Rule: Q[1, 4, 93]

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)
338.18333791471914386 + 5.0261975619468609551e-4298j 4.34e-2010, 4.34e-2010j
309.12564091708566434 + 3.4725085881476098237e-4309j 7.98e-2007, 7.98e-2007j
275.51626483065097805 + 4.0776759877463076983e-4366j 1.93e-2003, 1.93e-2003j
285.85832922212201131 - 2.4255989118566030034e-4436j 1.95e-2004, 1.95e-2004j
239.6990163238993228 - 4.7792129266660785916e-4482j 3.28e-2000, 3.28e-2000j
22.684010254089909171 - 8.0020160411241587629e-4518j 1.8e-2009, 1.8e-2009j
78.468513595749207531 + 6.6910104777442230215e-4505j 6.86e-1997, 6.86e-1997j
131.88607059405529927 - 3.9925218279257384282e-4501j 7.67e-1995, 7.67e-1995j
95.41366606219895753 - 1.1054656887653687875e-4511j 1.17e-1995, 1.17e-1995j
247.9769239200312019 + 5.6555423919298514303e-4527j 6.58e-2001, 6.58e-2001j
27.619571744313315001 + 2.643286770768302886e-4570j 2.41e-2007, 2.41e-2007j
166.86443942181439597 - 4.9571939013228635014e-4558j 1.33e-1995, 1.33e-1995j
196.57815694401866092 + 1.4112386235399616832e-4583j 4.46e-1997, 4.46e-1997j
141.2087224088730503 - 8.9883511955101378797e-4599j 6.6e-1995, 6.6e-1995j
10.295086229767784798 - 9.9383866480660670938e-4637j 3.03e-2017, 3.03e-2017j
11.242378555161742866 + 7.4308588038850133178e-4635j 2.23e-2016, 2.23e-2016j
14.454581754642954132 + 5.4280701257378307315e-4634j 4.51e-2014, 4.51e-2014j
81.687992510140936167 + 1.0684805641410023169e-4615j 1.38e-1996, 1.38e-1996j
72.271372650731546984 - 2.8066751044853655153e-4616j 1.74e-1997, 1.74e-1997j
256.66423283622459814 + 9.9192101668058194241e-4613j 1.18e-2001, 1.18e-2001j
50.494138993103411297 + 3.0209349366743017278e-4627j 7.78e-2001, 7.78e-2001j
106.65625987910069945 - 1.7351601863856610535e-4620j 3.55e-1995, 3.55e-1995j
35.050492453020434175 - 3.5925829582967032004e-4638j 1.04e-2004, 1.04e-2004j
25.91426133734035899 + 5.9808151886578821562e-4642j 4.9e-2008, 4.9e-2008j
357.58302870893106228 - 3.4624985272372386346e-4646j 2.53e-2012, 2.53e-2012j
161.44096802171608685 - 4.8567920717602114398e-4628j 2.12e-1995, 2.12e-1995j
203.11678368755544328 + 2.3599610442336134863e-4649j 1.75e-1997, 1.75e-1997j
21.158817808840388499 - 1.3135183403405495043e-4688j 3.27e-2010, 3.27e-2010j
13.312017528518808854 + 1.1191355047712519552e-4693j 7.85e-2015, 7.85e-2015j
6.0165843328122930598 + 8.5925612105575178214e-4701j 3.18e-2022, 3.18e-2022j
322.62693149233917542 + 1.0214451283917856586e-4672j 2.64e-2008, 2.64e-2008j
156.170334751744304 + 3.1860190254383149789e-4675j 2.9e-1995, 2.9e-1995j
296.98910087451048336 - 2.3656916749365341169e-4693j 1.5e-2005, 1.5e-2005j
146.06027524404848974 + 2.4666639795802729776e-4705j 5.14e-1995, 5.14e-1995j
102.8137835643847428 + 2.2577789283375699759e-4750j 2.6e-1995, 2.6e-1995j
48.090385766810239284 + 5.2843894768024331278e-4783j 2.46e-2001, 2.46e-2001j
31.212157831973655671 + 8.2194106014366749791e-4799j 5.85e-2006, 5.85e-2006j
9.3804270640232782496 - 3.0676912026913828568e-4811j 3.7e-2018, 3.7e-2018j
37.063227765827549017 - 4.9157487311814501659e-4797j 4.32e-2004, 4.32e-2004j
