024 - 9.0853587274440812057e-3168j 8.42e-983, 8.42e-983j
5.1384848875831238418 - 5.3824681538836443089e-3211j 1.28e-1003, 1.28e-1003j
59.18619992228455139 + 7.5351757222605195876e-3188j 3.24e-983, 3.24e-983j
36.071107184837554553 + 2.8201603165776715022e-3206j 2.26e-987, 2.26e-987j
16.215549377978967353 - 3.0047113880458402944e-3214j 1.14e-994, 1.14e-994j
25.973960230251449295 - 1.3703279758173878676e-3209j 2.05e-990, 2.05e-990j
33.90293133538218071 - 5.1513874756443446562e-3207j 6.25e-988, 6.25e-988j
43.039477555220059867 - 8.3125184381550071563e-3201j 9.23e-986, 9.23e-986j
2.1050079771947339222 - 5.9518271305759675708e-3241j 3.74e-1009, 3.74e-1009j
1.6786596582430743671 + 5.7665171444829474397e-3242j 3.32e-1010, 3.32e-1010j
53.462214190702341603 + 6.9375149662060723784e-3213j 5.4e-984, 5.4e-984j
82.181970068238677618 + 6.9273057031226492819e-3277j 2.43e-981, 2.43e-981j
3.7497627773016839769 + 3.4096579636089937657e-3354j 7.77e-1006, 7.77e-1006j
4.4173064682392971291 + 2.7187125955625799007e-3354j 9.98e-1005, 9.98e-1005j
1.3115011993668193733 + 3.8016485638632243022e-3363j 2.8e-1011, 2.8e-1011j
145.74479174601296915 - 7.2254327600903412303e-3347j 1.59e-981, 1.59e-981j
62.182606503908912272 - 1.6028907658948086099e-3387j 7.27e-983, 7.27e-983j
206.67042164297971845 + 3.270887646682846257e-3423j 1.75e-985, 1.75e-985j
40.638159045324739063 - 1.424205979532411297e-3454j 2.71e-986, 2.71e-986j
17.669319417524203123 - 1.1786232827074261489e-3468j 6.76e-994, 6.76e-994j
22.442572172865494178 - 1.3197962773208664366e-3466j 9.03e-992, 9.03e-992j
140.20095970995921736 + 6.8611867443629294444e-3454j 2.65e-981, 2.65e-981j
97.643002682700109206 - 5.7255658521713129338e-3465j 8.72e-981, 8.72e-981j
2.5922508199253002476 - 6.4273701401232916605e-3493j 4.56e-1008, 4.56e-1008j
6.6536638598539060687 + 1.6444639378569130474e-3486j 2.23e-1001, 2.23e-1001j
0.73806909005365324171 + 7.6460872850028292989e-3498j 1.75e-1013, 1.75e-1013j
45.521079352745179391 - 4.5121545548828755611e-3470j 2.73e-985, 2.73e-985j
19.191413413783770655 + 2.3972661335788611116e-3478j 3.53e-993, 3.53e-993j
106.09668780890544875 + 2.2486662973472351203e-3464j 1.09e-980, 1.09e-980j
0.33190874966882503003 + 5.3154260671262069267e-3504j 5.9e-1016, 5.9e-1016j
0.18296039898248679851 - 2.4902454241295389079e-3506j 2.05e-1017, 2.05e-1017j
12.262373944311842902 - 9.5544907664619472672e-3486j 5.37e-997, 5.37e-997j
244.19691891611926183 - 3.6780579170107772068e-3476j 6.01e-989, 6.01e-989j
163.61666615501104417 - 2.9592696682173389998e-3468j 2.03e-982, 2.03e-982j
31.810145632686782497 + 5.5242731261730261391e-3482j 1.57e-988, 1.57e-988j
0.51732888896872373418 - 3.5524891792027233047e-3508j 1.05e-1014, 1.05e-1014j
1 + 1.5369828091453836657e-3506j 2.07e-1012, 2.07e-1012j
0.014473616652573163785 + 3.2014255972476817202e-3578j 1.22e-1020, 1.22e-1020j
3.1407405638546833101 + 2.1997107897341460249e-3500j 6.16e-1007, 6.16e-1007j
176.72395910411082623 - 1.7605903361438178275e-3473j 3.18e-983, 3.18e-983j
13.511934960933230382 - 3.3754847565651897973e-3492j 3.2e-996, 3.2e-996j
11.082400750804597523 - 1.3156040643229109702e-3493j 8.84e-998, 8.84e-998j
0.075623735861171484173 + 1.1837061584246655349e-3571j 5.2e-1019, 5.2e-1019j
119.78823255628577055 - 3.0398018030128590254e-3475j 9.22e-981, 9.22e-981j

Weights

