Rule: Q[2, 47, 48]

Type

This rule is of Legendre 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)
-0.99877127460442347627 - 2.9018012617084394384e-1715j 2.87e-475, 2.87e-475j
-0.96222350509601121361 + 1.1254842622538082043e-1716j 1.15e-475, 1.15e-475j
-0.93140215666618488959 + 7.9411866909613782039e-1718j 2e-476, 2e-476j
0.98928706494661816558 + 3.1765751554525110031e-1712j 4.27e-475, 4.27e-475j
0.95299817578723574359 - 3.7399957258885248847e-1724j 7.05e-476, 7.05e-476j
0.91903568270568604389 + 2.5851479775478078221e-1727j 8.63e-477, 8.63e-477j
-0.95299817578723574359 - 7.4977871454122353214e-1728j 6.97e-476, 6.97e-476j
-0.91903568270568604389 - 3.8806690106189183635e-1728j 8.55e-477, 8.55e-477j
-0.97059808285834143067 + 4.6799261233561217085e-1727j 1.8e-475, 1.8e-475j
0.99672797106645946478 - 1.6020541665996434306e-1723j 3.72e-475, 3.72e-475j
0.87660074215907825536 + 2.121323115465679157e-1737j 4.82e-478, 4.82e-478j
0.94278267026445047826 - 8.5342743583839321704e-1734j 3.73e-476, 3.73e-476j
-0.94278267026445047826 - 9.4375875168125405661e-1736j 3.8e-476, 3.8e-476j
-0.87660074215907825536 - 2.7039555575840258604e-1738j 4.54e-478, 4.54e-478j
-0.99977986203932756662 - 2.227488223396036595e-1735j 1.05e-475, 1.05e-475j
0.86044665664187674155 - 4.9217349307753488657e-1738j 1.49e-478, 1.49e-478j
0.84362541678283465762 + 1.6257465979322585521e-1738j 4.86e-479, 4.86e-479j
0.96222350509601121361 + 1.4121627621677099059e-1733j 1.18e-475, 1.18e-475j
-0.78743732698896138153 - 8.3670667062455145235e-1756j 7.71e-481, 7.71e-481j
-0.90590066140665415315 + 2.7631019544085296542e-1752j 3.46e-477, 3.46e-477j
0.89182545456511655046 + 1.0977953346527774709e-1749j 1.26e-477, 1.26e-477j
0.76721733015127739453 + 1.2557998935693425943e-1755j 1.7e-481, 1.7e-481j
-0.60326886161042005162 + 4.0423499084182095608e-1762j 4.26e-487, 4.26e-487j
-0.86044665664187674155 + 2.166872612770327363e-1753j 1.52e-478, 1.52e-478j
-0.80711315914550387862 + 1.6467924482903980262e-1755j 3.24e-480, 3.24e-480j
-0.99353158340902401503 + 7.4989099463122545089e-1750j 4.4e-475, 4.4e-475j
0.74620658240895877638 + 2.370652844098727781e-1756j 3.39e-482, 3.39e-482j
0.80711315914550387862 - 2.0864667338297832837e-1754j 3.49e-480, 3.49e-480j
0.99877127460442347627 + 2.303310886427896721e-1747j 2.97e-475, 2.97e-475j
-0.62897187230986167454 - 9.6827207291250451716e-1797j 3.45e-486, 3.45e-486j
0.99977986203932756662 + 3.9013383707350889154e-1783j 1.06e-475, 1.06e-475j
0.82593072323147927664 - 1.8918847758529428687e-1813j 1.35e-479, 1.35e-479j
0.67795903906343622049 - 6.6977557242764546682e-1818j 1.87e-484, 1.87e-484j
-0.98928706494661816558 - 5.513793762818600332e-1806j 4.34e-475, 4.34e-475j
-0.74620658240895877638 + 4.3250237064073870508e-1818j 3.63e-482, 3.63e-482j
-0.76721733015127739453 - 5.1648818081435195846e-1818j 1.75e-481, 1.75e-481j
0.99353158340902401503 + 1.8458746410488300407e-1808j 4.09e-475, 4.09e-475j
0.65399510054320166777 + 1.1359129255072599977e-1837j 2.57e-485, 2.57e-485j