52.966102201820073449 + 4.1341852197664740838e-4788j 2.59e-2000, 2.59e-2000j
114.63940869263431411 - 1.911708453344710324e-4871j 5.76e-1995, 5.76e-1995j
2.4003188633378834536 - 7.1653036749541443898e-4994j 2.06e-2028, 2.06e-2028j
2.8500082985710811872 + 1.2735054637086538054e-4990j 1.96e-2027, 1.96e-2027j
29.385398723745703643 - 6.1289744765699703836e-4960j 1.26e-2006, 1.26e-2006j
190.255042498145792 + 1.5691197218438996636e-5023j 9.42e-1997, 9.42e-1997j
184.13360122700238542 - 1.5214669053443307819e-5148j 2.05e-1996, 2.05e-1996j
224.19742078473909146 + 8.6253184686266955579e-5222j 5.69e-1999, 5.69e-1999j
19.693750157715230898 - 3.283658007929520787e-5277j 5.71e-2011, 5.71e-2011j
265.81885766931590273 + 1.2825800649767369463e-5259j 1.72e-2002, 1.72e-2002j
15.667395787295750422 - 2.4878408581681983169e-5304j 2.73e-2013, 2.73e-2013j
88.377435317730786974 - 7.4289649718098502886e-5285j 4.43e-1996, 4.43e-1996j
127.40565362336803602 + 1.2351213884093228914e-5343j 8.05e-1995, 8.05e-1995j
209.88678899320474077 - 2.8270686016525422877e-5444j 5.83e-1998, 5.83e-1998j
151.04555194067260258 - 2.0803404234440957125e-5574j 4.23e-1995, 4.23e-1995j
4.588721043238190302 - 4.2761084903659184388e-5691j 2.38e-2024, 2.38e-2024j
12.242591477169202248 - 6.5064616977913925407e-5677j 1.45e-2015, 1.45e-2015j
99.067085239348759666 - 3.7604192374346512872e-5714j 1.83e-1995, 1.83e-1995j
178.20166842705834456 - 2.9709527838413627772e-5829j 4.04e-1996, 4.04e-1996j
33.100338393052324295 - 7.8337624644957562505e-5888j 2.48e-2005, 2.48e-2005j
8.4900048989527441736 + 1.4653126041989331094e-5944j 3.95e-2019, 3.95e-2019j
2.015896283327478525 - 7.2787286811828475662e-5959j 1.89e-2029, 1.89e-2029j
66.386190518064166969 - 2.7060198787220998406e-5923j 3.38e-1998, 3.38e-1998j
231.78480977632324167 - 5.0905982762059419595e-5984j 1.54e-1999, 1.54e-1999j
24.269142976945725454 + 2.2994913582503822749e-6027j 9.67e-2009, 9.67e-2009j
58.118728676312341865 + 2.7016122107460168238e-6016j 1.92e-1999, 1.92e-1999j
60.801567653141954047 + 5.4627636815905092163e-6013j 5.24e-1999, 5.24e-1999j
1.3173941715598329308 - 3.8790547329590617089e-6056j 9.27e-2032, 9.27e-2032j
75.330185591123976638 + 3.6087895614041554011e-6018j 3.55e-1997, 3.55e-1997j
172.44847731888277999 - 1.7679571303636620854e-6049j 7.6e-1996, 7.6e-1996j
5.2780281043693819986 + 5.6255148508645912593e-6123j 2.72e-2023, 2.72e-2023j
7.6278006710153606171 + 3.7746452764976525443e-6120j 3.96e-2020, 3.96e-2020j
18.28933266041173853 + 7.4365993220902047089e-6112j 9.41e-2012, 9.41e-2012j
84.990354468473068224 + 6.3887435077479194564e-6094j 2.52e-1996, 2.52e-1996j
0.15769548012154955374 + 1.8649806584021824605e-6185j 1.15e-2038, 1.15e-2038j
136.48560499498435344 - 7.7278135574725372804e-6141j 7.61e-1995, 7.61e-1995j
63.556974035227723908 + 7.010735786289339254e-6170j 1.34e-1998, 1.34e-1998j
216.90652295414458901 + 9.3696939001596635964e-6191j 1.87e-1998, 1.87e-1998j
39.13920346500510482 - 8.3149823789128720639e-6228j 1.73e-2003, 1.73e-2003j
123.04023317674940612 + 5.9199141503121096871e-6218j 7.61e-1995, 7.61e-1995j
69.290528524699178739 - 1.1900447921741787643e-6243j 7.96e-1998, 7.96e-1998j
