Rule: Q[3, 70]

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)
0.089583044873726149742 - 3.0176941834648443812e-5023j 4.4e-2040, 4.4e-2040j
0.41577455678347908331 + 1.0420831772071330851e-5020j 3.17e-2037, 3.17e-2037j
1.3714043508950208337 - 4.6329169433873439244e-5018j 3.09e-2033, 3.09e-2033j
1.8086721404379686976 + 9.6855374145323004908e-5016j 4.82e-2032, 4.82e-2032j
0.6721779151240883589 + 4.0229016887708864039e-5019j 7.38e-2036, 7.38e-2036j
0.9912161004750419671 + 1.0119896084763872691e-5017j 1.51e-2034, 1.51e-2034j
0.22195115873012389122 + 4.2663823022663769265e-5022j 1.16e-2038, 1.16e-2038j
0.01690973010548553727 + 1.3130546376425670453e-5024j 9.2e-2042, 9.2e-2042j
264.07286852617639528 - 1.2229296047570815263e-5001j 5.35e-2019, 5.35e-2019j
199.97704250555738878 - 6.9170843674234772092e-4989j 3.18e-2012, 3.18e-2012j
174.34881837867215736 + 5.6638130113690182636e-4989j 5.43e-2010, 5.43e-2010j
220.61094898947277411 + 2.6213562038909122157e-5001j 3.15e-2014, 3.15e-2014j
166.78655745588303275 - 5.4536003523523281712e-5014j 2.27e-2009, 2.27e-2009j
232.65845174488701608 - 1.7140139354986062033e-5033j 1.64e-2015, 1.64e-2015j
32.767424079722447643 - 9.2131305441339732981e-5046j 3.15e-2012, 3.15e-2012j
17.491098687822807107 - 4.7148545107041992082e-5070j 1.77e-2017, 1.77e-2017j
146.25932994672453248 - 4.3961200625613798488e-5057j 5.08e-2008, 5.08e-2008j
77.372151735090318342 - 5.0434461599736414002e-5094j 7.76e-2007, 7.76e-2007j
13.07607572001573352 + 4.4740818415440733971e-5132j 8.18e-2020, 8.18e-2020j
37.432253431706567622 - 4.8299072906106978146e-5118j 3.59e-2011, 3.59e-2011j
56.71373745692851166 - 4.2809769974614521148e-5128j 2.86e-2008, 2.86e-2008j
28.451588645730617661 + 3.0364103356289485438e-5153j 2.06e-2013, 2.06e-2013j
117.47886634922379193 + 8.7616302881434569601e-5156j 9.38e-2007, 9.38e-2007j
209.82680076386028392 + 2.32859497347686172e-5177j 3.74e-2013, 3.74e-2013j
30.566631117852464615 + 5.0090498248327607944e-5194j 8.42e-2013, 8.42e-2013j
19.117523059509704311 - 3.0707174359770477008e-5203j 9.76e-2017, 9.76e-2017j
81.239325429505269243 + 1.189168156894487725e-5191j 1.01e-2006, 1.01e-2006j
10.512871139861224297 + 6.8678514603382875831e-5269j 1.77e-2021, 1.77e-2021j
8.2500796040347676302 - 6.5162919849778307451e-5271j 3.16e-2023, 3.16e-2023j
4.6498834410350740213 - 5.7961174894564884997e-5271j 7.42e-2027, 7.42e-2027j
2.2942803602790417198 - 4.8247459091679498865e-5272j 7.36e-2031, 7.36e-2031j
152.77984163386939547 + 1.1641581646030340197e-5253j 2.03e-2008, 2.03e-2008j
140.021446211845811 + 2.5676446317147836121e-5318j 1.06e-2007, 1.06e-2007j
39.89954795295435167 + 3.8459383642805442396e-5353j 1.18e-2010, 1.18e-2010j
3.9629140730528821189 - 2.1221207811292133069e-5412j 9.6e-2028, 9.6e-2028j
5.4276515451024166239 + 5.7433372317557836955e-5410j 5.99e-2026, 5.99e-2026j
128.30377885585736942 + 1.2528626736108695374e-5406j 3.83e-2007, 3.83e-2007j
