Rule: Q[2, 4, 37, 44]

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.

Warning: This rule has negative weights!

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)
-0.99595303196868299522 - 4.3781875218476199612e-1767j 1e-478, 1e-478j
-0.96320947642682331194 + 4.2423230267488837739e-1782j 4.04e-479, 4.04e-479j
-0.92721561993401173868 - 1.1468736702240255782e-1789j 8.95e-480, 8.95e-480j
0.99595303196868299522 + 7.5187501063278450208e-1795j 9.86e-479, 9.86e-479j
0.91248695683407599658 + 2.0815874345501388907e-1797j 6.04e-480, 6.04e-480j
0.92721561993401173868 + 6.1226682376275088255e-1796j 8.97e-480, 8.97e-480j
-0.9985033617835308753 + 2.504673085434841201e-1792j 7.38e-479, 7.38e-479j
-0.91248695683407599658 - 1.341673171599762097e-1806j 6.11e-480, 6.11e-480j
-0.97246818630922115364 + 3.4736274795203111531e-1804j 5.89e-479, 5.89e-479j
0.9868731177910260499 - 8.8741631878740475767e-1813j 1.02e-478, 1.02e-478j
0.87902558400256699957 - 6.3199242427538664474e-1817j 1.03e-480, 1.03e-480j
0.95257867843701226505 - 3.7037008820040319254e-1815j 2.53e-479, 2.53e-479j
-0.94058083526894862902 - 4.9960016823146090498e-1813j 1.49e-479, 1.49e-479j
-0.8928107582522787686 - 3.8289517583893935993e-1821j 1.01e-479, 1.01e-479j
0.99975284743748866209 + 1.6675266554077980266e-1824j 2.69e-479, 2.69e-479j
0.86032780093317475415 - 3.6213128088086077094e-1828j 1.27e-481, 1.27e-481j
0.89639894566995214562 + 1.6310810959798211994e-1826j 1.25e-479, 1.25e-479j
-0.95257867843701226505 + 4.6862445493058062117e-1823j 2.51e-479, 2.51e-479j
-0.79667953649742200176 - 3.6927888574100720064e-1840j 7.01e-484, 7.01e-484j
-0.81912856617098761924 + 3.7972120691157906504e-1839j 4.01e-483, 4.01e-483j
0.94058083526894862902 - 1.1117357120513751361e-1835j 1.52e-479, 1.52e-479j
0.81912856617098761924 - 1.4820824496952292988e-1838j 3.78e-483, 3.78e-483j
0.99206935952458725579 + 1.3596760342780319138e-1833j 1.06e-478, 1.06e-478j
-0.87902558400256699957 + 4.1212329556812944008e-1836j 9.91e-481, 9.91e-481j
-0.77304072217807722869 + 2.5290985360925639564e-1851j 1.15e-484, 1.15e-484j
0.9985033617835308753 + 2.1713361485866017328e-1843j 7.44e-479, 7.44e-479j
0.74824654784780181402 + 1.9816468980369778588e-1862j 1.71e-485, 1.71e-485j
0.84035449227944888752 + 1.4413670532409080866e-1857j 2.17e-482, 2.17e-482j
-0.99975284743748866209 - 5.7633537518116985513e-1853j 2.67e-479, 2.67e-479j
-0.66729704788913271822 + 7.5268388677300175556e-1893j 4.54e-488, 4.54e-488j
0.98035068300028038832 - 8.5598203764229503748e-1881j 8.09e-479, 8.09e-479j
0.8928107582522787686 - 6.6255729961075381156e-1891j 1.06e-479, 1.06e-479j
0.72233236096349723369 + 9.8331236354454470388e-1912j 2.53e-486, 2.53e-486j
-0.99206935952458725579 - 1.7972844393664400733e-1901j 1.03e-478, 1.03e-478j
-0.74824654784780181402 + 6.252400695421282997e-1940j 1.86e-485, 1.86e-485j
-0.86032780093317475415 - 2.4368393696952177964e-1934j 1.29e-481, 1.29e-481j
-0.9868731177910260499 + 3.829865155284466128e-1950j 9.93e-479, 9.93e-479j
0.57735026918962576451 + 1.8938571687546175998e-1990j 6.09e-491, 6.09e-491j
0.97246818630922115364 - 4.6411741633035464366e-1977j 5.68e-479, 5.68e-479j
-0.98035068300028038832 + 7.9310979895283453661e-1981j 8.12e-479, 8.12e-479j
-0.57735026918962576451 + 2.2499385364054989023e-2008j 6.04e-491, 6.04e-491j
-0.54557221397321554183 - 5.0335160529568338598e-2009j 5.59e-492, 5.59e-492j
