Rule: Q[1, 2, 46, 50]

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)
0.99373313949023041129 + 1.0911879641703188385e-1635j 1.65e-474, 1.65e-474j
-0.95446766723776514625 - 5.3089615301457041396e-1667j 2.86e-475, 2.86e-475j
-0.92166640697270519492 + 1.0317179858354716614e-1666j 3.86e-476, 3.86e-476j
0.99880954492634771519 + 4.3061217886695013631e-1663j 1.05e-474, 1.05e-474j
0.90885375188839683921 - 5.6994051738763320707e-1683j 1.7e-476, 1.7e-476j
0.96347704240713760777 + 1.0801419947915295106e-1691j 5.13e-475, 5.13e-475j
-0.99980240631625889588 + 7.2494428855397116127e-1702j 3.78e-475, 3.78e-475j
-0.90885375188839683921 - 4.7881327424378762183e-1714j 1.59e-476, 1.59e-476j
-0.94449006659801940568 + 5.5565917742435381017e-1711j 1.69e-475, 1.69e-475j
0.56501910744482497338 + 4.0492388492871457018e-1724j 4.79e-488, 4.79e-488j
0.8951218383113935661 - 5.1301405536844753686e-1710j 6.09e-477, 6.09e-477j
0.98462302116407822151 + 9.1315771103298039184e-1719j 1.4e-474, 1.4e-474j
-0.93355058768832886286 - 3.6798586781966071215e-1737j 7.63e-476, 7.63e-476j
-0.88048214147436821779 + 3.6806489229965265581e-1738j 2.33e-477, 2.33e-477j
-0.99880954492634771519 - 2.8776296418949026533e-1734j 1.03e-474, 1.03e-474j
0.84855619933027379318 + 1.343493986216474008e-1738j 2.32e-478, 2.32e-478j
0.94449006659801940568 + 6.5188776409056438892e-1735j 1.53e-475, 1.53e-475j
-0.99373313949023041129 + 6.6583462259700180486e-1739j 1.58e-474, 1.58e-474j
-0.75411482047359037358 + 6.0299646204747364216e-1748j 2.25e-481, 2.25e-481j
-0.8951218383113935661 - 1.2674241547416105676e-1743j 6.25e-477, 6.25e-477j
0.93355058768832886286 - 2.6489541356814394511e-1740j 7.96e-476, 7.96e-476j
0.79430155220717925601 + 2.8937493946626454789e-1752j 4.53e-480, 4.53e-480j
-0.97857073033497888219 - 2.5833378040434181465e-1744j 1.07e-474, 1.07e-474j
-0.83130340569535410905 + 2.9978614994382846175e-1750j 6.82e-479, 6.82e-479j
-0.81321122267737656915 + 6.4956839742822076905e-1751j 1.77e-479, 1.77e-479j
-0.99679136876864238608 + 6.1016442213942966007e-1744j 1.51e-474, 1.51e-474j
0.73287537465803831504 + 1.2055197174220798624e-1753j 4.26e-482, 4.26e-482j
0.92166640697270519492 + 3.2900909584540723253e-1747j 3.55e-476, 3.55e-476j
0.99980240631625889588 + 1.0945238008959175477e-1755j 3.77e-475, 3.77e-475j
-0.61615800055643761832 - 4.8153915899612099395e-1791j 3.78e-486, 3.78e-486j
0.98967304765001552877 - 3.9455432663982452943e-1777j 1.61e-474, 1.61e-474j
0.81321122267737656915 - 8.977221310298445013e-1798j 1.81e-479, 1.81e-479j
0.75411482047359037358 - 2.8525504338526509245e-1801j 2.13e-481, 2.13e-481j
-0.98967304765001552877 + 2.0396008086031536574e-1792j 1.57e-474, 1.57e-474j
-0.66485606495536633107 + 1.0204190287574581423e-1803j 2.1e-484, 2.1e-484j
-0.77459666924148337704 + 3.1721150839150798586e-1800j 1e-480, 1e-480j
-0.96347704240713760777 + 4.2394928720080275286e-1794j 4.9e-475, 4.9e-475j
0.61615800055643761832 - 8.3265703537986405048e-1805j 3.67e-486, 3.67e-486j
0.86495385330232214022 - 3.118323464056292368e-1796j 7.45e-478, 7.45e-478j
