Rule: Q[13, 28, 40]

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)
0.9969979402176134177 - 8.4420129276849666465e-1700j 3.16e-481, 3.16e-481j
-0.86508502130841265999 + 2.9204303106387278824e-1703j 8.13e-484, 8.13e-484j
-0.9318486970343282526 + 4.3721385323933338594e-1715j 3.46e-482, 3.46e-482j
-0.99469965430131955395 + 7.6963113446819563075e-1742j 4.9e-481, 4.9e-481j
0.9318486970343282526 - 5.7385910264785794381e-1772j 3.36e-482, 3.36e-482j
0.94552003904703088969 - 2.3118532070356377636e-1772j 6.17e-482, 6.17e-482j
0.96775951626391108868 - 1.2876676447177254502e-1770j 1.96e-481, 1.96e-481j
-0.88416234043030430681 + 4.7960006470307464195e-1785j 2.34e-483, 2.34e-483j
-0.99084192949999074669 + 3.1702665183385933495e-1822j 4.15e-481, 4.15e-481j
-0.99938065963663877686 - 1.0206266097082689924e-1853j 5.47e-482, 5.47e-482j
0.86508502130841265999 - 2.8323825622762203137e-1881j 8.16e-484, 8.16e-484j
-0.9969979402176134177 - 6.1170767322856118796e-1878j 2.86e-481, 2.86e-481j
-0.91759839922297796521 + 1.1827509006888153663e-1887j 1.63e-482, 1.63e-482j
-0.84541175979433656285 - 1.1194481734306520891e-1888j 2.49e-484, 2.49e-484j
0.99084192949999074669 + 9.0053616501478947161e-1885j 3.97e-481, 3.97e-481j
0.88416234043030430681 - 2.0848030816374816391e-1889j 2.3e-483, 2.3e-483j
0.91759839922297796521 - 4.1351272870212071312e-1888j 1.56e-482, 1.56e-482j
0.99938065963663877686 + 4.4509349661987832386e-1888j 5.15e-482, 5.15e-482j
-0.77751990383542365598 - 8.7610742583116433561e-1891j 4.01e-486, 4.01e-486j
-0.9761846491874812015 + 8.0582777337022197786e-1886j 2.65e-481, 2.65e-481j
0.9578198556812191027 + 1.8591305369949768357e-1892j 1.19e-481, 1.19e-481j
0.77751990383542365598 + 3.6442662711855419066e-1899j 4.19e-486, 4.19e-486j
0.84541175979433656285 + 6.7187027036247973802e-1897j 2.61e-484, 2.61e-484j
-0.82444758317623514086 + 3.6348784874102360454e-1897j 7.42e-485, 7.42e-485j
-0.80157809073330991279 + 3.0605256531009646385e-1898j 1.74e-485, 1.74e-485j
0.90193732983760631472 + 2.1659105213521107268e-1895j 6.37e-483, 6.37e-483j
0.7529237068328764254 + 5.6276717398858778687e-1900j 8.92e-487, 8.92e-487j
0.99469965430131955395 + 2.8937870189223998429e-1892j 5.04e-481, 5.04e-481j
-0.94552003904703088969 - 7.8397212420606422245e-1894j 6.31e-482, 6.31e-482j
-0.64234933944034022064 - 3.3837987041481305187e-1906j 6.34e-490, 6.34e-490j
-0.9578198556812191027 - 5.7387592097337494146e-1896j 1.25e-481, 1.25e-481j
0.69974076698664806642 - 8.8532229555577530999e-1920j 2.68e-488, 2.68e-488j
0.67125858771458620135 + 5.9926810017810081352e-1919j 4.47e-489, 4.47e-489j
-0.98418305471858814947 - 2.7340225366343538054e-1909j 2.83e-481, 2.83e-481j
-0.69974076698664806642 - 5.1590981585142440005e-1928j 2.72e-488, 2.72e-488j
-0.7529237068328764254 - 2.5246474802054824115e-1926j 8.68e-487, 8.68e-487j
0.9761846491874812015 + 2.9044297256849632358e-1921j 2.51e-481, 2.51e-481j
0.61246500385835982021 + 4.095200484664736624e-1935j 9.14e-491, 9.14e-491j
0.82444758317623514086 - 3.6854772343765131041e-1927j 7.09e-485, 7.09e-485j
-0.96775951626391108868 - 4.9710208340345829033e-1927j 1.95e-481, 1.95e-481j