0.69533579136017117188 - 8.3433047201608975852e-2003j 3.44e-487, 3.44e-487j
0.66729704788913271822 + 2.4990509622681968126e-2003j 4.46e-488, 4.46e-488j
-0.69533579136017117188 - 3.5309752314613528109e-2004j 3.6e-487, 3.6e-487j
-0.60826087804424837241 + 1.5325303950997978977e-2007j 5.63e-490, 5.63e-490j
-0.63825786066849826941 + 1.1070280529998328285e-2005j 5.46e-489, 5.46e-489j
0.96320947642682331194 - 7.09021293881019676e-1998j 3.67e-479, 3.67e-479j
0.47960424805625979706 + 6.9692667899607425217e-2014j 3.68e-494, 3.68e-494j
0.51297422214928271025 - 4.588493155790974641e-2013j 4.75e-493, 4.75e-493j
-0.84035449227944888752 - 1.2141667489012815171e-2002j 2.2e-482, 2.2e-482j
-0.47960424805625979706 + 9.0847007210807510275e-2016j 3.83e-494, 3.83e-494j
0.077159460936340872255 + 2.1935406388485461286e-2030j 4.22e-508, 4.22e-508j
0.63825786066849826941 - 9.784877998338292557e-2013j 5.25e-489, 5.25e-489j
0.60826087804424837241 + 1.4507925906483680605e-2012j 5.94e-490, 5.94e-490j
-0.19012288010294503036 + 2.8352274597367765478e-2026j 1.82e-503, 1.82e-503j
-0.51297422214928271025 - 4.0678076850621222412e-2015j 4.57e-493, 4.57e-493j
-0.89639894566995214562 + 1.5770410089064608681e-2010j 1.3e-479, 1.3e-479j
0.79667953649742200176 + 5.0718460143569202947e-2016j 7.21e-484, 7.21e-484j
0.44551098658899530318 + 5.6078733551240477187e-2029j 2.73e-495, 2.73e-495j
0.77304072217807722869 - 2.8530058062065862799e-2021j 1.14e-484, 1.14e-484j
-0.16268981350277032876 - 2.2777553848326720847e-2039j 8.78e-504, 8.78e-504j
-0.41074467808495256322 + 1.9244704262421469478e-2031j 1.91e-496, 1.91e-496j
-0.077159460936340872255 - 7.258861322792002975e-2044j 4.15e-508, 4.15e-508j
0.54557221397321554183 - 2.5441476598459404849e-2028j 5.41e-492, 5.41e-492j
0.37535635160613926943 + 1.0981213133950009732e-2033j 1.16e-497, 1.16e-497j
-0.038596381447100407696 - 5.414238440901780671e-2045j 1.17e-509, 1.17e-509j
-0.37535635160613926943 - 8.9991229186801972488e-2034j 1.15e-497, 1.15e-497j
-0.72233236096349723369 - 2.087920327118356702e-2036j 2.48e-486, 2.48e-486j
0.41074467808495256322 + 4.0021325490955117258e-2047j 1.84e-496, 1.84e-496j
0.33939515608281001006 + 8.0532962919067515764e-2051j 7.39e-499, 7.39e-499j
0.11574191404350462325 - 1.039803581131650879e-2057j 1.85e-506, 1.85e-506j
-0.44551098658899530318 - 3.0680135655916781425e-2046j 2.59e-495, 2.59e-495j
-0.33939515608281001006 + 2.6596046332152469284e-2050j 7.24e-499, 7.24e-499j
-2.4246989601823014676e-2110 + 6.5715701111495898518e-2110j 6.09e-2108, 6.09e-2108j
0.30290567277598982598 + 4.947409881447363977e-2051j 4.17e-500, 4.17e-500j
0.16268981350277032876 - 3.8667686889068687654e-2055j 8.91e-504, 8.91e-504j
-0.11574191404350462325 - 8.1197737479451388614e-2058j 1.79e-506, 1.79e-506j
-0.30290567277598982598 - 2.4821209592723729078e-2052j 4.35e-500, 4.35e-500j
-0.15655801081562154215 - 1.2921982650956809962e-2055j 5.01e-504, 5.01e-504j
0.19012288010294503036 + 1.0837247226114252891e-2054j 1.91e-503, 1.91e-503j
0.26592387515597359985 + 2.592488718358648774e-2052j 2.59e-501, 2.59e-501j
0.038596381447100407696 - 7.3117330084932641567e-2061j 1.55e-509, 1.55e-509j
-0.26592387515597359985 + 3.7604032018885348648e-2054j 2.6e-501, 2.6e-501j
-0.22844979333481706632 + 2.6916156591597009941e-2054j 1.7e-502, 1.7e-502j
0.15655801081562154215 + 6.2414724714258333799e-2055j 4.86e-504, 4.86e-504j
0.22844979333481706632 - 1.1350252023835356815e-2053j 1.78e-502, 1.78e-502j

