Rule: Q[8, 34, 43]

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)
-0.9997204887247897498 + 1.3421801431498937085e-1834j 1.46e-480, 1.46e-480j
-0.97003590406850542458 - 1.2442039979823448787e-1854j 3.81e-480, 3.81e-480j
-0.90877598962425348466 + 1.4951277784657189897e-1873j 2.08e-481, 2.08e-481j
-0.9954784430647757014 - 1.5600206450324259598e-1880j 5.79e-480, 5.79e-480j
0.93697787409570507852 - 4.5998817851571611504e-1897j 8.91e-481, 8.91e-481j
0.9234788957504865991 + 5.0020528833897680033e-1898j 4.79e-481, 4.79e-481j
0.99117777590470037198 + 4.2844484465286266501e-1895j 6.22e-480, 6.22e-480j
-0.9234788957504865991 - 8.2018175577499047126e-1904j 4.3e-481, 4.3e-481j
-0.97843964888199510446 + 2.0815271231951707439e-1911j 4.98e-480, 4.98e-480j
0.97843964888199510446 + 6.3293852137102770347e-1925j 4.86e-480, 4.86e-480j
0.85778834031142911844 - 8.9317273809237388912e-1929j 1.15e-482, 1.15e-482j
0.9954784430647757014 - 1.8355756895669454344e-1924j 6.19e-480, 6.19e-480j
-0.94925430572982692442 - 3.2765228334434753965e-1928j 1.56e-480, 1.56e-480j
-0.83852801286566864936 + 3.3297433557166707063e-1939j 3.63e-483, 3.63e-483j
0.9997204887247897498 + 1.2019858872219095295e-1932j 1.42e-480, 1.42e-480j
0.8759146438048195034 - 8.2968421745329501474e-1941j 3.27e-482, 3.27e-482j
0.89291043296926433527 + 7.0116978990287764964e-1941j 9.02e-482, 9.02e-482j
0.98548604753859052152 - 1.0537056283089577897e-1936j 6.57e-480, 6.57e-480j
-0.7740751019926284172 - 4.2317960456843934495e-1950j 5.59e-485, 5.59e-485j
-0.96028985649753623168 - 1.6902192955139516352e-1946j 2.55e-480, 2.55e-480j
0.90877598962425348466 + 1.5258829840210794249e-1970j 2.11e-481, 2.11e-481j
0.79666647741362673959 + 1.5425382576363945437e-1975j 2.49e-484, 2.49e-484j
-0.98548604753859052152 + 2.0660330533962465111e-1968j 6.17e-480, 6.17e-480j
-0.89291043296926433527 - 4.7417126897453371286e-1987j 8.57e-482, 8.57e-482j
-0.79666647741362673959 + 9.1342925881019425608e-1996j 2.56e-484, 2.56e-484j
0.99832037416984394053 + 7.0478988397382489068e-1990j 4.11e-480, 4.11e-480j
0.7256189546140015131 + 3.6020182653608718562e-1999j 2.27e-486, 2.27e-486j
0.83852801286566864936 - 6.6946020930942579445e-1997j 3.76e-483, 3.76e-483j
-0.85778834031142911844 + 6.443406208755555255e-1992j 1.17e-482, 1.17e-482j
-0.64524043728326823552 - 9.7286967667462982582e-2003j 9.19e-489, 9.19e-489j
-0.93697787409570507852 - 1.2495245702240670915e-1992j 8.48e-481, 8.48e-481j
0.7740751019926284172 - 5.2956082450300844445e-2024j 6.28e-485, 6.28e-485j
0.69981930882596395391 - 7.825259423097480439e-2028j 3.63e-487, 3.63e-487j
-0.99832037416984394053 - 2.8265517875564915103e-2018j 4.13e-480, 4.13e-480j
-0.81814978132512159638 - 5.3266174286044529359e-2048j 1.04e-483, 1.04e-483j
-0.75038252812253361829 - 1.0858952651138982309e-2051j 1.19e-485, 1.19e-485j
-0.5870066479770320582 + 5.9174267123847864855e-2056j 1.5e-490, 1.5e-490j
0.61655322632546962265 - 3.8785870175163305649e-2054j 1.05e-489, 1.05e-489j
0.94925430572982692442 - 2.1333415196578080438e-2043j 1.58e-480, 1.58e-480j
-0.99117777590470037198 - 2.0440262370552496409e-2052j 6.43e-480, 6.43e-480j
-0.55664945370254513497 - 5.0393993075317825974e-2078j 1.5e-491, 1.5e-491j
-0.073761583831423372732 - 3.0533107463392997907e-2094j 2.65e-508, 2.65e-508j