66.521179943908780105 + 5.5568257729571856912e-5495j 1.73e-2007, 1.73e-2007j
63.14079284650069289 + 2.0842737069050936024e-5580j 9.98e-2008, 9.98e-2008j
246.60111828088937609 - 5.0791597496859119266e-5654j 4.88e-2017, 4.88e-2017j
2.8139871612955936189 - 9.4139468522620493875e-5712j 9.79e-2030, 9.79e-2030j
102.68143454832377536 + 1.1862963820296445125e-5810j 1.77e-2006, 1.77e-2006j
159.6109254593792557 + 2.0543104337521641732e-5952j 6.96e-2009, 6.96e-2009j
93.65938631529409124 - 1.1970016807553751449e-6022j 1.71e-2006, 1.71e-2006j
47.862969769542212554 + 1.8339039961049399633e-6076j 2.59e-2009, 2.59e-2009j
15.942565377246059126 - 1.3131657900552431152e-6134j 3.34e-2018, 3.34e-2018j
14.471126355690968888 + 1.9442401331787398342e-6136j 5.38e-2019, 5.38e-2019j
190.8625393621293134 + 1.1480325806685313687e-6143j 2.26e-2011, 2.26e-2011j
26.42091992304545561 + 2.277362040985875813e-6205j 4.78e-2014, 4.78e-2014j
85.239309052308271197 - 1.0587935872780320444e-6292j 1.29e-2006, 1.29e-2006j
11.756813201841518648 + 2.3956729774692298732e-6372j 1.25e-2020, 1.25e-2020j
6.2899450829374791969 + 4.7833543140589631649e-6380j 4.81e-2025, 4.81e-2025j
112.36565150821580097 - 2.7999754121114557872e-6391j 1.3e-2006, 1.3e-2006j
98.091701556896428112 + 9.6539193881433400882e-6450j 1.77e-2006, 1.77e-2006j
70.017321743552501834 - 2.1122532023254593789e-6503j 3.32e-2007, 3.32e-2007j
3.3615611385330008976 + 1.5386936771098051783e-6589j 1.06e-2028, 1.06e-2028j
50.711515192992285173 + 6.4393223429889369547e-6582j 5.52e-2009, 5.52e-2009j
134.04284815168017893 + 2.2000803559361912212e-6675j 2.13e-2007, 2.13e-2007j
107.43647777712434721 - 2.4996993481819330991e-6744j 1.57e-2006, 1.57e-2006j
45.112910391040894956 - 2.0701630665409787987e-6779j 8.8e-2010, 8.8e-2010j
89.377392001188952678 - 6.1026653069125249489e-6807j 1.69e-2006, 1.69e-2006j
9.3439638016490399416 - 3.1539910293265492171e-6857j 2.27e-2022, 2.27e-2022j
22.607644120244945982 - 5.6798012896769710262e-6850j 2.47e-2015, 2.47e-2015j
24.473338579815618151 + 2.6867099221853367927e-6850j 1.1e-2014, 1.1e-2014j
73.632958266369159845 - 3.1630167298655388885e-6840j 5.08e-2007, 5.08e-2007j
42.459124492087832542 - 4.7188255443268654612e-6858j 3.35e-2010, 3.35e-2010j
35.055440021074124868 + 2.4752724066799913361e-6866j 1.17e-2011, 1.17e-2011j
20.822718376304048889 + 1.2010558353187144133e-6884j 4.94e-2016, 4.94e-2016j
53.660920849171211572 + 1.6900000240902748455e-6887j 1.29e-2008, 1.29e-2008j
182.35100868963295253 - 1.2692224388138508491e-6945j 1.19e-2010, 1.19e-2010j
122.78732543207274161 - 8.2032530998261672799e-6983j 6.48e-2007, 6.48e-2007j
7.2316589720199838316 - 3.0355759483331812265e-7017j 3.81e-2024, 3.81e-2024j
59.872709176410885061 - 1.919287872667028079e-6999j 5.13e-2008, 5.13e-2008j

Weights

Weight (ball center) Error (ball radius)
0.093446555040946328322 - 1.1511924791104025876e-5017j 3.21e-225, 1.06e-1734j