0.90590066140665415315 + 6.7536726292620463773e-1827j 3.47e-477, 3.47e-477j
-0.43852848414671947045 - 4.9702387493755611802e-1856j 3.43e-493, 3.43e-493j
-0.57735026918962576451 + 8.3743976731817467794e-1852j 5.31e-488, 5.31e-488j
0.93140215666618488959 - 8.0687166892068729695e-1837j 1.82e-476, 1.82e-476j
0.78743732698896138153 + 7.5354431634056540274e-1852j 8.03e-481, 8.03e-481j
0.62897187230986167454 - 4.5515935833580191776e-1857j 3.33e-486, 3.33e-486j
-0.99672797106645946478 - 6.4789289182350029636e-1843j 3.93e-475, 3.93e-475j
-0.65399510054320166777 + 9.065991076973550325e-1863j 2.62e-485, 2.62e-485j
-0.7241055530593450436 + 3.2755964745243056427e-1861j 6.41e-483, 6.41e-483j
0.12892588867549655499 + 2.5822819399616472311e-1884j 1.26e-505, 1.26e-505j
0.49519282336540386957 - 3.5536416528235051578e-1869j 4.62e-491, 4.62e-491j
0.7241055530593450436 - 1.6342324362991385845e-1861j 6.45e-483, 6.45e-483j
-0.70123024150410433422 + 3.3358607157717839095e-1862j 1.11e-483, 1.11e-483j
-0.52331183798672471998 - 5.6661509464943004903e-1868j 5.01e-490, 5.01e-490j
-0.98412806292317475249 + 6.5996856089494651455e-1851j 3.83e-475, 3.83e-475j
0.60326886161042005162 - 1.3413449258959037953e-1886j 4.39e-487, 4.39e-487j
0.52331183798672471998 + 2.6791317781556527182e-1889j 5.15e-490, 5.15e-490j
-0.82593072323147927664 + 1.7916974689169548599e-1876j 1.28e-479, 1.28e-479j
-0.55085227202713078514 + 9.5655442748369919534e-1889j 5.68e-489, 5.68e-489j
-0.31896102474071359638 - 8.0301001585433039684e-1898j 6.7e-498, 6.7e-498j
0.98412806292317475249 + 2.1375024665755171243e-1872j 3.48e-475, 3.48e-475j
0.40890790550998596622 + 6.6550917183623902486e-1934j 2.28e-494, 2.28e-494j
0.97059808285834143067 + 6.1328825920197973267e-1914j 1.85e-475, 1.85e-475j
-0.97794591249197104501 + 5.877127879461780517e-1937j 2.74e-475, 2.74e-475j
-0.4670848893284414086 + 2.0062636227252782278e-1954j 4.2e-492, 4.2e-492j
0.97794591249197104501 + 4.0291516141727680145e-1942j 2.71e-475, 2.71e-475j
0.55085227202713078514 + 8.7344614910210627234e-1962j 5.69e-489, 5.69e-489j
0.57735026918962576451 + 2.235821260696940326e-1961j 4.94e-488, 4.94e-488j
-0.89182545456511655046 - 6.4238357329132617094e-1950j 1.37e-477, 1.37e-477j
-0.3788089385993293122 - 8.8617592610952303374e-1970j 1.55e-495, 1.55e-495j
-0.84362541678283465762 - 1.2469379715416955345e-1964j 4.7e-479, 4.7e-479j
0.70123024150410433422 + 2.8145515428501494883e-1973j 1.09e-483, 1.09e-483j
0.34902942781705166406 - 1.002176844299198525e-1984j 1.04e-496, 1.04e-496j
-0.49519282336540386957 - 6.6046652870158671845e-1977j 4.99e-491, 4.99e-491j
-0.1618761893827070744 + 5.4299895855356649099e-1991j 2.82e-504, 2.82e-504j
-0.40890790550998596622 + 1.6546735329937514163e-1980j 2.25e-494, 2.25e-494j
0.4670848893284414086 - 2.9236565714734187233e-1980j 3.99e-492, 3.99e-492j
0.3788089385993293122 + 2.9825950068569203044e-1983j 1.55e-495, 1.55e-495j
0.43852848414671947045 + 1.8687128503088153606e-1982j 3.15e-493, 3.15e-493j
-0.035423315473384171354 + 9.7019477170257819142e-1997j 1.43e-509, 1.43e-509j
