Rule: Q[1, 7, 47]

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)
185.31933379922163717 - 9.2644319279725325327e-2042j 1.98e-1003, 1.98e-1003j
169.90025446761098907 + 1.0298548859603780242e-2034j 1.1e-1001, 1.1e-1001j
129.42555858030063041 - 5.521356496845219085e-2033j 8.84e-998, 8.84e-998j
147.20352477523465853 - 1.803050946216385669e-2040j 2.1e-999, 2.1e-999j
157.68585429701093283 + 1.1317254414266679085e-2049j 1.97e-1000, 1.97e-1000j
24.950425592239705313 + 6.7908674320188657263e-2065j 5.89e-998, 5.89e-998j
12.755431708942418397 - 3.0135445657181658601e-2076j 2.32e-1000, 2.32e-1000j
10.609250458207418466 - 2.3002139155474963856e-2078j 9.26e-1003, 9.26e-1003j
121.65193312498060022 + 1.2094085415291732593e-2071j 3.6e-997, 3.6e-997j
70.097376062687050779 - 2.1531045982767553516e-2098j 1.04e-994, 1.04e-994j
27.23573439347614817 + 2.1429180857245052695e-2115j 1.66e-997, 1.66e-997j
7.9509208918881512072 + 1.7478058118643426382e-2122j 7.24e-1005, 7.24e-1005j
9.2206056582280395483 + 2.3331763287863283642e-2122j 7.67e-1004, 7.67e-1004j
46.925435925679186168 - 1.5145958936820956601e-2112j 2.84e-995, 2.84e-995j
32.171461361616046023 - 1.9113320540079316384e-2122j 1.08e-996, 1.08e-996j
61.61738055696887465 + 7.5710892161864241899e-2134j 8.91e-995, 8.91e-995j
53.918183857732307934 + 5.5898569169092331293e-2179j 6.31e-995, 6.31e-995j
3.1570155819938148631 + 6.5519788767418122178e-2227j 7.18e-1010, 7.18e-1010j
22.778539744627225471 - 5.1033116571923596056e-2212j 1.89e-998, 1.89e-998j
137.88262798623687119 - 1.9426281081371066959e-2251j 1.53e-998, 1.53e-998j
16.886646060861748393 - 3.080651092900334396e-2282j 4.4e-1000, 4.4e-1000j
4.7673099177671066141 - 2.1453697793785658213e-2289j 7.2e-1008, 7.2e-1008j
1.430101061529368292 - 3.2630648944514597318e-2290j 3.58e-1013, 3.58e-1013j
15.101380116793933122 - 4.7007831241481429739e-2292j 1.55e-1000, 1.55e-1000j
84.504337827359551345 + 1.9540635805403105047e-2331j 5.04e-995, 5.04e-995j
101.39425838101312293 - 8.7491989855422987488e-2385j 9.26e-996, 9.26e-996j
37.635559774303498222 - 5.4512092308729891818e-2417j 5.17e-996, 5.17e-996j
0.64336829240185923307 - 5.4084385642009825113e-2452j 1.17e-1015, 1.17e-1015j
2.5000206754193299535 + 1.9481418793109620227e-2449j 6.41e-1011, 6.41e-1011j
20.714357062775040705 - 8.8632462427345184084e-2447j 5.61e-999, 5.61e-999j
57.675277582882006787 + 3.3273982913213462521e-2505j 8.02e-995, 8.02e-995j
79.455944932837411082 + 9.6338908526769850202e-2568j 8.14e-995, 8.14e-995j
43.675239768081944574 - 3.127488137800904201e-2590j 1.87e-995, 1.87e-995j
1.928704209731764729 - 5.5722802510374180146e-2627j 5.5e-1012, 5.5e-1012j
40.580581347848660109 - 8.8493339399452890951e-2609j 1.05e-995, 1.05e-995j
89.825763563440413557 + 8.3380694149233880176e-2659j 3.38e-995, 3.38e-995j
6.7870329452902910753 + 1.619751763842016034e-2712j 7.4e-1006, 7.4e-1006j
1 - 1.1064054041432798448e-2726j 2.27e-1014, 2.27e-1014j
13.155459811411549988 + 2.2743215466859907938e-2707j 1.97e-1000, 1.97e-1000j
65.754324277395464877 + 1.8427539907295437512e-2743j 9.71e-995, 9.71e-995j
107.71024936112641952 + 3.9498618536918410471e-2824j 3.75e-996, 3.75e-996j
34.834444209886613426 - 9.0583886891785170114e-2892j 2.52e-996, 2.52e-996j
3.911199094806295407 - 4.6729388483151148478e-2946j 7.13e-1009, 7.13e-1009j
74.659540832164030097 - 6.4075362940555770245e-2959j 9.63e-995, 9.63e-995j
12.35199612685986194 - 6.5658258806593958715e-3004j 8.35e-1001, 8.35e-1001j
95.445481027756775797 - 1.7207724968156797404e-2996j 1.8e-995, 1.8e-995j
50.337457674618939796 + 1.5960822335530754789e-3010j 4.53e-995, 4.53e-995j
0.091757419202714714556 + 8.5883028587892689609e-3042j 4.33e-1019, 4.33e-1019j
0.18807558052466950658 - 5.7088574707027241672e-3041j 6.13e-1018, 6.13e-1018j
18.75251539166561618 - 3.9124504502781211373e-3022j 1.62e-999, 1.62e-999j
0.020727208186411494474 + 2.4301084431396562164e-3073j 1.74e-1020, 1.74e-1020j
114.44181213613080926 - 1.163130086052136929e-3020j 1.31e-996, 1.31e-996j
29.640633213967054313 - 9.1421599525315758759e-3034j 4.37e-997, 4.37e-997j
5.725998207999312916 - 3.8197360271898994629e-3044j 7.04e-1007, 7.04e-1007j
0.36866340472364444637 - 1.7101314758874331907e-3054j 7.48e-1017, 7.48e-1017j