-0.58109501657195363168 + 1.0400948262830537551e-1943j 9.73e-492, 9.73e-492j
0.98418305471858814947 + 1.6767479408301811001e-1939j 2.92e-481, 2.92e-481j
0.64234933944034022064 + 1.2850158142870186546e-1947j 6.78e-490, 6.78e-490j
0.54885886819669941822 - 9.8001748366388986212e-1951j 1.01e-492, 1.01e-492j
-0.72718178160868271068 - 1.2884058281440655894e-1944j 1.66e-487, 1.66e-487j
-0.54885886819669941822 - 2.9663933987644484264e-1950j 1.02e-492, 1.02e-492j
-0.90193732983760631472 - 9.7713947798300563354e-1945j 6.46e-483, 6.46e-483j
0.80157809073330991279 + 1.6731029388602224212e-1948j 1.71e-485, 1.71e-485j
0.48305122499446407817 - 2.9150304167052150704e-1959j 9.75e-495, 9.75e-495j
0.58109501657195363168 + 8.1910679338326398847e-1956j 9.87e-492, 9.87e-492j
-0.61246500385835982021 + 1.6614445394114169302e-1957j 8.22e-491, 8.22e-491j
-0.51634640124151093842 + 1.8152310347518050978e-1959j 9.95e-494, 9.95e-494j
0.03900032914808238216 + 6.8718193754999865577e-1977j 1.21e-509, 1.21e-509j
0.51634640124151093842 + 5.7159580145737512331e-1958j 1.05e-493, 1.05e-493j
0.44849275103644685288 + 3.1205913339077454236e-1960j 7.79e-496, 7.79e-496j
-0.41326489870027208158 - 1.7487285048883154768e-1963j 5.93e-497, 5.93e-497j
-0.48305122499446407817 - 9.495339799159041197e-1961j 9.12e-495, 9.12e-495j
-0.67125858771458620135 - 3.0818369464152823843e-1955j 4.28e-489, 4.28e-489j
0.07743926262886708714 + 1.5069149905428454642e-1974j 2.66e-508, 2.66e-508j
0.41326489870027208158 - 1.9515714445714825213e-1961j 5.61e-497, 5.61e-497j
0.72718178160868271068 + 3.2353763447752088079e-1966j 1.59e-487, 1.59e-487j
-0.15441300414438573558 - 9.1554450841088362406e-1988j 1.11e-505, 1.11e-505j
-0.44849275103644685288 - 4.3527137547845466753e-1976j 7.27e-496, 7.27e-496j
-0.19283431255645505718 + 5.6030950807555988545e-1987j 2.53e-504, 2.53e-504j
0.37794181353855315337 - 1.5985910609474502344e-1978j 4.45e-498, 4.45e-498j
0.26773341101770944825 + 6.3762470622451251009e-1982j 8.52e-502, 8.52e-502j
-7.6996346492683172819e-2032 - 2.0341848048360722432e-2031j 1.76e-2029, 1.76e-2029j
-0.34204616453060987873 + 2.9729128068247876381e-1980j 2.7e-499, 2.7e-499j
-0.37794181353855315337 - 8.6977479953032232765e-1979j 4.15e-498, 4.15e-498j
0.23045831595513479407 - 1.3507085299929774832e-1983j 4.59e-503, 4.59e-503j
0.34204616453060987873 + 2.5359204897102115782e-1979j 2.66e-499, 2.66e-499j
0.11576103878046372137 - 2.5391166708147041706e-1989j 4.83e-507, 4.83e-507j
-0.23045831595513479407 + 4.785620651141712483e-1986j 4.42e-503, 4.42e-503j
-0.26773341101770944825 - 5.6875289037655301606e-1983j 7.94e-502, 7.94e-502j
-0.03900032914808238216 + 3.0583627078798539168e-1991j 1.05e-509, 1.05e-509j
0.30511766440256551373 + 1.9062394340784050792e-1980j 1.55e-500, 1.55e-500j
0.19283431255645505718 + 7.8691191217433007706e-1985j 2.55e-504, 2.55e-504j
-0.07743926262886708714 + 1.2389025354621627558e-1990j 2.64e-508, 2.64e-508j
-0.30511766440256551373 - 5.5032957167642884034e-1982j 1.48e-500, 1.48e-500j
-0.11576103878046372137 - 1.4818364827486082307e-1990j 4.96e-507, 4.96e-507j
0.15441300414438573558 - 1.9002717744589998589e-1986j 1.12e-505, 1.12e-505j

Weights

Weight (ball center) Error (ball radius)