-0.28770907139190237059 + 9.4320720101749141918e-1986j 3.86e-499, 3.86e-499j
-0.67795903906343622049 + 1.312099659818592464e-1984j 1.8e-484, 1.8e-484j
0.25605498113213613519 - 4.4522128856968196439e-1999j 2.03e-500, 2.03e-500j
0.31896102474071359638 - 5.5207568542996763241e-1997j 6.37e-498, 6.37e-498j
0.098101286411945432969 + 6.2080572677571296604e-2006j 6.87e-507, 6.87e-507j
-0.34902942781705166406 - 1.7348437420110348368e-1995j 1.05e-496, 1.05e-496j
-0.19434817618672562782 + 8.7552440702233409485e-2002j 6.08e-503, 6.08e-503j
0.068355827092934714124 - 6.9244893504154366465e-2007j 3.86e-508, 3.86e-508j
0.28770907139190237059 + 6.9448628561939976425e-1998j 3.89e-499, 3.89e-499j
0.1618761893827070744 + 3.9200018154595689515e-2003j 2.83e-504, 2.83e-504j
-0.098101286411945432969 - 5.7850656485492411715e-2006j 7.01e-507, 7.01e-507j
-0.25605498113213613519 + 2.8648388004971544999e-1999j 2.09e-500, 2.09e-500j
-0.068355827092934714124 + 3.3034560636281783467e-2008j 3.72e-508, 3.72e-508j
0.19434817618672562782 - 5.6962273915696354821e-2002j 6e-503, 6e-503j
0.22522197187736901628 + 1.8345341136904343354e-2000j 1.13e-501, 1.13e-501j
0.035423315473384171354 + 1.5095784743363820834e-2008j 1.43e-509, 1.43e-509j
-0.22522197187736901628 - 1.7409017792106573675e-2000j 1.25e-501, 1.25e-501j
-0.12892588867549655499 + 1.5451100221563306735e-2005j 1.39e-505, 1.39e-505j
-6.6883525946916740363e-2279 - 9.7391060819100620413e-2279j 1.15e-2276, 1.15e-2276j

Weights

Weight (ball center) Error (ball radius)
0.0014875237252371793787 + 1.864217033667047952e-1715j 2.5e-112, 1.83e-340j
0.008807780192879099153 - 1.3699640201702195427e-1714j 1.24e-112, 9.1e-341j
0.011926754722065877361 + 1.8758582078332606547e-1714j 4.44e-113, 3.24e-341j
0.0047087072817662874755 - 5.0329175009718527878e-1713j 8.36e-114, 6.11e-342j
0.0096725929174529982746 + 8.7001173966542563073e-1713j 5.21e-114, 3.81e-342j
0.012759560988901359987 - 5.7693445781415506882e-1713j 3.42e-114, 2.5e-342j
0.0096725929174529982746 + 1.5567327530926050669e-1714j 3.72e-113, 2.72e-341j
0.012759560988901359987 - 2.0799758326159805144e-1714j 6.95e-114, 5.08e-342j
0.007903402581477522186 + 1.1830997303128422786e-1714j 6.07e-114, 4.44e-342j
0.0026207771144520506066 + 1.118831726505819242e-1712j 1.12e-116, 8.16e-345j
0.015754174452365329967 + 4.3424487451487585825e-1713j 1.44e-116, 1.05e-344j
0.010797082882119453901 - 7.375012100727852229e-1713j 1.04e-115, 7.61e-344j
0.010797082882119453901 - 1.7181680999910136771e-1714j 1.33e-113, 9.76e-342j
0.015754174452365329967 + 2.5881794666248127762e-1714j 3.02e-116, 2.21e-344j
0.000572420255719269216 - 2.3870518819784827213e-1715j 1.68e-115, 1.23e-343j
0.016497922834772479453 - 4.0673424736358762921e-1713j 2.28e-117, 1.67e-345j
0.017188781308932657443 + 3.8334301083067906282e-1713j 6.01e-118, 4.39e-346j
0.008807780192879099153 - 1.0337977659702318518e-1712j 3.78e-118, 2.77e-346j
0.019960232467515271019 - 3.5429996108872716014e-1714j 1.3e-119, 9.49e-348j