-0.79430155220717925601 - 4.7893245849341558875e-1799j 4.7e-480, 4.7e-480j
-0.59088116794699891837 - 1.5382366214586970667e-1807j 4.81e-487, 4.81e-487j
0.51164256855683468754 - 2.3293780766085028732e-1809j 4.97e-490, 4.97e-490j
0.77459666924148337704 + 4.7696819788511229902e-1799j 1.08e-480, 1.08e-480j
0.66485606495536633107 - 6.2202398155778412577e-1804j 2.01e-484, 2.01e-484j
-0.98462302116407822151 + 1.2301561944914802429e-1793j 1.44e-474, 1.44e-474j
-0.56501910744482497338 + 1.9095275271948453182e-1807j 4.91e-488, 4.91e-488j
-0.71090296067047761644 - 2.427731445651535806e-1802j 7.46e-483, 7.46e-483j
0.88048214147436821779 + 2.2780714675867402864e-1795j 2.26e-477, 2.26e-477j
0.48418664482206799331 + 8.6557846055171183401e-1810j 4.48e-491, 4.48e-491j
0.83130340569535410905 - 9.0268645853922762626e-1797j 6.87e-479, 6.87e-479j
-0.73287537465803831504 - 2.1878145923890464834e-1801j 4.65e-482, 4.65e-482j
-0.48418664482206799331 + 2.4152701076508767105e-1810j 4.57e-491, 4.57e-491j
0.95446766723776514625 + 1.7505009594910334255e-1792j 3.07e-475, 3.07e-475j
0.64082547895039062277 + 2.4488603220736265136e-1805j 2.94e-485, 2.94e-485j
0.59088116794699891837 + 1.8938085661176079829e-1807j 4.44e-487, 4.44e-487j
-0.86495385330232214022 + 1.8557060627219667316e-1798j 7.85e-478, 7.85e-478j
-0.45625481952473340147 + 6.2400700287573585927e-1813j 3.77e-492, 3.77e-492j
-0.68822268105219173651 - 2.9089354566864700586e-1805j 1.32e-483, 1.32e-483j
0.97151599496815703805 - 1.9049692525308493626e-1793j 7.23e-475, 7.23e-475j
0.39907334519718009376 + 1.0174275091325084372e-1825j 2.24e-494, 2.24e-494j
0.97857073033497888219 + 4.4864584756288539111e-1805j 1.08e-474, 1.08e-474j
-0.64082547895039062277 + 3.3475171096863544324e-1843j 2.74e-485, 2.74e-485j
-0.42787353090337220704 - 7.1505849600954726078e-1851j 3e-493, 3e-493j
-0.97151599496815703805 + 6.9813494094862081993e-1836j 7.4e-475, 7.4e-475j
0.42787353090337220704 + 2.0626727413929531231e-1853j 3.1e-493, 3.1e-493j
0.53859654618667324447 - 3.7195160352661186337e-1849j 5.52e-489, 5.52e-489j
0.99679136876864238608 - 5.2431098869304319019e-1845j 1.59e-474, 1.59e-474j
-0.39907334519718009376 - 2.6678961770848274108e-1891j 2.22e-494, 2.22e-494j
-0.53859654618667324447 + 2.5286936543524696891e-1885j 5.28e-489, 5.28e-489j
0.71090296067047761644 - 1.173025379422341161e-1880j 8.16e-483, 8.16e-483j
0.3403361383336095418 - 1.4264162952840858973e-1895j 9.83e-497, 9.83e-497j
0.68822268105219173651 + 1.9986812736098045022e-1881j 1.36e-483, 1.36e-483j
-0.51164256855683468754 - 1.3935930084555570172e-1886j 5.12e-490, 5.12e-490j
-0.36988510986301243741 + 3.5059690816805126763e-1892j 1.47e-495, 1.47e-495j
-0.84855619933027379318 + 3.8403838303373936987e-1901j 2.36e-478, 2.36e-478j
0.36988510986301243741 + 6.4661828211840362201e-1918j 1.48e-495, 1.48e-495j
0.45625481952473340147 + 7.7638303834605938966e-1915j 4.01e-492, 4.01e-492j
-0.15711944788745964192 + 3.004626565633547164e-1928j 2.52e-504, 2.52e-504j
-0.31045396544146596841 - 5.4436875802713024542e-1922j 6.22e-498, 6.22e-498j
-0.12587836098052821846 - 6.2491817189105435744e-1930j 1.13e-505, 1.13e-505j