0.002838886045756515578 + 1.2731344487761399868e-1699j 2.85e-136, 2.33e-368j
0.019384653907647027105 + 8.9271280591005313072e-1702j 1.35e-136, 1.11e-368j
0.013975091595326225754 + 6.110271192004768954e-1702j 9.65e-137, 7.89e-369j
0.0021833715082543688366 - 2.2645496090014047044e-1702j 2.32e-137, 1.9e-369j
0.013975091595326225754 + 1.8271017994775568707e-1700j 9.98e-138, 8.16e-370j
0.013198146054956481144 - 1.9677760590881030484e-1700j 7.48e-138, 6.12e-370j
0.0088428893354061919194 - 3.0491451356687421819e-1700j 2.96e-138, 2.42e-370j
0.018620387849531070216 - 7.6820436182975842872e-1702j 8.02e-138, 6.56e-370j
0.0055703975042917445478 + 2.3557443569040508537e-1702j 8.86e-139, 7.25e-371j
0.0015714745838475124781 - 1.876960365623647769e-1703j 1.64e-139, 1.34e-371j
0.019384653907647027105 + 1.2560051116118284558e-1700j 4.14e-143, 3.39e-375j
0.002838886045756515578 + 1.1956959305457471079e-1702j 5.29e-139, 4.33e-371j
0.014709562318931811166 - 7.0367281394201875736e-1702j 9.67e-141, 7.91e-373j
0.020114677195008167973 - 1.0163186409330309051e-1701j 2.19e-141, 1.79e-373j
0.0055703975042917445478 + 7.6482615781542895627e-1700j 1.67e-143, 1.37e-375j
0.018620387849531070216 - 1.3254125906357637324e-1700j 1.31e-143, 1.07e-375j
0.014709562318931811166 - 1.7182287997158344983e-1700j 3.76e-143, 3.07e-375j
0.0015714745838475124781 + 1.5806529337458877242e-1700j 4.77e-144, 3.9e-376j
0.024336005434999624607 + 1.1818341561635541684e-1701j 3.59e-146, 2.93e-378j
0.008255024997441159888 + 3.5235618192605190116e-1702j 9.1e-144, 7.44e-376j
0.011198404068302755434 + 2.4282329242178652144e-1700j 3.33e-143, 2.72e-375j
0.024336005434999624607 + 9.490055963487236675e-1701j 1.91e-147, 1.56e-379j
0.020114677195008167973 - 1.1969886397043330833e-1700j 1.52e-145, 1.24e-377j
0.021943972664897325387 + 1.0463545250549440011e-1701j 5.68e-146, 4.65e-378j
0.023643115716377938638 - 1.0878485707791129923e-1701j 1.49e-146, 1.22e-378j
0.016758215914588354972 + 1.5045695408724127792e-1700j 6.64e-145, 5.43e-377j
0.024989904267656374449 - 9.1116100149303102161e-1701j 6.58e-149, 5.38e-381j
0.0021833715082543688366 - 1.9728209386332850421e-1699j 2.99e-145, 2.45e-377j
0.013198146054956481144 - 5.1716435833418327328e-1702j 2.51e-146, 2.05e-378j
0.029233828184723056269 - 1.5788689965396528671e-1701j 3.14e-152, 2.57e-384j
0.011198404068302755434 + 4.8315292854118338677e-1702j 1.46e-146, 1.19e-378j
0.028129971382984732931 - 7.8384937450820981429e-1701j 1.19e-151, 9.75e-384j
0.028705194285976165151 + 7.5462959189840943578e-1701j 2.47e-152, 2.02e-384j
0.0075335041501989154099 - 2.5258022776196985889e-1702j 6.56e-147, 5.36e-379j
0.028129971382984732931 - 1.3779769620866661089e-1701j 1.31e-152, 1.07e-384j
0.024989904267656374449 - 1.2775713565648886415e-1701j 4.77e-151, 3.9e-383j
0.008255024997441159888 + 3.3608853829688192643e-1700j 1.31e-148, 1.07e-380j
0.03064545915154968097 + 6.826138374596957722e-1701j 1.14e-155, 9.3e-388j
0.021943972664897325387 + 1.0879110254315591342e-1700j 3.86e-151, 3.16e-383j
0.0088428893354061919194 - 4.5078737724838054181e-1702j 6.87e-149, 5.62e-381j
0.031963715298177244541 - 1.6912718363455461163e-1701j 5.5e-157, 4.5e-389j