Weight (ball center) Error (ball radius)
4.4396269074264631329e-116 + 1.2754903503598600394e-2582j 1.26e-137, 5.01e-880j
2.3512187285592361815e-122 - 7.5916478111103674724e-2586j 1.07e-139, 4.24e-882j
3.6344700058675662877e-130 + 7.4544283171987926744e-2590j 2.23e-142, 8.87e-885j
2.8737462657967065774e-101 - 5.485669322840500798e-2575j 3.79e-134, 1.51e-876j
1.185800805568323414e-79 - 9.0624477648291899454e-2564j 2.73e-127, 1.09e-869j
1.0339701895751919387e-24 + 4.0093223087810201233e-2533j 1.34e-89, 5.33e-832j
4.0870297500885269634e-97 + 7.6965903637982026735e-2573j 3.01e-133, 1.2e-875j
3.4116704617811330817e-21 - 7.828562205198810583e-2532j 2.85e-85, 1.14e-827j
4.2593635351910085274e-86 - 3.9847382078113894588e-2567j 8.54e-130, 3.4e-872j
5.6070684892866696744e-11 + 1.7674322575263987691e-2526j 2.43e-64, 9.67e-807j
1.5322873484494687242e-09 + 1.318510632840539195e-2525j 1.01e-59, 4e-802j
2.5977124664604269354e-34 + 2.1558538325221670884e-2539j 2.85e-102, 1.13e-844j
4.8568901875842241203e-50 - 4.1608479130210738125e-2548j 3.75e-115, 1.49e-857j
4.3486967508810751139e-39 - 4.177952691925243211e-2542j 4.56e-107, 1.82e-849j
8.1973943208262842625e-33 - 1.6155497569977480674e-2538j 2.23e-101, 8.87e-844j
6.0247496743299609257e-30 - 8.6463250869727138707e-2537j 4.28e-99, 1.71e-841j
4.9663136796229568225e-05 + 2.7315271978789861678e-2522j 1.05e-46, 4.16e-789j
5.226751647200089055e-17 - 8.2104703672423354369e-2530j 8e-84, 3.18e-826j
8.8816033825661138357e-41 + 4.7815561570427489147e-2543j 5.95e-109, 2.37e-851j
2.558561781009800856e-68 - 7.8583313141750286052e-2558j 2.71e-127, 1.08e-869j
2.4968097641169867137e-22 + 2.7078150198119969613e-2532j 5.06e-92, 2.02e-834j
4.9026074191073530387e-07 + 6.065451462748487721e-2524j 7.93e-62, 3.16e-804j
3.1508414316343859935e-93 - 7.9253004484570057522e-2571j 1.43e-136, 5.71e-879j
0.00042916582895666688822 - 4.3122715700060776131e-2521j 4.35e-46, 1.73e-788j
1.4456239827751692526e-58 - 1.1306801454393459325e-2552j 5.79e-123, 2.31e-865j
1.2366761650439925889e-110 - 8.0920343936477246319e-2580j 1.56e-143, 6.19e-886j
1.8980899596842002282e-37 + 3.4871470101164417748e-2541j 3.4e-108, 1.35e-850j
0.00012582744991859988871 - 7.6120877595939593097e-2522j 2.52e-55, 1e-797j
9.4867057357548095131e-66 + 1.7742084628188348288e-2556j 1.38e-126, 5.49e-869j
2.2837365378029683051e-13 - 7.4500675990065746742e-2528j 2.36e-85, 9.41e-828j
3.6347602673974852158e-54 - 2.5211619704359733138e-2550j 5.59e-121, 2.23e-863j
2.5832534523932178961e-44 + 5.3780008209005949084e-2545j 3.69e-115, 1.47e-857j
8.4629256704686741141e-83 + 2.0739794372806092585e-2565j 1.69e-134, 6.72e-877j
2.335649504451674236e-31 + 1.1858031363815726904e-2537j 6.89e-106, 2.75e-848j
0.0021112907641488292752 - 6.8178237945321286745e-2521j 4.11e-57, 1.63e-799j
1.5385511504861737588e-12 + 2.1863355754790696055e-2527j 1.19e-87, 4.73e-830j
2.4905686138535957971e-56 + 1.7569583441467587841e-2551j 2.17e-122, 8.64e-865j
0.00026206201955383502772 + 2.1126832130036037084e-2521j 2.07e-64, 8.24e-807j
4.5091283521942078332e-48 + 4.8238869036824752218e-2547j 7.05e-118, 2.81e-860j
1.4104059844492348134e-28 + 6.4221912452230522465e-2536j 2.43e-105, 9.67e-848j
9.3223275180520578897e-74 - 1.0958909312278007505e-2560j 3.04e-132, 1.21e-874j
0.0043692002163089267292 + 8.418314686609230195e-2521j 2.68e-62, 1.07e-804j