0.18821086465036125365 + 3.4568477184096900782e-1926j 4.97e-503, 4.97e-503j
0.28027011340419795441 - 2.9820613248747803842e-1922j 3.44e-499, 3.44e-499j
0.031544502997420745717 - 9.3603656381565501634e-1933j 1.15e-509, 1.15e-509j
-0.3403361383336095418 + 2.4108281573023594687e-1921j 1e-496, 1e-496j
-0.28027011340419795441 + 2.5665409134846892281e-1923j 3.54e-499, 3.54e-499j
2.8126866402081995406e-1983 + 2.6851721051380518385e-1983j 3.85e-1981, 3.85e-1981j
0.31045396544146596841 + 7.0695756080736415697e-1921j 6.27e-498, 6.27e-498j
0.15711944788745964192 - 1.9296881583262571828e-1927j 2.59e-504, 2.59e-504j
-0.094515946476295116317 + 1.5966539724416339458e-1930j 5.12e-507, 5.12e-507j
-0.24981627852576530216 - 2.7157730023593913782e-1924j 1.98e-500, 1.98e-500j
-0.063060576950221367751 + 1.4515677150026157206e-1932j 2.22e-508, 2.22e-508j
0.12587836098052821846 + 1.2792484218295541169e-1929j 1.27e-505, 1.27e-505j
0.21912048736433116275 - 1.5082112681884467091e-1924j 9.85e-502, 9.85e-502j
-0.031544502997420745717 + 7.3970503477100997043e-1933j 1.15e-509, 1.15e-509j
-0.21912048736433116275 + 1.0421574435563604117e-1925j 1.06e-501, 1.06e-501j
-0.18821086465036125365 - 3.3812861918381319461e-1927j 5.38e-503, 5.38e-503j
0.063060576950221367751 - 2.329607011794263874e-1932j 2.29e-508, 2.29e-508j
0.24981627852576530216 + 7.946249652496438807e-1924j 1.89e-500, 1.89e-500j
0.094515946476295116317 - 3.4981143117145857221e-1930j 5.14e-507, 5.14e-507j

Weights

Weight (ball center) Error (ball radius)
0.0035644614200879546587 - 1.618330277760687105e-1636j 2.32e-113, 1.89e-340j
0.0094935828286610193799 - 5.5372116640682801167e-1638j 9.95e-114, 8.11e-341j
0.012350411758686694353 + 7.5083552894813976414e-1638j 6.46e-114, 5.27e-341j
0.0014911342074187700892 + 3.3767340728757569961e-1636j 1.93e-114, 1.58e-341j
0.013273586814995628906 - 1.8398521152961511585e-1636j 3.97e-115, 3.24e-342j
0.0085251781057157228814 + 3.1763102685499636381e-1636j 7.84e-115, 6.39e-342j
0.00053226613861283935886 + 2.9252995606857218637e-1639j 1.52e-116, 1.24e-343j
0.013273586814995628906 - 8.2080624822930856173e-1638j 1.54e-114, 1.26e-341j
0.010460698295109030359 + 6.1745982778770110883e-1638j 1.04e-114, 8.51e-342j
0.026146802175818836399 + 9.126450985936553711e-1637j 1.3e-117, 1.06e-344j
0.014188449321546017304 + 1.709949467147156701e-1636j 2.06e-116, 1.68e-343j
0.0055490806519096681201 - 6.7759105465214825659e-1636j 5.68e-116, 4.63e-343j
0.011415113613760552929 - 6.8296720098251211644e-1638j 9.82e-115, 8e-342j
0.015087559975069486748 - 9.6711409604241644961e-1638j 1.65e-116, 1.34e-343j
0.0014911342074187700892 - 8.6029129202259195822e-1639j 4.85e-117, 3.95e-344j
0.016827396961722384949 - 1.4273571722418043867e-1636j 6.24e-119, 5.09e-346j
0.010460698295109030359 + 2.4303417653585867731e-1636j 5.19e-118, 4.23e-345j
0.0035644614200879546587 - 1.9570130278359592226e-1638j 6.69e-118, 5.45e-345j
0.020864338878134438521 + 1.5750549119877284217e-1637j 1.01e-120, 8.22e-348j
0.014188449321546017304 + 8.9271195452861873217e-1638j 3.01e-117, 2.45e-344j
