Rule: Q[2, 3, 6, 12, 24]

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)
0.9994073121541606647 + 1.6996908463686630833e-881j 1.15e-235, 1.15e-235j
0.9943548302018225407 + 1.2773505918620372612e-899j 2.13e-235, 2.13e-235j
-0.92582009977255146157 + 1.1866280511520591653e-911j 1.18e-237, 1.18e-237j
-0.99789629329501009199 - 8.1445929658984504333e-908j 2.58e-235, 2.58e-235j
0.94762394404543075549 + 7.4564128980297829119e-911j 4.55e-237, 4.55e-237j
0.97829968677949671651 + 5.2211372820142282767e-909j 4.62e-236, 4.62e-236j
-0.9943548302018225407 - 1.1983075645824249312e-915j 2.03e-235, 2.03e-235j
-0.94762394404543075549 - 1.0041372267663707895e-920j 4.64e-237, 4.64e-237j
-0.98785368285261173498 + 9.5264447943035733653e-918j 1.02e-235, 1.02e-235j
0.96502643103930765951 + 8.237880705424599877e-916j 1.56e-236, 1.56e-236j
0.92582009977255146157 - 6.0574717245282750144e-921j 1.16e-237, 1.16e-237j
-0.9994073121541606647 + 8.7908169508065669339e-931j 1.12e-235, 1.12e-235j
-0.89933770191560515435 - 1.4278078224997558075e-934j 2.58e-238, 2.58e-238j
-0.86794828602803889807 + 2.4439556648224845009e-935j 4.58e-239, 4.58e-239j
0.98785368285261173498 - 1.5481868901723203797e-930j 1e-235, 1e-235j
0.83153029173181677019 - 6.3227189111319410982e-950j 7.16e-240, 7.16e-240j
0.86794828602803889807 - 3.3811378690406245486e-947j 4.52e-239, 4.52e-239j
-0.97829968677949671651 + 1.6764551095091988257e-950j 4.88e-236, 4.88e-236j
-0.74371458010679239394 + 3.5071532015889368783e-958j 1.1e-241, 1.1e-241j
-0.96502643103930765951 + 4.8791430873013897144e-953j 1.58e-236, 1.58e-236j
0.89933770191560515435 - 8.2363630283512007812e-955j 2.43e-238, 2.43e-238j
0.79008322340119373077 - 2.0467914431326544309e-965j 9.16e-241, 9.16e-241j
0.99789629329501009199 - 5.5515587123852724909e-992j 2.23e-235, 2.23e-235j
-0.83153029173181677019 - 2.1025713090044987015e-1013j 7.38e-240, 7.38e-240j
-0.79008322340119373077 + 4.7722932626645202447e-1017j 9.36e-241, 9.36e-241j
0.23037270405390110293 - 3.2239377400258048098e-1026j 1.69e-251, 1.69e-251j
0.74371458010679239394 - 7.616431643001528703e-1019j 1.01e-241, 1.01e-241j
0.57735026918962576451 - 1.3707147832236632936e-1021j 5.76e-245, 5.76e-245j
-0.30476216915276288265 + 5.1554382410995190881e-1031j 3.78e-250, 3.78e-250j
-0.6926188473346906128 - 1.1487761203250885088e-1021j 1.03e-242, 1.03e-242j
-0.23037270405390110293 - 6.9609461514712825618e-1031j 1.69e-251, 1.69e-251j
0.6926188473346906128 - 5.0848152774041806025e-1021j 9.94e-243, 9.94e-243j
0.63705857890684353822 - 3.1089669611231260352e-1024j 8.07e-244, 8.07e-244j
0.15444378242844441647 - 9.5271950501225370335e-1033j 5.75e-253, 5.75e-253j
-0.57735026918962576451 + 8.1193374562406481884e-1023j 5.4e-245, 5.4e-245j
-0.63705857890684353822 + 1.8445050853457939081e-1024j 8.47e-244, 8.47e-244j
0.07748135076194010496 - 5.0883819266873742233e-1035j 2.64e-254, 2.64e-254j
0.51385435850953775564 + 1.0453201048408656866e-1025j 3.46e-246, 3.46e-246j
0.30476216915276288265 + 2.2652762359236317237e-1030j 3.74e-250, 3.74e-250j
-0.15444378242844441647 - 2.352508105858662682e-1034j 6.08e-253, 6.08e-253j
-0.51385435850953775564 - 7.25581560685721767e-1027j 3.55e-246, 3.55e-246j
-0.07748135076194010496 + 2.0260587802689766538e-1035j 2.64e-254, 2.64e-254j
0.3771191758151618032 - 1.9619229455123768083e-1029j 8.25e-249, 8.25e-249j
0.44696796404999669242 - 2.2695099516346126797e-1027j 1.85e-247, 1.85e-247j
1.6827341871880621999e-1058 - 1.8829672714925164522e-1059j 7.96e-1057, 7.96e-1057j
-0.44696796404999669242 - 2.2614009300398049578e-1028j 1.77e-247, 1.77e-247j
-0.3771191758151618032 - 9.2934204936763999849e-1031j 8.71e-249, 8.71e-249j