0.013547226458456883682 + 2.2841834743010688136e-1714j 1.88e-116, 1.38e-344j
0.014649495287280892259 - 4.7745142543855105446e-1713j 1.11e-117, 8.1e-346j
0.0205325582373799229 + 3.0036521615160074018e-1713j 9.13e-121, 6.67e-349j
0.025830883281629183614 - 5.1346538945382028983e-1714j 3.1e-122, 2.26e-350j
0.016497922834772479453 - 2.800659555043035127e-1714j 1.78e-118, 1.3e-346j
0.019324339933336369797 + 3.3164123321455861632e-1714j 9.07e-120, 6.63e-348j
0.0037511539981931479335 + 3.9707949670532370671e-1715j 1.76e-118, 1.28e-346j
0.021555222327270258076 - 2.8165025585772422877e-1713j 6.25e-122, 4.57e-350j
0.019324339933336369797 + 3.2964483850566206535e-1713j 7.32e-121, 5.35e-349j
0.0014875237252371793787 - 5.5771128679393017766e-1713j 4.68e-122, 3.42e-350j
0.025475867130715422862 + 4.8624704392203212302e-1714j 2.01e-125, 1.47e-353j
0.000572420255719269216 + 1.7329450446518028901e-1713j 2.36e-122, 1.73e-350j
0.018255797345687121908 - 3.5496939450793907861e-1713j 5.7e-122, 4.17e-350j
0.023517138825481307272 + 2.4568832334579459763e-1713j 2.35e-126, 1.72e-354j
0.0047087072817662874755 - 6.2916770909792356323e-1715j 2.02e-122, 1.47e-350j
0.021555222327270258076 - 3.9222257037807273123e-1714j 4.1e-126, 3e-354j
0.0205325582373799229 + 3.7732175457854754594e-1714j 2.19e-125, 1.6e-353j
0.0037511539981931479335 - 2.6753635967824839906e-1712j 6.68e-124, 4.89e-352j
0.024491847794224449204 - 2.3199716603530004681e-1713j 4.48e-129, 3.27e-357j
0.013547226458456883682 + 5.2845470875358680607e-1713j 4.71e-124, 3.44e-352j
0.02907902329916537674 - 6.4554103060812752835e-1714j 5.19e-133, 3.79e-361j
0.026083377005800959234 + 5.4135952775962136785e-1714j 1.44e-130, 1.05e-358j
0.011926754722065877361 + 6.3867420918658868378e-1713j 2.3e-124, 1.68e-352j
0.019960232467515271019 - 3.1409053072449058909e-1713j 4.75e-126, 3.47e-354j
0.025475867130715422862 + 2.1916108403732970476e-1713j 9.3e-131, 6.8e-359j
0.0026207771144520506066 - 8.7517761817067519597e-1716j 1.84e-126, 1.34e-354j
0.024491847794224449204 - 4.7152019851026975824e-1714j 4.21e-131, 3.08e-359j
0.022581200772318672178 + 4.0716260491451244084e-1714j 2.1e-130, 1.54e-358j
0.032264110349496395766 - 1.1904641193071864281e-1713j 5.88e-139, 4.3e-367j
0.028141991140309284307 - 1.8087648209398037827e-1713j 2.22e-136, 1.63e-364j
0.022581200772318672178 + 2.6444982973731553086e-1713j 8.06e-131, 5.89e-359j
0.023088586634231294498 - 4.3174430406619904248e-1714j 3.38e-131, 2.47e-359j
0.027969759805433091527 + 5.6971240997787830446e-1714j 4.55e-135, 3.33e-363j
0.0056322372084045783307 + 8.3993479472412199191e-1715j 3.53e-129, 2.58e-357j
0.025830883281629183614 - 2.1252091968259101342e-1713j 2.28e-134, 1.67e-362j
0.027969759805433091527 + 1.8538801316652671351e-1713j 1.76e-136, 1.28e-364j
0.018255797345687121908 - 3.1659613372377013864e-1714j 6.02e-131, 4.4e-359j
0.027015070851541133021 - 5.5556086134708342383e-1714j 2.24e-134, 1.64e-362j
0.030637306631556926661 - 7.4269084267333714748e-1714j 2.95e-140, 2.16e-368j
0.0056322372084045783307 + 3.59739680772888584e-1712j 1.25e-131, 9.16e-360j