0.1484637889636769456 - 3.5149022773923957956e-5017j 1.11e-225, 3.67e-1735j
0.10396360141269802647 + 1.561107347318126557e-5016j 3.18e-229, 1.05e-1738j
0.075940499591038266915 + 7.5024571335495872859e-5019j 4.96e-238, 1.64e-1747j
0.14695901605227535602 + 5.418928975090147355e-5017j 2.43e-226, 8.06e-1736j
0.12990336679246791568 - 8.0173490194481284356e-5017j 1.31e-227, 4.35e-1737j
0.13042516793106803804 + 2.2094435934500296443e-5017j 1.22e-225, 4.03e-1735j
0.042726731200192349091 + 3.3607454588370580724e-5018j 6.35e-226, 2.1e-1735j
4.2479887929441490316e-114 - 1.7628987114846938804e-5077j 1.54e-394, 5.1e-1904j
1.338974218250417612e-86 + 1.7358389983995259104e-5063j 3.69e-386, 1.22e-1895j
1.4853005786781628642e-75 - 7.6325758901934278273e-5058j 2.11e-382, 6.99e-1892j
1.7566246094967592591e-95 + 5.1547135982766703558e-5068j 1.38e-389, 4.56e-1899j
2.7068401270813782378e-72 + 3.5649118336397815669e-5056j 1.31e-381, 4.33e-1891j
1.1655849614758029542e-100 - 1.1925316673262754639e-5070j 1.64e-391, 5.44e-1901j
1.3192908944207951605e-14 + 7.2748201803508830188e-5026j 1.42e-338, 4.72e-1848j
4.0214440374884290537e-08 + 5.1295642239665157849e-5022j 3.52e-321, 1.17e-1830j
1.9268937669545311593e-63 - 1.2418350146712209463e-5051j 4.29e-379, 1.42e-1888j
9.5008150508752276274e-34 - 3.2085898749797325666e-5036j 3.38e-363, 1.12e-1872j
2.8427166320340061079e-06 - 8.5990033166587533842e-5021j 2.49e-315, 8.26e-1825j
1.3412529367181204315e-16 + 5.5137771386723324749e-5027j 2.31e-343, 7.65e-1853j
7.2720538635565728784e-25 - 1.6905708999741292742e-5031j 3.47e-355, 1.15e-1864j
9.1233562513112993133e-13 + 8.216387245018758357e-5025j 1.65e-336, 5.45e-1846j
4.9695662583494074174e-51 + 3.1160331731361409411e-5045j 5.61e-375, 1.86e-1884j
7.6771788360031981731e-91 - 1.1925547904451192413e-5065j 2.08e-389, 6.88e-1899j
1.1456920690848582453e-13 - 2.4913738486837162128e-5025j 5.73e-339, 1.9e-1848j
8.297565158436729147e-09 - 1.8996579934960170449e-5022j 8.12e-329, 2.69e-1838j
2.0554371051594034646e-35 + 4.2680324197499375019e-5037j 2.56e-365, 8.48e-1875j
3.2795020488326906236e-05 - 5.044438051086560979e-5020j 1.01e-316, 3.34e-1826j
0.00027593941976302158147 - 2.7978378559451969354e-5019j 5.45e-312, 1.81e-1821j
0.0070113379353696320932 - 8.4802690784356872615e-5018j 2e-300, 6.61e-1810j
0.050947299527197914372 - 1.5647740582152400627e-5016j 2.06e-285, 6.84e-1795j
2.9698112909155155429e-66 + 4.46179652682404726e-5053j 2.67e-381, 8.84e-1891j
9.4432461867338494216e-61 + 3.0038997489268014689e-5050j 1.58e-379, 5.24e-1889j
1.1804853802103509234e-17 - 1.4278386633184416521e-5027j 1.68e-349, 5.56e-1859j
0.012185993494723485217 + 1.9140268925120500828e-5017j 2.87e-302, 9.52e-1812j
0.0036074814543956222597 + 3.6043236243780897561e-5018j 2.23e-308, 7.37e-1818j
1.0678515826402677347e-55 + 1.2068266117517785679e-5047j 4.31e-378, 1.43e-1887j