0.011415113613760552929 - 2.1871315410203240596e-1636j 3.62e-119, 2.95e-346j
0.01931062197493711541 + 1.2409975054999776106e-1636j 1.75e-121, 1.43e-348j
0.0065556102537496675979 + 3.7029336596323160386e-1638j 1.64e-118, 1.33e-345j
0.017675671694456050978 + 1.2078339428453548295e-1637j 2.75e-120, 2.24e-347j
0.018504904523869770288 - 1.2941362401855335331e-1637j 9.57e-121, 7.8e-348j
0.0025444019842923796459 + 1.4038241101618012764e-1638j 6.41e-118, 5.22e-345j
0.021610332778076550771 - 1.1095188552477747403e-1636j 4.37e-124, 3.56e-351j
0.012350411758686694353 + 1.9955810141188174057e-1636j 1.27e-120, 1.03e-347j
0.00053226613861283935886 - 9.608555404665157086e-1637j 6.37e-122, 5.19e-349j
0.024976453520991710445 + 2.2485637876800618001e-1637j 1.08e-126, 8.77e-354j
0.0045538556782022729692 + 1.2387049556102354533e-1635j 1.51e-121, 1.23e-348j
0.018504904523869770288 - 1.2953730075358521329e-1636j 6.09e-124, 4.96e-351j
0.020864338878134438521 + 1.148892340972298657e-1636j 6.39e-125, 5.2e-352j
0.0045538556782022729692 + 2.5356661259377418476e-1638j 2.62e-121, 2.13e-348j
0.023702735184016287487 + 2.0060730335701059809e-1637j 9.3e-128, 7.58e-355j
0.020096227425675929824 - 1.4778366407101076222e-1637j 1.72e-125, 1.4e-352j
0.0085251781057157228814 + 4.9101906754903495697e-1638j 4.61e-122, 3.76e-349j
0.024976453520991710445 + 9.5873444682772400119e-1637j 5.56e-130, 4.53e-357j
0.015965698036783893604 + 1.5075678516033513565e-1636j 9.79e-126, 7.98e-353j
0.01931062197493711541 + 1.3841683468748442888e-1637j 2.99e-125, 2.44e-352j
0.02557328724624028365 - 2.3770684836503515238e-1637j 5.18e-130, 4.22e-357j
0.027209574937660174042 + 8.7151458208969336159e-1637j 4.05e-132, 3.3e-359j
0.020096227425675929824 - 1.1925457142013837066e-1636j 2.26e-127, 1.84e-354j
0.023702735184016287487 + 1.0117005210881875819e-1636j 4.17e-130, 3.39e-357j
0.0055490806519096681201 - 3.1202342669086084121e-1638j 2.33e-123, 1.9e-350j
0.026146802175818836399 + 2.5101087155697577552e-1637j 8.06e-132, 6.57e-359j
0.022330216507912131899 + 1.7819251365027540766e-1637j 2.38e-129, 1.94e-356j
0.015087559975069486748 - 1.6004980521099578047e-1636j 4.05e-127, 3.3e-354j
0.027698023552131641721 - 8.5237697520710960215e-1637j 3.14e-134, 2.56e-361j
0.017675671694456050978 + 1.3571044135257353101e-1636j 1.47e-127, 1.2e-354j
0.021610332778076550771 - 1.6762723353178897293e-1637j 3.75e-129, 3.06e-356j
0.027698023552131641721 - 2.9387636897677307313e-1637j 1.44e-135, 1.18e-362j
0.0094935828286610193799 - 2.7473501812484110435e-1636j 1.94e-128, 1.58e-355j
0.024353822002575772938 - 9.8415672265334807452e-1637j 7.68e-132, 6.26e-359j
0.02557328724624028365 - 9.3501757345780908354e-1637j 1.05e-132, 8.56e-360j
0.015965698036783893604 + 1.0445196666364485899e-1637j 2.78e-129, 2.27e-356j
0.028161310158760766758 + 3.0908852046681023695e-1637j 1.38e-137, 1.12e-364j
0.023026860971723321192 - 1.8919016537220719435e-1637j 1.36e-131, 1.11e-358j
0.0075502914635874422945 - 3.8008220851379342263e-1636j 3.76e-131, 3.07e-358j
0.028999058243037802165 + 7.9841431872606165928e-1637j 4.28e-141, 3.49e-368j