0.030041405872557935615 + 1.5882590458190108475e-1713j 2.05e-141, 1.5e-369j
0.007903402581477522186 + 1.3040746975128442975e-1712j 4.69e-132, 3.43e-360j
0.0067635061487934668218 - 1.0126654886233091861e-1714j 1.43e-132, 1.04e-360j
0.028170082479004200395 + 6.326374500847891886e-1714j 1.04e-139, 7.59e-368j
0.0067635061487934668218 - 1.8944001472874217953e-1712j 4.39e-132, 3.21e-360j
0.027015070851541133021 - 1.9568422606862167653e-1713j 2.77e-139, 2.02e-367j
0.026083377005800959234 + 2.0649266858556866344e-1713j 1.05e-138, 7.67e-367j
0.014649495287280892259 - 2.4362638509379649859e-1714j 6.44e-135, 4.71e-363j
0.029985610560067701348 - 6.9492713337433719095e-1714j 1.03e-143, 7.53e-372j
0.017188781308932657443 + 3.0157554627745278284e-1714j 1.81e-135, 1.32e-363j
0.023088586634231294498 - 2.54575022117004417e-1713j 3.35e-137, 2.45e-365j
0.029697892706216673731 + 1.5347275487108763986e-1713j 5.52e-146, 4.04e-374j
0.028141991140309284307 - 6.0068721865223713389e-1714j 3.89e-141, 2.84e-369j
0.033119330735624645782 + 8.4158850311077670369e-1714j 5.14e-149, 3.75e-377j
0.030041405872557935615 + 6.5817398979938238706e-1714j 2.99e-143, 2.18e-371j
0.028170082479004200395 + 1.767953275657745374e-1713j 6.35e-144, 4.65e-372j
0.029985610560067701348 - 1.559690217566550239e-1713j 2.21e-146, 1.61e-374j
0.02907902329916537674 - 1.6766261892969231633e-1713j 7.5e-145, 5.49e-373j
0.034604803846254298101 + 7.7639787311871589947e-1714j 2.54e-152, 1.86e-380j
0.031707304431068972741 + 7.5118237793174628156e-1714j 3.25e-149, 2.37e-377j
0.023517138825481307272 + 4.5681722897233601408e-1714j 6.39e-143, 4.67e-371j
0.031340661283256790976 - 1.3570945622033677022e-1713j 8.3e-151, 6.07e-379j
0.030637306631556926661 - 1.4512286537965219785e-1713j 3.66e-149, 2.68e-377j
0.029490474713274174785 + 1.2200015613081470967e-1713j 1.14e-152, 8.32e-381j
0.029697892706216673731 + 7.332311042136523607e-1714j 2.68e-149, 1.96e-377j
0.031603151573797440462 - 8.4708674522207968069e-1714j 1.61e-152, 1.18e-380j
0.030991611466350620151 - 1.0682118469353771535e-1713j 2.06e-153, 1.51e-381j
0.031707304431068972741 + 1.3687420640910753621e-1713j 2.19e-151, 1.6e-379j
0.033119330735624645782 + 1.1715491993133748825e-1713j 3.57e-153, 2.61e-381j
0.029490474713274174785 + 9.9953488959721306083e-1714j 9.32e-155, 6.81e-383j
0.031340661283256790976 - 7.9828663467108454526e-1714j 1.2e-153, 8.77e-382j
0.030991611466350620151 - 9.2991728113903590291e-1714j 7.98e-155, 5.83e-383j
0.031603151573797440462 - 1.2621465728952528943e-1713j 2.24e-154, 1.64e-382j
0.030491276246093650473 + 1.3496771296500552506e-1713j 3.13e-154, 2.29e-382j
0.034604803846254298101 + 8.3416392186430362864e-1714j 6.82e-156, 4.99e-384j
0.030491276246093650473 + 8.4841763861246465727e-1714j 7.04e-156, 5.21e-384j
0.032264110349496395766 - 9.1554426484038544479e-1714j 2.95e-156, 2.2e-384j
0.035821959788139842855 - 7.2602608265416194541e-1714j 2.05e-156, 1.47e-384j

Download

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