Weights

Weight (ball center) Error (ball radius)
5.9947385153128089565e-80 + 1.4133810500631460607e-2102j 1.38e-189, 4.77e-942j
2.192809771652577402e-73 - 5.1512277212864130084e-2099j 1.1e-187, 3.8e-940j
5.0029039663336318408e-56 + 1.4619250378456762691e-2088j 1.56e-182, 5.37e-935j
1.1566489747403913313e-63 - 1.4547430501728693032e-2093j 2.82e-185, 9.74e-938j
3.6958682707516084821e-68 + 3.9991195442063244239e-2096j 1.21e-186, 4.19e-939j
3.2509112477749960125e-11 + 4.8684792143039590279e-2065j 1.67e-150, 5.78e-903j
-1.4953882006361283235e-05 - 4.7279087937384732396e-2060j 1.02e-136, 3.51e-889j
3.6101370992173007585e-05 - 9.0759887374292424927e-2061j 4.45e-133, 1.54e-885j
1.098675538395427888e-52 - 2.1063715119088932156e-2087j 2.97e-182, 1.03e-934j
1.6050315238320836673e-30 + 2.8645114790543765088e-2076j 8.15e-173, 2.81e-925j
3.4804693050277932036e-12 - 1.1550376781811309194e-2065j 2.1e-153, 7.26e-906j
0.0004284191791980706791 - 2.0622033612716553474e-2060j 1.65e-130, 5.71e-883j
0.00013115393963038828926 + 1.2629795072344532405e-2060j 7.87e-133, 2.72e-885j
1.3899165786881929015e-20 + 9.8737801300539846314e-2071j 1.22e-165, 4.22e-918j
2.7694765056152301927e-14 - 5.5837653908918283372e-2067j 4.57e-158, 1.58e-910j
7.0154195794911384788e-27 + 2.7880652764923249824e-2074j 2.76e-171, 9.54e-924j
1.4060709968132226893e-23 + 1.9340325010959327403e-2072j 1.14e-168, 3.92e-921j
0.029967623979228583556 + 3.3646252719387374751e-2059j 3.51e-123, 1.21e-875j
2.7111424177908893174e-10 - 1.9726229980450571033e-2064j 6.67e-153, 2.3e-905j
1.1624424690191803573e-59 + 3.9202754151443563291e-2091j 6.19e-187, 2.14e-939j
8.4445589632379028587e-08 + 1.2648845478433895407e-2062j 5.55e-149, 1.92e-901j
0.0077161536012004066333 + 1.1279352240384123918e-2059j 2.75e-132, 9.5e-885j
0.11117511346447624583 - 1.0133208575328106531e-2058j 2.1e-117, 7.25e-870j
4.8642239375887930875e-07 - 6.1549889019884727956e-2062j 3.45e-147, 1.19e-899j
1.0343159707869072277e-36 - 1.4459666355597453784e-2079j 3.47e-179, 1.2e-931j
5.6514474528191766519e-44 + 2.6627954117715415503e-2083j 6.37e-183, 2.2e-935j
1.2980341851498421018e-16 - 2.1367230717990026753e-2068j 1.25e-164, 4.33e-917j