4.4308018235835003533e-29 + 9.4706014397547962689e-5034j 3.57e-363, 1.18e-1872j
1.2586982915495684583e-27 - 5.6247539398074429583e-5033j 5.71e-362, 1.89e-1871j
1.219639339015280778e-106 + 1.0845782897401701963e-5073j 3.06e-399, 1.01e-1908j
0.031927358087083050376 + 7.2483713515676824786e-5017j 9.19e-305, 3.04e-1814j
1.1896781110054911593e-44 - 6.3482140584924953873e-5042j 8.6e-375, 2.85e-1884j
3.363365501668072508e-69 - 1.3739127269940213665e-5054j 4.36e-384, 1.45e-1893j
9.1904432540856546471e-41 - 6.7367180680795265843e-5040j 6.4e-373, 2.12e-1882j
4.5747453671554724602e-21 + 1.9131508220087024146e-5029j 2.95e-359, 9.76e-1869j
1.7995697313146007358e-07 - 1.3466762039671156555e-5021j 2.64e-339, 8.74e-1849j
7.4397249652652294727e-07 + 3.4439907672538430672e-5021j 7.57e-338, 2.51e-1847j
1.1315648935618223695e-82 - 1.7537787839494269835e-5061j 5.84e-391, 1.93e-1900j
6.6704807207711246628e-12 - 2.6125066733644614733e-5024j 5.1e-349, 1.69e-1858j
3.8943158514714623484e-37 - 5.3214516970975941917e-5038j 3.88e-371, 1.29e-1880j
1.0041813915997077862e-05 + 2.1016975000155178881e-5020j 1.14e-337, 3.78e-1847j
0.0016742460818399406891 - 1.5296831448919937347e-5018j 1.51e-330, 5.01e-1840j
7.9592667831513356897e-49 - 4.3185570936155883844e-5044j 1.11e-377, 3.66e-1887j
1.131020693223859263e-42 + 6.7974163878489688022e-5041j 1.22e-374, 4.06e-1884j
1.389096681247083891e-30 - 1.5080759051609881631e-5034j 1.13e-368, 3.74e-1878j
0.019686853039528057866 - 3.8869370439288908932e-5017j 6.49e-330, 2.15e-1839j
2.7444285292330945563e-22 - 4.1500872438946966344e-5030j 4.7e-364, 1.56e-1873j
3.5769829173089516386e-58 - 6.3891960963023315413e-5049j 1.76e-382, 5.81e-1892j
1.0612692423306388619e-46 + 5.4655020253817757418e-5043j 4.78e-377, 1.58e-1886j
6.9076073471657897278e-20 - 8.4211513688640064471e-5029j 1.37e-363, 4.55e-1873j
6.4279595331290102109e-39 + 6.2020583135044965317e-5039j 2.76e-373, 9.13e-1883j
9.899044810248337641e-05 + 1.1936302305082079361e-5019j 1.26e-346, 4.17e-1856j
2.7728017695884237192e-10 - 2.3785750071225982014e-5023j 4.07e-356, 1.35e-1865j
4.4832022513600412735e-11 + 8.0184292411619018728e-5024j 8.73e-357, 2.89e-1866j
3.8643088381383446904e-32 + 2.2666174460742697888e-5035j 5.51e-371, 1.83e-1880j
9.4682363277152648102e-19 + 3.54403211229250025e-5028j 1.11e-363, 3.67e-1873j
1.3911408151322970349e-15 - 2.0432763000244526389e-5026j 1.73e-361, 5.71e-1871j
1.579710027172676361e-09 + 6.8282448159927417348e-5023j 4.61e-357, 1.53e-1866j
1.4879094048341584046e-23 + 8.5841149238081909886e-5031j 2.49e-367, 8.26e-1877j
5.2732823117518811736e-79 + 1.3131238330233282216e-5059j 2.02e-396, 6.7e-1906j
2.5547854365934495667e-53 - 2.0415806910536243123e-5046j 1.9e-383, 6.3e-1893j
0.00070911962558767353802 + 6.5338492344347811058e-5019j 3.65e-356, 1.18e-1865j
3.1954033936381937165e-26 + 3.1652266567524824041e-5032j 2.5e-369, 8.29e-1879j

Download

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