Weights

Weight (ball center) Error (ball radius)
0.0013007701035269931187 - 2.4802986478064073711e-881j 4.35e-58, 1.15e-169j
0.005098056306415712393 - 8.5325517218715988726e-882j 3.25e-58, 8.58e-170j
0.024098306637720057561 + 1.2981366033033150003e-885j 4.08e-59, 1.08e-170j
0.0020350610607348240039 + 2.3798773029913093069e-884j 1.77e-59, 4.67e-171j
0.019557024096029771973 - 9.3997765189937197217e-884j 1.05e-59, 2.78e-171j
0.011316627477342627322 - 8.1719960795795330321e-883j 1.8e-59, 4.76e-171j
0.005098056306415712393 - 2.1622721520434262447e-884j 1.16e-59, 3.06e-171j
0.019557024096029771973 - 2.4999705889310610915e-885j 9.02e-61, 2.38e-172j
0.0079222101064478182543 + 1.4487779987154867322e-884j 3.24e-60, 8.55e-172j
0.015291319553784755231 + 2.7222919046066327471e-883j 1.13e-60, 2.98e-172j
0.024098306637720057561 + 3.396253360087291708e-884j 8.01e-62, 2.12e-173j
0.0013007701035269931187 - 1.1061090965151010478e-884j 5.3e-60, 1.4e-171j
0.02890558560614935072 - 6.7690872575520081704e-886j 8.78e-63, 2.32e-174j
0.033893683021706417325 + 3.5944912911380688946e-886j 8.78e-64, 2.32e-175j
0.0079222101064478182543 + 2.4919442472377696433e-882j 6.1e-61, 1.61e-172j
0.038942122079346426629 - 2.148628333394804528e-885j 2.63e-65, 6.96e-177j
0.033893683021706417325 + 5.1059205540471281734e-885j 1.3e-64, 3.42e-176j
0.011316627477342627322 - 8.7217890164716719915e-885j 3.64e-62, 9.61e-174j
0.048770827008948785688 - 6.7610005956332553366e-887j 5.31e-68, 1.4e-179j
0.015291319553784755231 + 4.7644668422390087372e-885j 1.16e-62, 3.06e-174j
0.02890558560614935072 - 1.2843830059336092077e-884j 2.22e-65, 5.88e-177j
0.043933725402938488974 + 9.6278795448007244422e-886j 3.89e-68, 1.03e-179j
0.0020350610607348240039 + 3.1457830516181013182e-881j 8.6e-63, 2.27e-174j
0.038942122079346426629 - 1.9700579737932425586e-886j 1.17e-67, 3.1e-179j
0.043933725402938488974 + 1.1262127808422828615e-886j 1.59e-68, 4.19e-180j
0.07524258216714996123 - 1.2183919331911665975e-887j 2.31e-74, 6.09e-186j
0.048770827008948785688 - 4.609144756470590098e-886j 3.98e-70, 1.05e-181j
0.061665449468426604955 + 7.5197016408443667314e-887j 1.21e-72, 3.2e-184j
0.073454109526749105719 + 8.3663183361829595719e-888j 6.05e-75, 1.6e-186j
0.053376646680255613331 + 4.277700914883659642e-887j 2.85e-72, 7.52e-184j
0.07524258216714996123 - 7.6191314747763915398e-888j 3.57e-75, 9.44e-187j
0.053376646680255613331 + 2.3592744449214350495e-886j 3.03e-72, 8.01e-184j
0.057690978214134901753 - 1.2899951309995207591e-886j 5.1e-73, 1.35e-184j
0.076530865026562695003 + 9.9516591033075674382e-888j 1.16e-76, 3.06e-188j
0.061665449468426604955 + 2.0128287798087024119e-887j 7.19e-76, 1.9e-187j
0.057690978214134901753 - 2.8563265764728271201e-887j 4.9e-75, 1.29e-186j
0.07730816119614763839 - 8.5493710105748989224e-888j 1.07e-77, 2.83e-189j
0.065260092358615063009 - 4.6621189907166861076e-887j 1.5e-76, 3.96e-188j
0.073454109526749105719 + 1.5707440201487708999e-887j 1.26e-77, 3.32e-189j
0.076530865026562695003 + 7.2875859303141882454e-888j 9.54e-79, 2.52e-190j
0.065260092358615063009 - 1.4959115730409936862e-887j 2.4e-78, 6.34e-190j
0.07730816119614763839 - 7.3191290424394719699e-888j 4.34e-79, 1.15e-190j
0.071180538335901490931 - 2.1354065624601679913e-887j 6.86e-79, 1.81e-190j
0.068441267742452222701 + 3.0667344058069307393e-887j 7.88e-79, 2.08e-190j
0.077567981645025347568 + 7.7185554996861842773e-888j 2.01e-79, 5.31e-191j
0.068441267742452222701 + 1.1713313853087845157e-887j 3.4e-80, 9e-192j
0.071180538335901490931 - 9.653560477719050243e-888j 2.71e-80, 7.15e-192j

Download

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