0.67301355968167539674 - 9.9637751284134221436e-2074j 5.72e-488, 5.72e-488j
0.64524043728326823552 - 2.6138005510515957818e-2075j 8.82e-489, 8.82e-489j
0.97003590406850542458 + 1.6908210954392899312e-2064j 3.64e-480, 3.64e-480j
-0.52553240991632898582 - 1.1334206120256002161e-2083j 1.36e-492, 1.36e-492j
-0.69981930882596395391 - 2.4221194423135242284e-2078j 3.53e-487, 3.53e-487j
0.96028985649753623168 - 2.0847011104423961506e-2074j 2.64e-480, 2.64e-480j
0.49371226184585709053 - 6.377178425276305569e-2087j 1.36e-493, 1.36e-493j
0.21952766343009901555 + 5.6945101511319552064e-2096j 4.85e-503, 4.85e-503j
-0.7256189546140015131 + 7.3857681621249091619e-2079j 2.23e-486, 2.23e-486j
-0.46124311661959894904 - 1.7876091165232184651e-2087j 1.18e-494, 1.18e-494j
0.81814978132512159638 - 7.4394968561998387631e-2077j 1.02e-483, 1.02e-483j
0.55664945370254513497 - 1.8306054398719044601e-2085j 1.45e-491, 1.45e-491j
0.5870066479770320582 + 5.476020199396832332e-2084j 1.36e-490, 1.36e-490j
0.073761583831423372732 + 3.6294784025880604396e-2101j 2.25e-508, 2.25e-508j
-0.67301355968167539674 - 7.869617764895703549e-2081j 5.99e-488, 5.99e-488j
-0.8759146438048195034 - 2.8817505582023652754e-2085j 3.43e-482, 3.43e-482j
0.11050211792867690275 - 1.922102344564766721e-2109j 5.44e-507, 5.44e-507j
0.42817127151684024839 - 3.6559910673583324564e-2097j 8.73e-496, 8.73e-496j
0.75038252812253361829 - 4.6403116110060809483e-2094j 1.19e-485, 1.19e-485j
-0.42817127151684024839 + 2.635084839661657573e-2102j 8.9e-496, 8.9e-496j
-0.39454119918649796261 - 3.3861161352276178413e-2103j 6.46e-497, 6.46e-497j
-0.49371226184585709053 + 1.4145406954639119636e-2099j 1.26e-493, 1.26e-493j
0.46124311661959894904 + 1.0466171930849779143e-2101j 1.15e-494, 1.15e-494j
0.52553240991632898582 + 7.7523184981009186499e-2100j 1.36e-492, 1.36e-492j
-0.036909197537821205694 + 2.9467090442525115916e-2117j 1.37e-509, 1.37e-509j
-0.36039924529648698982 + 1.7101282775317573499e-2104j 4.12e-498, 4.12e-498j
-0.61655322632546962265 - 2.1330340176516503415e-2106j 1.14e-489, 1.14e-489j
0.36039924529648698982 + 4.7187263051147028525e-2114j 4.08e-498, 4.08e-498j
0.32578858192130330182 - 6.6105908751042719307e-2116j 2.89e-499, 2.89e-499j
0.14707705646955515679 - 2.977297248323506071e-2122j 1.11e-505, 1.11e-505j
-0.25531276429021805999 - 2.6942555261391528941e-2118j 9.29e-502, 9.29e-502j
-0.32578858192130330182 + 1.5204633024452205344e-2115j 2.7e-499, 2.7e-499j
-2.7749700214619290677e-2171 - 1.4027402524567176848e-2171j 2.64e-2169, 2.64e-2169j
0.25531276429021805999 + 7.2583342038751124591e-2118j 9.66e-502, 9.66e-502j
0.39454119918649796261 - 4.8064076262307489437e-2113j 6.61e-497, 6.61e-497j
-0.11050211792867690275 - 7.6920958851162816084e-2124j 5.54e-507, 5.54e-507j
-0.2907470327947588496 - 2.1341871549969188946e-2117j 1.77e-500, 1.77e-500j
-0.14707705646955515679 + 7.1152176083384718617e-2122j 1.1e-505, 1.1e-505j
0.18343464249564980494 + 5.4217216939363158799e-2121j 2.39e-504, 2.39e-504j
0.2907470327947588496 - 9.703291307341139583e-2117j 1.89e-500, 1.89e-500j
0.036909197537821205694 + 8.5171475282566469733e-2127j 1.17e-509, 1.17e-509j
-0.18343464249564980494 - 1.0478623650782831276e-2120j 2.53e-504, 2.53e-504j
-0.21952766343009901555 + 1.9907338490945183314e-2119j 5.16e-503, 5.16e-503j

Weights

Weight (ball center) Error (ball radius)