Weights

Weight (ball center) Error (ball radius)
0.0032212729524776051908 - 6.838394288167548576e-1768j 1.7e-124, 4.35e-355j
0.00994611030367054293 + 1.280194857912270324e-1767j 8.87e-125, 2.28e-355j
0.014048463825917686439 - 1.3696361402372834998e-1767j 4.52e-125, 1.16e-355j
0.0032212729524776051908 - 7.0803223607467142815e-1770j 5.74e-126, 1.47e-356j
0.015406542324704633522 + 8.8064038782969045295e-1769j 4.95e-126, 1.27e-356j
0.014048463825917686439 - 4.8953191710942186491e-1769j 4.11e-126, 1.06e-356j
0.0018805118095198646503 - 3.4517072288085732394e-1767j 6.9e-126, 1.77e-356j
0.015406542324704633522 + 2.0135717765314162824e-1767j 4.22e-126, 1.08e-356j
0.0085701920761274000933 - 1.4929720134930710192e-1767j 6.74e-126, 1.73e-356j
0.0058538661601239588455 - 1.225231342261656213e-1769j 4.94e-128, 1.27e-358j
0.018055272357066629158 - 1.3415857930430044337e-1768j 4.79e-128, 1.23e-358j
0.011314541094336791344 - 2.6372150762668911245e-1769j 2.85e-128, 7.32e-359j
0.012681425948732943595 + 1.1962410627243161791e-1767j 2.44e-126, 6.27e-357j
-9.7046122106579677513e-05 + 9.8328312360867171117e-1767j 1.99e-127, 5.11e-358j
0.00066716596558203871868 - 1.5155688441304728323e-1770j 4.46e-129, 1.14e-359j
0.019338689850154112707 + 5.9030565447869567666e-1769j 3.49e-129, 8.95e-360j
0.016822128580988835052 - 4.9828946061591031209e-1768j 3.63e-128, 9.32e-359j
0.011314541094336791344 - 1.1847317100677697591e-1767j 1.63e-127, 4.19e-358j
0.023049623587154286049 - 2.0707111954342089929e-1768j 9.64e-132, 2.47e-362j
0.021842828503054004303 + 2.9201073865018380914e-1768j 2.21e-131, 5.67e-362j
0.012681425948732943595 + 3.4204666670744005867e-1769j 7.83e-130, 2.01e-360j
0.021842828503054004303 + 2.84475601107581121e-1769j 9.84e-133, 2.53e-363j
0.0045413181335679934967 + 9.6573836366737206322e-1770j 1.69e-130, 4.33e-361j
0.018055272357066629158 - 2.1512867313886875498e-1767j 8.54e-132, 2.19e-362j
0.024222268327930583592 + 1.5593425184174894794e-1768j 5.61e-134, 1.44e-364j
0.0018805118095198646503 + 4.4137299192564484091e-1770j 1.88e-130, 4.84e-361j
0.025360220084301292766 - 1.7452137530290887924e-1769j 3.37e-136, 8.64e-367j
0.020604056923799795579 - 3.8106581514033230667e-1769j 3.13e-133, 8.05e-364j
0.00066716596558203871868 + 7.9599382593878417873e-1768j 5.76e-134, 1.48e-364j
0.02854599299157509185 + 7.3631360714822373224e-1769j 6.04e-139, 1.55e-369j
0.0071974648520204179793 + 1.490509997848517722e-1769j 6.22e-132, 1.6e-362j
-9.7046122106579677513e-05 + 5.3695468751072285938e-1768j 4.81e-131, 1.23e-361j
0.026461887438327370881 + 1.6001622461377885387e-1769j 1.34e-137, 3.45e-368j
0.0045413181335679934967 + 4.9435412458988396026e-1767j 1.76e-134, 4.52e-365j
0.025360220084301292766 - 1.2288742079265918267e-1768j 1.11e-138, 2.86e-369j
0.019338689850154112707 + 8.079419025472508421e-1768j 2.27e-136, 5.82e-367j
0.0058538661601239588455 - 2.6755987968693599231e-1767j 4.86e-135, 1.25e-365j
0.031352179044261089604 - 1.4910564743631738829e-1769j 4.38e-145, 1.13e-375j
0.0085701920761274000933 - 1.7812354888886771279e-1769j 7.64e-136, 1.96e-366j
0.0071974648520204179793 + 1.887985233449106054e-1767j 3.86e-135, 9.91e-366j
0.031352179044261089604 - 5.6040816781881397171e-1769j 5.26e-145, 1.35e-375j
0.032195993648134625393 + 5.368808298590707337e-1769j 1.05e-145, 2.69e-376j
0.027524526585793251116 - 1.5074855350640601107e-1769j 3.57e-144, 9.17e-375j