0.48656392026195255279 - 9.026353293971023675e-6290j 7.63e-2036, 7.63e-2036j
0.72112104418484001102 - 1.0248893127447443018e-6288j 1.97e-2034, 1.97e-2034j
6.8012731663745347326 + 1.6678232978487867195e-6275j 3.68e-2021, 3.68e-2021j
118.78599672448589786 - 5.6712696273808717918e-6249j 6.86e-1995, 6.86e-1995j
0.011741073271057548781 + 3.8424554918700757276e-6321j 1.17e-2041, 1.17e-2041j
0.062853394031526865974 - 3.4485829022945430119e-6319j 3.76e-2040, 3.76e-2040j
3.3698935954574949143 + 2.2393640504772193674e-6305j 1.96e-2026, 1.96e-2026j
1.6607058982374340308 - 2.1758246776444104666e-6309j 1.77e-2030, 1.77e-2030j
110.59718313779560037 + 1.1453353716858020216e-6272j 4.48e-1995, 4.48e-1995j
41.279127577710764625 + 9.1779925004684231272e-6295j 6.21e-2003, 6.21e-2003j
45.753891495690077451 - 2.2676897817977052369e-6293j 7.48e-2002, 7.48e-2002j
43.48375584412207942 + 2.2170129667743407896e-6295j 2.26e-2002, 2.26e-2002j
0.29860743708074633776 - 1.6673078536471862544e-6328j 3.02e-2037, 3.02e-2037j
55.507279135635926612 - 1.3304095785025697543e-6291j 7.08e-2000, 7.08e-2000j
16.946607850446817732 + 2.3099945302750378575e-6304j 1.62e-2012, 1.62e-2012j
91.851182865792045283 - 5.401595184484962077e-6286j 7.47e-1996, 7.47e-1996j
3.9514757288792970428 + 1.8075819052611498233e-6327j 2.09e-2025, 2.09e-2025j
1 - 3.6016051934969052795e-6335j 4.6e-2033, 4.6e-2033j

Weights

Weight (ball center) Error (ball radius)
2.2865076990555614965e-146 - 5.8154736691065609726e-4444j 4.33e-354, 2.38e-1857j
7.1393058703143420128e-134 - 8.3954947050633733579e-4439j 1.81e-350, 9.94e-1854j
2.2120941819588370746e-119 + 8.669098149916302853e-4432j 2.31e-346, 1.27e-1849j
7.6384030242391291609e-124 - 5.6579701865766650264e-4434j 9.61e-348, 5.29e-1851j
6.4261221240675560413e-104 + 3.9557908742658430464e-4424j 5.1e-342, 2.81e-1845j
2.1889596673936537077e-10 + 1.5213187111742049527e-4375j 1.29e-250, 7.09e-1754j
2.6533623826996641525e-34 + 1.0099581679952285562e-4388j 5.88e-300, 3.24e-1803j
2.3965831323519122164e-57 + 1.2601243801523008318e-4400j 1.75e-320, 9.63e-1824j
1.3170020614495204014e-41 - 1.5775691322141476286e-4392j 4.83e-308, 2.66e-1811j
1.7103480079211268966e-107 - 6.571359955467263058e-4426j 1.37e-343, 7.54e-1847j
1.7554909571401479276e-12 - 8.0513968445349368312e-4377j 7.96e-263, 4.38e-1766j
1.8717456891651407861e-72 - 2.5936564264161532024e-4408j 3.42e-330, 1.88e-1833j
2.7245490848414950588e-85 + 8.5239881410505765495e-4415j 2.09e-336, 1.15e-1839j
2.258647112393303213e-61 + 1.1101755866410043149e-4402j 8.55e-324, 4.71e-1827j
3.1372780622731029288e-05 + 5.6911803128728840035e-4372j 2.38e-231, 1.31e-1734j
1.271496338242263097e-05 - 3.2173017695135863827e-4372j 1.57e-234, 8.66e-1738j
6.2192230345716706094e-07 + 3.3511599709957846812e-4373j 7.1e-244, 3.91e-1747j
1.0880685348437926587e-35 - 1.8974186378428718511e-4389j 3.68e-305, 2.03e-1808j
1.2384768919077543346e-31 + 2.5514009385684387247e-4387j 1.6e-301, 8.78e-1805j
3.0340395733787136188e-111 + 9.0245321825199514404e-4428j 4.92e-347, 2.71e-1850j
2.8684910794011115323e-22 + 2.5373376259502106345e-4382j 4.3e-291, 2.37e-1794j