0.00075208017756146905986 + 1.4359540970647369575e-1834j 5.23e-136, 2.97e-367j
0.0090812704414575720038 + 5.1826209893860339076e-1835j 2.01e-136, 1.14e-367j
0.015291989319972309728 - 4.049146906029057382e-1835j 6.88e-137, 3.91e-368j
0.0035813836646771691752 + 1.1736641123174182727e-1834j 1.9e-136, 1.08e-367j
0.012889195296700021715 - 1.4003732547908843577e-1836j 2.15e-137, 1.22e-368j
0.01410619525485787916 + 1.6549621402089476772e-1836j 1.86e-137, 1.06e-368j
0.0050068626855164117267 - 3.5848548855924862105e-1837j 1.19e-138, 6.78e-370j
0.01410619525485787916 + 4.1746532899076341864e-1835j 7.43e-138, 4.22e-369j
0.0077241097659169920755 - 5.8002519860444176141e-1835j 1e-137, 5.68e-369j
0.0077241097659169920755 - 6.2398504153559508459e-1837j 1e-138, 5.69e-370j
0.018694524029369031462 + 2.7935492973268603272e-1836j 1.04e-139, 5.91e-371j
0.0035813836646771691752 + 2.4953585703380150392e-1837j 3.96e-139, 2.25e-370j
0.011661353172992803705 + 4.5093042875303193159e-1835j 2.11e-138, 1.2e-369j
0.019822844604685737012 - 3.4867327914527078355e-1835j 1.93e-140, 1.1e-371j
0.00075208017756146905986 + 5.0485465275761311899e-1838j 9.75e-140, 5.54e-371j
0.017559188979114230238 - 2.5118111117720457379e-1836j 1.53e-140, 8.71e-372j
0.016433154917425876032 + 2.2192912539068412659e-1836j 1.53e-140, 8.69e-372j
0.0063704298196350577928 + 4.8348183247388208214e-1837j 6.47e-140, 3.67e-371j
0.023145334813110440952 + 2.9093597283098697805e-1835j 5.05e-144, 2.87e-375j
0.010401066528980383968 - 4.7751785663763651856e-1835j 8.45e-141, 4.8e-372j
0.015291989319972309728 - 1.9295169853907916147e-1836j 9.9e-141, 5.63e-372j
0.02203655520903466654 - 3.5138956700136225503e-1836j 2.48e-144, 1.41e-375j
0.0063704298196350577928 + 6.7428800431050065892e-1835j 3.29e-141, 1.87e-372j
0.016433154917425876032 + 3.9324942035450359624e-1835j 1.28e-142, 7.3e-374j
0.02203655520903466654 - 3.1086883441615942592e-1835j 1.7e-144, 9.65e-376j
0.0021008689008822217031 - 1.4995462005959223741e-1837j 1.04e-140, 5.93e-372j
0.025286806615149235433 + 4.024248516308672021e-1836j 9.05e-147, 5.14e-378j
0.019822844604685737012 - 3.0574489293867069725e-1836j 1.46e-143, 8.27e-375j
0.018694524029369031462 + 3.6560022110143041932e-1835j 1.41e-144, 8e-376j
0.02823971862489082292 - 2.0840986627691304442e-1835j 1.53e-149, 8.71e-381j
0.012889195296700021715 - 4.322581400096617603e-1835j 8.41e-143, 4.78e-374j
0.023145334813110440952 + 3.7010104460341970796e-1836j 1.22e-146, 6.92e-378j
0.026307835909369432608 - 4.1755956516143412721e-1836j 1.71e-148, 9.69e-380j
0.0021008689008822217031 - 2.1399353174390868753e-1834j 7.8e-144, 4.43e-375j
0.020931175488304009356 + 3.3031991469484107524e-1835j 4.58e-146, 2.6e-377j
0.024234315391752325422 - 2.7150339470102663245e-1835j 2.53e-148, 1.44e-379j
0.029959806321602234482 - 1.8711741981616092379e-1835j 2.7e-152, 1.53e-383j
0.029125429656062222151 + 4.6697520247549528485e-1836j 3.31e-153, 1.88e-384j
0.011661353172992803705 + 1.1676260565399253291e-1836j 8.12e-148, 4.61e-379j
0.0050068626855164117267 - 8.3545842181312594989e-1835j 4.24e-145, 2.41e-376j
0.030746214945082382224 + 1.7858884043150389248e-1835j 1.44e-153, 8.16e-385j
0.036805494201913832164 + 1.0676959511754981443e-1835j 7.88e-158, 4.48e-389j
0.027297336338336700607 + 4.3285158217009284259e-1836j 3.49e-152, 1.98e-383j