5.8307122214544254942e-26 + 5.2349667060700318118e-2534j 6.54e-104, 2.6e-846j
4.7661679559442984175e-16 + 2.6047450619503069635e-2529j 2.31e-96, 9.2e-839j
1.2879012740090038941e-07 - 2.3696240741732359627e-2524j 7.92e-84, 3.15e-826j
9.6315777979646911725e-12 - 6.2814991434533916268e-2527j 9.83e-91, 3.91e-833j
4.0233228384463578817e-15 - 8.1241983082809600646e-2529j 1.28e-95, 5.1e-838j
4.9636510436067078886e-19 - 7.8934657260864034031e-2531j 2.2e-100, 8.77e-843j
0.055638926378415376574 - 4.9737373488382924093e-2520j 3.26e-60, 1.3e-802j
0.073965630577988587081 + 7.1045592473992575487e-2520j 2.07e-57, 8.24e-800j
1.6780549988126736876e-23 - 1.20115096113566896e-2532j 1.7e-103, 6.76e-846j
7.4116591917376310968e-36 - 2.792218055120965619e-2540j 2.08e-112, 8.28e-855j
0.015025951112571086775 + 1.5917391828172351246e-2520j 4.21e-70, 1.68e-812j
0.0083933932279667078287 - 1.1282261514832724336e-2520j 1.18e-71, 4.69e-814j
0.091212765580130778744 - 9.6186291606085845209e-2520j 3.12e-60, 1.24e-802j
2.8520978303890671796e-63 - 3.6138216488170403814e-2555j 2.03e-130, 8.08e-873j
3.0034881764468069569e-27 - 5.1317587045182429302e-2535j 3.78e-107, 1.51e-849j
1.4482492490222713307e-89 + 6.2876807813708416281e-2569j 4.07e-143, 1.62e-885j
5.3000917635741015916e-18 + 2.5542078618695296418e-2530j 2.15e-101, 8.57e-844j
3.1540984105728551292e-08 + 9.1721862118620337811e-2525j 4.79e-93, 1.91e-835j
3.0375832818897134984e-10 - 4.8737158477361039645e-2526j 4.98e-95, 1.98e-837j
7.0439356350298765237e-61 + 6.6864736738049318824e-2554j 2.5e-129, 9.96e-872j
1.6107738860554833676e-42 - 5.2075675845009681157e-2544j 4.71e-119, 1.88e-861j
0.038765579781721841712 + 3.3973684013919140637e-2520j 9.99e-81, 3.98e-823j
0.00092779354950580041967 + 5.9040240414787990529e-2521j 1.55e-86, 6.15e-829j
0.11468228229659873595 - 1.2699710077313986152e-2519j 5.25e-79, 2.09e-821j
4.2877307274153208518e-20 + 2.451641591140465575e-2531j 1.13e-104, 4.52e-847j
7.2010750117758913431e-09 - 3.5048013192305601569e-2525j 1.99e-96, 7.93e-839j
3.6467582389486636879e-46 - 5.2485227049812446756e-2546j 1.45e-121, 5.77e-864j
0.12047981692627453805 - 8.507162500944442692e-2520j 5.01e-83, 1.99e-825j
0.10747398268298759391 + 5.297899490589331297e-2520j 3.08e-83, 1.23e-825j
5.7429230251526250031e-06 + 3.9523741089953643816e-2523j 2.45e-95, 9.74e-838j
9.5774185286915339183e-106 + 2.6794598174789199748e-2577j 7.03e-153, 2.8e-895j
5.5119378611811880762e-71 + 3.1156694040419730974e-2559j 4.34e-136, 1.73e-878j
3.1472791620454065161e-14 + 2.4855899455830345831e-2528j 4.62e-104, 1.84e-846j
0.12081022325889760966 + 1.1398446002387767866e-2519j 1.03e-89, 4.11e-832j
0.10501018565294722148 + 1.1858478528076794455e-2519j 3.23e-90, 1.28e-832j
0.036539585990866518708 + 7.268000996744326429e-2521j 4.94e-91, 1.97e-833j
0.025040548252419309417 - 2.3113166399117764591e-2520j 6.38e-93, 2.54e-835j
1.2130557081739137924e-76 + 3.3841065759452819086e-2562j 4.92e-139, 1.96e-881j
1.7391803485642228208e-06 - 1.5460139148714608614e-2523j 6.88e-100, 2.72e-842j
1.7599961557614828771e-05 - 1.0242038731391405817e-2522j 5.85e-99, 2.31e-841j
0.078660383553614550538 - 2.6107963168413215475e-2520j 2.85e-95, 1.1e-837j
4.5300890460965151241e-52 + 3.3558945642964608099e-2549j 2.52e-126, 1.01e-868j

Download

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