0.02854599299157509185 + 1.4549458080840728238e-1769j 3.11e-145, 7.99e-376j
0.027524526585793251116 - 8.481194996078252818e-1769j 2.81e-143, 7.22e-374j
0.030461327481679114557 + 5.9913564518088889981e-1769j 3.67e-145, 9.43e-376j
0.029525287904337452616 - 6.560715612200078172e-1769j 1.42e-144, 3.64e-375j
0.00994611030367054293 + 2.1395944060190939691e-1769j 3.31e-140, 8.49e-371j
0.033739847983692270489 + 1.858172228273022584e-1769j 5.89e-151, 1.51e-381j
0.032992004459876408958 - 1.68713866865120194e-1769j 2.12e-150, 5.44e-381j
0.020604056923799795579 - 4.4971760337436906971e-1768j 1.65e-142, 4.24e-373j
0.033739847983692270489 + 5.3100532903229726874e-1769j 2.01e-150, 5.15e-381j
0.038547413307207927575 + 1.5833710468629169245e-1768j 4.98e-155, 1.28e-385j
0.029525287904337452616 - 1.4360057844007486236e-1769j 1.41e-148, 3.61e-379j
0.030461327481679114557 + 1.4479377552038071278e-1769j 3.55e-149, 9.1e-380j
0.039562764937170897981 + 5.5147307339461354659e-1768j 3.84e-156, 9.86e-387j
0.032992004459876408958 - 5.2709755932274448025e-1769j 1.14e-150, 2.93e-381j
0.016822128580988835052 - 9.4716257392342522328e-1767j 2.51e-143, 6.44e-374j
0.023049623587154286049 - 2.3018540736361186156e-1769j 1.99e-147, 5.1e-378j
0.034438290271169846142 - 2.1007804043893260232e-1769j 2.06e-154, 5.28e-385j
0.024222268327930583592 + 1.9649399084667725579e-1769j 7.17e-148, 1.84e-378j
-0.024814283701075668345 - 2.6722514926368680487e-1767j 1.11e-157, 2.85e-388j
0.035085770633550349317 + 5.8823931175423318303e-1769j 7.42e-156, 1.91e-386j
0.038547413307207927575 + 1.8493112107691179204e-1768j 1.07e-158, 2.74e-389j
0.032195993648134625393 + 1.5685816885228445987e-1769j 3.83e-153, 9.82e-384j
0.035682644651208443885 - 2.9540209223986140147e-1769j 1.37e-157, 3.51e-388j
0.03858264413907336587 - 1.4530414252467527931e-1768j 1.54e-159, 3.96e-390j
0.035682644651208443885 - 6.5273900720756467339e-1769j 6.04e-158, 1.55e-388j
0.026461887438327370881 + 1.0048712342380010356e-1768j 1.08e-152, 2.78e-383j
0.035085770633550349317 + 2.447167979737933806e-1769j 3.65e-157, 9.37e-388j
0.036232280622299656094 + 3.7291264811058970028e-1769j 4.85e-159, 1.25e-389j
0.038696972748536163824 - 2.3972580981734933478e-1768j 2.7e-161, 6.94e-392j
0.034438290271169846142 - 5.5013954497779150347e-1769j 6.17e-158, 1.58e-388j
0.036232280622299656094 + 7.584529060504636344e-1769j 6.23e-160, 1.6e-390j
0.038603625643902858451 + 1.3161871688853687221e-1768j 1.33e-161, 3.42e-392j
0.036740431431182842837 - 5.0027152287569797343e-1769j 2.34e-161, 6.02e-392j
-0.024814283701075668345 - 1.9218078185248648245e-1767j 1.74e-162, 4.48e-393j
0.038696972748536163824 - 3.0277051240936485215e-1768j 6.75e-162, 1.73e-392j
0.036740431431182842837 - 9.3757232258973266279e-1769j 2.23e-162, 5.71e-393j
0.059642139990562466407 + 2.447139246239908563e-1767j 2.62e-161, 6.73e-392j
0.039562764937170897981 + 3.7467553801616149658e-1768j 8.91e-164, 2.29e-394j
0.037221157543511369953 + 7.3615375988436244138e-1769j 6.82e-164, 1.75e-394j
0.03858264413907336587 - 1.3446229381643522126e-1768j 1.22e-163, 3.14e-394j
0.037221157543511369953 + 1.2724634639892702901e-1768j 4.24e-164, 1.09e-394j
0.037753995526849397438 - 2.0496138798339525325e-1768j 5.73e-164, 1.47e-394j
0.059642139990562466407 + 1.7822965881520565802e-1767j 6.6e-164, 1.71e-394j
0.037753995526849397438 - 1.2847775733705545617e-1768j 4.86e-165, 1.24e-395j

Download

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