0.02823971862489082292 - 4.491118235740929825e-1836j 6.66e-153, 3.78e-384j
0.0090812704414575720038 + 7.8103034498951883833e-1837j 1.02e-148, 5.82e-380j
0.031478212457372656089 - 1.712057832575720816e-1835j 9.7e-156, 5.51e-387j
0.026307835909369432608 - 2.3663097927098986932e-1835j 3.46e-153, 1.97e-384j
0.010401066528980383968 - 9.6064957171893101457e-1837j 6.78e-149, 3.85e-380j
0.032152953947735418461 + 5.5824497127293327325e-1836j 1.89e-158, 1.07e-389j
0.035946162851105309348 + 7.9852367099044549082e-1836j 2.89e-161, 1.64e-392j
0.025286806615149235433 + 2.5330740003004189019e-1835j 4.38e-153, 2.49e-384j
0.032777770206811241795 - 1.5900004547373660868e-1835j 9.9e-159, 5.62e-390j
0.020931175488304009356 + 3.299268466373765182e-1836j 7.28e-152, 4.14e-383j
0.030746214945082382224 + 5.0841088751688797015e-1836j 1.52e-157, 8.66e-389j
0.029959806321602234482 - 4.8669961719858503942e-1836j 1.27e-156, 7.24e-388j
0.036805494201913832164 + 9.2096794067119826385e-1836j 1.62e-163, 9.18e-395j
0.027297336338336700607 + 2.2161929088041269653e-1835j 2.82e-156, 1.6e-387j
0.017559188979114230238 - 3.8053463231589069599e-1835j 1.7e-153, 9.66e-385j
0.036666609574525321512 - 8.8915137102041428399e-1836j 1.66e-163, 9.45e-395j
0.03335859130299244076 + 6.1522055331532396571e-1836j 6.51e-162, 3.7e-393j
0.024234315391752325422 - 3.8681210237150909113e-1836j 2.04e-155, 1.16e-386j
0.03335859130299244076 + 1.5369951219627515372e-1835j 1.98e-162, 1.12e-393j
0.033893701161755242384 - 1.487008849151287774e-1835j 1.8e-163, 1.02e-394j
0.032152953947735418461 + 1.6476042851766509662e-1835j 3.73e-161, 2.12e-392j
0.032777770206811241795 - 5.8603736833759839962e-1836j 7.51e-163, 4.27e-394j
0.031478212457372656089 - 5.3226413479452632869e-1836j 1.65e-161, 9.35e-393j
0.036890126639903825342 - 1.0275659744001076182e-1835j 2.21e-167, 1.26e-398j
0.034382958261929931752 + 1.4387607909583320013e-1835j 2.02e-165, 1.14e-396j
0.029125429656062222151 + 1.9697918361168296123e-1835j 3.33e-161, 1.89e-392j
0.034382958261929931752 + 6.7628629661289807194e-1836j 2.74e-166, 1.56e-397j
0.034832197967497847105 - 7.0728076971544323877e-1836j 6.76e-167, 3.84e-398j
0.03647457879464433915 + 8.5847992447464433111e-1836j 4.52e-168, 2.57e-399j
0.035616871867701416124 - 1.2955481042168165821e-1835j 2.23e-169, 1.27e-400j
0.034832197967497847105 - 1.3911005938241482338e-1835j 5.06e-168, 2.88e-399j
0.036918760947126672571 + 9.8983012497670298065e-1836j 1.75e-169, 9.96e-401j
0.035616871867701416124 - 7.6843861613922605976e-1836j 5.64e-169, 3.2e-400j
0.033893701161755242384 - 6.4543619513397069032e-1836j 1.62e-167, 9.19e-399j
0.036666609574525321512 - 1.1101389549115951255e-1835j 1.2e-170, 6.8e-402j
0.035244607320571611686 + 1.3433724319086551177e-1835j 3.98e-170, 2.26e-401j
0.03647457879464433915 + 1.1546475733497970942e-1835j 3.17e-171, 1.8e-402j
0.036232736097536590792 - 8.284333233500004227e-1836j 1.38e-170, 7.86e-402j
0.035244607320571611686 + 7.3803902831271814078e-1836j 2.29e-170, 1.3e-401j
0.036890126639903825342 - 9.5439300620349880788e-1836j 3.84e-171, 2.18e-402j
0.036232736097536590792 - 1.2007621373364006755e-1835j 2.85e-172, 1.62e-403j
0.035946162851105309348 + 1.2478947238963598613e-1835j 2.76e-172, 1.56e-403j

Download

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