0.0075335041501989154099 - 3.9272214490567739089e-1700j 7.82e-149, 6.39e-381j
0.029233828184723056269 - 7.2805282384945472827e-1701j 3.87e-155, 3.17e-387j
0.032384733339825035185 + 6.1910295645036545754e-1701j 3.87e-158, 3.17e-390j
0.026612789478871313631 + 1.3270056745258976587e-1701j 4.51e-154, 3.68e-386j
0.032384733339825035185 + 1.7975633964598855242e-1701j 1.23e-158, 1e-390j
0.016758215914588354972 + 7.3991191794171166702e-1702j 4.18e-151, 3.42e-383j
0.023643115716377938638 - 9.9166153103202087351e-1701j 4.29e-153, 3.51e-385j
0.033943411623120217227 + 5.6590676940779854912e-1701j 2.05e-160, 1.68e-392j
0.031963715298177244541 - 6.4057924979231972455e-1701j 6.77e-158, 5.54e-390j
0.03064545915154968097 + 1.6343062678454040483e-1701j 4.58e-158, 3.74e-390j
0.032751751264356931655 - 1.9057799905827913949e-1701j 1.02e-160, 8.35e-393j
0.03873355627228891609 + 3.466171992537192981e-1701j 4.26e-166, 3.49e-398j
0.032751751264356931655 - 5.9922279820519867433e-1701j 7.06e-160, 5.78e-392j
0.035048464273487830331 - 5.3465697005571917995e-1701j 6.05e-162, 4.95e-394j
0.035286868303817324438 + 2.1461760827730016608e-1701j 1.5e-164, 1.22e-396j
0.033943411623120217227 + 1.9674549525563927444e-1701j 8.9e-163, 7.28e-395j
0.028705194285976165151 + 1.4776961035067891375e-1701j 3.11e-159, 2.54e-391j
0.03824229128865182319 - 3.6396427250174271776e-1701j 1.21e-167, 9.89e-400j
0.035286868303817324438 + 5.180312424718549873e-1701j 2.48e-164, 2.03e-396j
0.026612789478871313631 + 8.4442501163585216515e-1701j 3.45e-159, 2.82e-391j
0.038686447606151383545 - 2.8222583607845183886e-1701j 1.13e-168, 9.24e-401j
0.035048464273487830331 - 2.0309223182982915068e-1701j 1.09e-164, 8.93e-397j
0.038037333188031589001 + 2.7411111405294356808e-1701j 1.19e-168, 9.71e-401j
0.035464611888475452063 - 5.0244642138826526143e-1701j 1.14e-166, 9.33e-399j
0.037342009098162230033 + 4.3886565216965423921e-1701j 5.54e-169, 4.53e-401j
0.039149495281076936058 - 3.299219704453684546e-1701j 1.07e-169, 8.75e-402j
0.036427581774767503237 + 2.3330522251282385033e-1701j 8.32e-169, 6.8e-401j
0.035464611888475452063 - 2.2640231069548983084e-1701j 5.65e-168, 4.62e-400j
0.037309333496354780065 - 4.2622409849157467579e-1701j 1.76e-170, 1.44e-402j
0.036427581774767503237 + 4.7666227370944351432e-1701j 3.21e-169, 2.63e-401j
0.038500041544628215473 + 3.7450671585125221751e-1701j 4.35e-171, 3.56e-403j
0.037309333496354780065 - 2.662868323260105611e-1701j 2.3e-171, 1.88e-403j
0.037342009098162230033 + 2.5318440513879591494e-1701j 2.23e-171, 1.82e-403j
0.03873355627228891609 + 3.2054156483783647939e-1701j 1.68e-172, 1.37e-404j
0.037308174501640541441 - 4.5222707606710289177e-1701j 1.7e-171, 1.39e-403j
0.038037333188031589001 + 4.054321387853519748e-1701j 1.61e-172, 1.31e-404j
0.03824229128865182319 - 3.1154069865767266131e-1701j 2.83e-173, 2.31e-405j
0.037308174501640541441 - 2.4043360694448334433e-1701j 4.17e-173, 3.42e-405j
0.038500041544628215473 + 2.9664578840451147838e-1701j 2.04e-173, 1.67e-405j
0.038686447606151383545 - 3.8556330843090005302e-1701j 1.86e-173, 1.52e-405j

Download

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