0.0065556102537496675979 + 4.8167216118616123327e-1636j 2.67e-131, 2.17e-358j
0.024353822002575772938 - 2.124833228235589626e-1637j 1.14e-134, 9.28e-362j
0.028596080872283414385 - 3.2475254925354535277e-1637j 1.62e-140, 1.32e-367j
0.0075502914635874422945 - 4.296829958481061587e-1638j 6.15e-131, 5.01e-358j
0.028596080872283414385 - 8.1587443818284418113e-1637j 7.67e-141, 6.25e-368j
0.026693377991722664109 - 8.915103298878114737e-1637j 6.08e-138, 4.95e-365j
0.0025444019842923796459 - 9.1371380042923717982e-1636j 1.2e-132, 9.76e-360j
0.028999058243037802165 + 3.4088360425807636304e-1637j 2.76e-142, 2.25e-369j
0.026693377991722664109 - 2.6479874287681485411e-1637j 7.83e-139, 6.38e-366j
0.022330216507912131899 + 1.0739780062163052843e-1636j 1.08e-136, 8.78e-364j
0.029720494072808662084 + 7.642431057047627673e-1637j 5.64e-145, 4.59e-372j
0.023026860971723321192 - 1.0415666339674723167e-1636j 3.37e-137, 2.75e-364j
0.027209574937660174042 + 2.7909907155434463975e-1637j 4.43e-140, 3.61e-367j
0.029372950308635920255 - 3.5742424541791051753e-1637j 2.26e-144, 1.84e-371j
0.016827396961722384949 - 1.1247926284700868142e-1637j 2.31e-136, 1.88e-363j
0.029372950308635920255 - 7.8126434751171095018e-1637j 2.43e-144, 1.98e-371j
0.028161310158760766758 + 8.3384690376980276524e-1637j 5.38e-142, 4.39e-369j
0.031171292414165945875 + 4.8157637085489185027e-1637j 2.96e-150, 2.41e-377j
0.030038506962106470919 - 3.9154036645351167715e-1637j 7.45e-148, 6.07e-375j
0.031306249046440391462 - 5.0002926301830726933e-1637j 1.12e-150, 9.09e-378j
0.031006094430330492998 - 6.7965549444270461985e-1637j 2.58e-151, 2.1e-378j
0.030323822412496747517 + 7.3054980620422847189e-1637j 1.57e-149, 1.28e-376j
0.031535347826651457708 + 5.9168503323419417154e-1637j 9.45e-153, 7.7e-380j
0.029720494072808662084 + 3.7430901207519801413e-1637j 2.66e-148, 2.17e-375j
0.030323822412496747517 + 4.091200507195446593e-1637j 4.79e-150, 3.91e-377j
0.031549012296149199292 - 5.7357636557708651516e-1637j 2.78e-153, 2.27e-380j
0.030038506962106470919 - 7.4734005715862381203e-1637j 2.15e-150, 1.75e-377j
0.031171292414165945875 + 6.6246036609386368274e-1637j 3.32e-153, 2.7e-380j
0.031413943628784329279 + 5.1846193440022970712e-1637j 1.84e-153, 1.5e-380j
0.030579266612641113201 - 4.2696803724914434803e-1637j 1.42e-152, 1.16e-379j
0.031491328050753621506 - 5.3687492428670376036e-1637j 5.4e-154, 4.4e-381j
0.031306249046440391462 - 6.450831721046471125e-1637j 6.36e-155, 5.18e-382j
0.03080771993617415842 + 6.9675636238621751943e-1637j 2.26e-154, 1.84e-381j
0.031535347826651457708 + 5.5527653366114348344e-1637j 1.48e-154, 1.21e-381j
0.03080771993617415842 + 4.4499705636639183242e-1637j 1.41e-154, 1.15e-381j
0.031006094430330492998 - 4.6320099604801690458e-1637j 1.01e-154, 8.2e-382j
0.031491328050753621506 - 6.0963014204712961325e-1637j 2.6e-156, 2.12e-383j
0.030579266612641113201 - 7.1373009820511079196e-1637j 1.7e-156, 1.44e-383j
0.031413943628784329279 + 6.2745211123954006405e-1637j 1.81e-156, 1.47e-383j

Download

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