1.8614993638408410938e-46 + 4.9022396072329173873e-4395j 9.29e-316, 5.12e-1819j
1.1877453219027329585e-15 - 1.1671506101248426049e-4378j 3.73e-279, 2.05e-1782j
9.3247658011492409911e-12 + 2.1893834124053399635e-4376j 2.15e-268, 1.19e-1771j
1.152389059544158983e-154 - 3.7539432604642461642e-4449j 3.03e-364, 1.67e-1867j
4.121862899083133588e-70 + 3.9962880018782253877e-4407j 5.35e-331, 2.95e-1834j
4.0777451438876489193e-88 - 3.2313533974450931517e-4416j 8.45e-340, 4.65e-1843j
9.6724612436630141719e-10 - 3.897381720135262216e-4375j 3.59e-266, 1.98e-1769j
1.8301597360322971743e-06 - 7.623220973794489001e-4373j 1.35e-252, 7.45e-1756j
0.0018582595902481989994 - 4.7922119693432001991e-4371j 4.03e-232, 2.22e-1735j
1.1022802750118916619e-139 + 1.7854903999754180223e-4441j 6.86e-359, 3.77e-1862j
7.7947944723339009882e-68 - 5.7185237311818532463e-4406j 2.2e-330, 1.21e-1833j
1.21148327917844515e-128 + 2.6471669909149349815e-4436j 8.94e-355, 4.92e-1858j
1.813728598308370298e-63 - 9.503453587760617194e-4404j 2.35e-328, 1.29e-1831j
8.46557482748097426e-45 - 3.516336003945372507e-4394j 3.73e-318, 2.05e-1821j
3.085699222962948546e-21 - 9.236293433789423229e-4382j 2.81e-297, 1.55e-1800j
5.1717020502482791132e-14 - 1.0174819008624897677e-4377j 1.19e-284, 6.54e-1788j
7.6131019205725342819e-05 - 9.2068499253962205468e-4372j 3.29e-254, 1.81e-1757j
1.6374833930920234187e-16 + 3.8038190902919971653e-4379j 6.16e-290, 3.39e-1793j
2.4897983138006660905e-23 - 6.7583476129876481844e-4383j 1.49e-300, 8.22e-1804j
6.6814752797580749981e-50 + 8.2525845873629962062e-4397j 3.08e-323, 1.69e-1826j
0.037485476578279734642 - 6.7609059830475472543e-4370j 1.96e-228, 1.08e-1731j
0.028118843449865333449 + 4.4933662841574688438e-4370j 2.06e-232, 1.14e-1735j
3.1077232207023283499e-13 + 2.8957080222440636992e-4377j 1.01e-283, 5.55e-1787j
1.4692095263920782795e-82 - 2.0273391143097029609e-4413j 2.46e-340, 1.35e-1843j
6.4823809874553505102e-80 + 4.3756759865398258113e-4412j 2.01e-339, 1.1e-1842j
3.1882466027185610002e-97 + 8.7347839931119611988e-4421j 6.37e-348, 3.5e-1851j
4.0172080829011843199e-09 + 9.813879461767878587e-4375j 6.16e-281, 3.39e-1784j
3.3884496065792490981e-115 - 9.9989178591398690751e-4430j 3.77e-354, 2.08e-1857j
1.9564150084873616699e-07 - 1.4250396816217901166e-4373j 4.09e-277, 2.25e-1780j
1.4238745893057056912e-38 - 5.9438969214446999764e-4391j 1.31e-319, 7.23e-1823j
2.0609706838378226924e-55 - 1.2299760544784338462e-4399j 2.37e-329, 1.3e-1832j
4.8489123875254610885e-91 + 1.0963495266988865272e-4417j 2.15e-345, 1.18e-1848j
1.2746395105513946778e-65 + 7.6251773383110057816e-4405j 1.11e-333, 6.09e-1837j
0.0067477574955292644352 - 1.1235637935873973699e-4370j 4.35e-264, 2.4e-1767j
4.9806795949046025508e-06 + 1.637212511639436679e-4372j 2.78e-278, 1.53e-1781j
3.4984272892011290398e-43 + 2.4086401648446578002e-4393j 2.46e-323, 1.35e-1826j
2.3685166399922206908e-77 - 8.6195050834949343025e-4411j 1.8e-339, 9.89e-1843j
8.0871707263704420051e-15 + 3.489613452193227085e-4378j 3.99e-299, 2.2e-1802j
0.0001803433207969042759 + 1.4121909092151322042e-4371j 6.68e-277, 3.68e-1780j