0.16671073251042188444 - 1.5879244377139452451e-2058j 3.69e-125, 1.27e-877j
0.05021420880660147188 - 5.3252998361143636154e-2059j 4.67e-131, 1.61e-883j
2.0301233562461078662e-09 + 7.7930598394923393379e-2064j 1e-154, 3.45e-907j
3.4449883762523001162e-25 - 2.4172469222495991399e-2073j 1.36e-171, 4.69e-924j
1.5297317994155472201e-34 + 2.0156139782112945623e-2078j 2.42e-178, 8.36e-931j
3.4145851204325662142e-19 - 6.3394810474021659456e-2070j 1.06e-167, 3.67e-920j
0.077504813752342185409 + 7.6764192008336899626e-2059j 2.29e-136, 7.9e-889j
7.1766706996266829145e-18 + 3.8033046327399861544e-2069j 1.14e-166, 3.95e-919j
5.3312923212792003221e-39 + 9.2691914559531959662e-2081j 1.26e-181, 4.35e-934j
0.0012549717478928243093 + 3.5711127118752483987e-2060j 5.92e-150, 2.05e-902j
0.14517573611277010286 + 1.2701764280245654369e-2058j 8.3e-139, 2.86e-891j
7.9864191539565989409e-06 + 2.0125783862196368315e-2060j 2.51e-154, 8.67e-907j
1.1760325748033179677e-28 - 2.9550496776768665693e-2075j 2.8e-175, 9.67e-928j
1.086241128402538267e-46 - 1.1939560048600224158e-2084j 2.66e-186, 9.17e-939j
2.032013312127267391e-15 + 1.1263969384559307905e-2067j 3.63e-167, 1.25e-919j
0.016109990903083578772 - 1.984200929417506391e-2059j 8.12e-152, 2.8e-904j
1.7607604202037993059e-32 - 2.5263302359655730186e-2077j 3.12e-178, 1.08e-930j
1.6943421293380397993e-05 + 3.1779150240545784134e-2060j 6.64e-158, 2.29e-910j
2.0435031439579694295e-41 - 5.279479618459185647e-2082j 1.39e-183, 4.78e-936j
4.8104755947555567862e-22 - 1.4334112517907461494e-2071j 1.71e-172, 5.89e-925j
0.073406483683288786573 + 1.9494342308244933931e-2058j 4.41e-155, 1.52e-907j
0.10720961052644875871 - 2.5909815069609769043e-2058j 5.18e-155, 1.79e-907j
1.3724551758374756308e-08 - 3.0726155850865839252e-2063j 1.47e-163, 5.09e-916j
0.050409536656655059125 - 5.467861014938645135e-2059j 4.54e-156, 1.57e-908j
1.3838481547490621267e-49 + 4.8957424941295084019e-2086j 3.38e-188, 1.17e-940j
3.306526824428930459e-13 + 2.6100623086157178317e-2066j 3.18e-167, 1.1e-919j
0.0032922971491135891514 - 6.3317573947757271719e-2060j 3.76e-160, 1.3e-912j
0.15924648972809206883 + 2.0740167030142233459e-2058j 5.94e-158, 2.07e-910j

Download

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