0.048344380501610786537 + 8.4433771022331208354e-4370j 3.46e-258, 1.91e-1761j
4.2286692610084192161e-29 + 5.5632236090699602656e-4386j 8.35e-317, 4.6e-1820j
1.6833407280159015275e-100 - 2.0079060399470661952e-4422j 2.85e-350, 1.57e-1853j
4.65849132971965755e-11 - 5.828999675830664893e-4376j 2.67e-294, 1.47e-1797j
1.5209085217405283807e-25 - 4.3583138322311180337e-4384j 2.38e-314, 1.31e-1817j
1.0680984371571546507e-26 + 1.053727144111768686e-4384j 2.01e-315, 1.11e-1818j
0.089229934232317822805 + 7.3092017412334648825e-4370j 1.76e-264, 9.67e-1768j
5.96541025321967083e-33 - 5.1726617637491040847e-4388j 1.74e-319, 9.6e-1823j
7.2433448235817147379e-75 + 1.557565517929880798e-4409j 3.8e-340, 2.09e-1843j
0.0036451895759749642093 + 7.2919148782444013267e-4371j 6.11e-282, 3.36e-1785j
0.00041156093609655914588 - 2.1214800077007770519e-4371j 1.83e-285, 1.01e-1788j
1.5666325184694281934e-08 - 2.4319572951638172162e-4374j 2.12e-295, 1.17e-1798j
4.1065497042166791393e-37 + 3.4268295789993804243e-4390j 1.91e-322, 1.05e-1825j
0.10043946372879866402 - 2.4290683368643633541e-4370j 1.16e-274, 6.4e-1778j
2.4745267267841298007e-59 - 1.2186920207124427415e-4401j 4.62e-334, 2.54e-1837j
6.9740918223493452663e-28 - 2.4632260686581521317e-4385j 8.22e-318, 4.53e-1821j
4.4987110997373479038e-94 - 3.3011001592230273133e-4419j 2.89e-350, 1.59e-1853j
2.1178493235384195549e-17 - 1.2070345521861828464e-4379j 2.08e-311, 1.14e-1814j
1.5801708718565238442e-53 + 1.1355870116901262351e-4398j 1.72e-332, 9.48e-1836j
2.3779391147927181851e-30 - 1.2130117126733177108e-4386j 2.34e-320, 1.29e-1823j
0.12998900004553788085 - 4.273743077651777439e-4370j 1.9e-288, 1.04e-1791j
0.12510324196027243788 + 5.159427041939514777e-4370j 9.16e-289, 5.04e-1792j
0.00089707616137064788121 + 3.179425249650126518e-4371j 1.39e-296, 7.62e-1800j
1.0842522189817043419e-51 - 9.935708835754067309e-4398j 5.83e-332, 3.21e-1835j
0.029905969254467518027 - 4.3348227630206264906e-4371j 1.21e-290, 6.63e-1794j
0.06807403518194387726 + 1.3966121640587628059e-4370j 2.19e-290, 1.2e-1793j
0.018986433023684576754 - 2.8048381597840686028e-4370j 5.43e-296, 2.99e-1799j
0.066573962127397012464 - 8.4184360112547685544e-4370j 2.78e-293, 1.53e-1796j
3.7097471579468334242e-48 - 6.5178035080639024656e-4396j 2.38e-330, 1.31e-1833j
2.5679806344086200039e-18 + 3.7265304604014572287e-4380j 1.07e-315, 5.86e-1819j
3.102152990026879562e-20 + 3.2620781609113270796e-4381j 1.63e-317, 8.99e-1821j
2.9171459536185718326e-19 - 1.1185719883077738864e-4380j 6.55e-317, 3.61e-1820j
0.12195192952838782878 + 3.3868463045391970245e-4370j 1.43e-301, 7.89e-1805j
2.0158726049885157807e-24 + 1.7441644735448467471e-4383j 3.97e-320, 2.18e-1823j
5.7266555063113996067e-08 + 5.934876181798250383e-4374j 4.4e-310, 2.42e-1813j
4.5269357048594255009e-40 + 9.8914078722802235902e-4392j 1.19e-328, 6.56e-1832j
0.011730957396097021774 + 1.7593512673230001398e-4370j 2.99e-306, 1.65e-1809j
0.11019826055070930007 - 6.1448939228381669396e-4370j 2.63e-305, 1.44e-1808j

Download

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