Rule: Q[3, 4, 22, 30]

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)
-0.99156661754319587051 - 5.8454780797561739105e-876j 2.03e-233, 2.03e-233j
-0.99947535900106179427 - 5.905299109081624072e-876j 5.61e-234, 5.61e-234j
-0.96049126870802028342 + 3.7545559178306337201e-879j 1.31e-233, 1.31e-233j
0.97321385973136869104 + 8.0057012385238183973e-879j 1.75e-233, 1.75e-233j
0.94549597031971691581 + 9.4682153253572783215e-882j 7.13e-234, 7.13e-234j
0.92826055731734907496 - 2.8664299186489591789e-889j 3.8e-234, 3.8e-234j
-0.97321385973136869104 + 1.6375885500631322113e-898j 1.78e-233, 1.78e-233j
-0.86283561423883964583 - 2.17756868996825604e-901j 1.98e-235, 1.98e-235j
-0.99685672297465999108 - 7.6418346969841097167e-899j 1.45e-233, 1.45e-233j
0.99947535900106179427 + 6.4433944907341137838e-897j 5.6e-234, 5.6e-234j
0.88704611060711153723 + 4.5879885686761269218e-915j 6.25e-235, 6.25e-235j
0.16811460704460127702 - 9.6057803418440175137e-944j 1.15e-251, 1.15e-251j
-0.90880405832801818853 - 5.2824447769013318007e-927j 1.74e-234, 1.74e-234j
-0.88704611060711153723 - 2.8827009498237672128e-927j 6.29e-235, 6.29e-235j
0.99156661754319587051 + 1.0177501451543134761e-922j 2.12e-233, 2.12e-233j
0.86283561423883964583 - 2.0419750297238838979e-940j 2.04e-235, 2.04e-235j
0.83605336860264937262 + 1.1287900585657037765e-942j 5.47e-236, 5.47e-236j
0.98361965975013195204 + 2.6779855676397721534e-947j 1.94e-233, 1.94e-233j
-0.7399551970814314666 + 1.8126332754073795651e-973j 3.71e-238, 3.71e-238j
-0.92826055731734907496 + 2.3123904671100013864e-968j 3.82e-234, 3.82e-234j
0.11239938358974068919 - 2.6750560883774547138e-989j 4.98e-253, 4.98e-253j
0.77459666924148337704 + 4.9269402266721688725e-968j 2.09e-237, 2.09e-237j
0.99685672297465999108 + 1.097745225267458364e-966j 1.55e-233, 1.55e-233j
-0.80664272532848289172 + 2.3003480790232025248e-983j 1.15e-236, 1.15e-236j
-0.83605336860264937262 - 2.5149414669943302335e-984j 5.25e-236, 5.25e-236j
0.90880405832801818853 - 1.1822706546502889123e-979j 1.74e-234, 1.74e-234j
0.7399551970814314666 + 1.5616204397223692283e-986j 3.53e-238, 3.53e-238j
0.96049126870802028342 + 5.062069918700053842e-981j 1.22e-233, 1.22e-233j
-0.94549597031971691581 + 5.4160249642952181941e-985j 7.83e-234, 7.83e-234j
-0.70280056519364656738 - 4.1213246421286618546e-992j 5.55e-239, 5.55e-239j
-0.98361965975013195204 + 5.1596108578121198682e-995j 1.94e-233, 1.94e-233j
0.80664272532848289172 - 1.4420956339908137459e-1002j 1.23e-236, 1.23e-236j
0.62141026677071998722 + 2.0555357003723739343e-1005j 7.61e-241, 7.61e-241j
1.0006740589572105501e-1038 - 4.2867160359865518725e-1039j 6.42e-1037, 6.42e-1037j
-0.62141026677071998722 - 4.5015512029723448743e-1004j 7.28e-241, 7.28e-241j
-0.77459666924148337704 - 1.0135419647004969083e-1004j 2.21e-237, 2.21e-237j
0.33102621368690377904 + 7.3646834460862653029e-1015j 1.12e-247, 1.12e-247j
0.5774405692895129059 - 1.7454061015057158431e-1008j 6.38e-242, 6.38e-242j
0.70280056519364656738 + 9.919499363771958881e-1007j 5.33e-239, 5.33e-239j
-0.66324325189934181564 - 2.2301300751125959482e-1010j 6.97e-240, 6.97e-240j
-0.5774405692895129059 + 1.9425169484035807192e-1012j 6.51e-242, 6.51e-242j
-0.22325031359655868096 - 1.1673079539402883207e-1020j 2.44e-250, 2.44e-250j
0.66324325189934181564 - 9.2578891068021226956e-1015j 6.7e-240, 6.7e-240j
0.53148341425790366185 + 7.2383346906034315351e-1018j 5.97e-243, 5.97e-243j
-0.16811460704460127702 + 5.5230893795349242214e-1026j 1.18e-251, 1.18e-251j
-0.434243749346802558 + 1.103392318842332514e-1019j 3.07e-245, 3.07e-245j
-0.53148341425790366185 - 6.2523289202001878053e-1018j 6.18e-243, 6.18e-243j
0.056296706472299648031 + 2.2916396556122026248e-1030j 2.11e-254, 2.11e-254j
0.48369641885145738589 - 5.8350610742112350852e-1021j 4.82e-244, 4.82e-244j
0.27761657896558057122 - 3.8713745532411512833e-1025j 5.88e-249, 5.88e-249j
-0.27761657896558057122 + 1.2995211001861022718e-1025j 5.38e-249, 5.38e-249j
-0.48369641885145738589 + 4.234797686690563109e-1020j 4.44e-244, 4.44e-244j
-0.11239938358974068919 - 3.0926689852140724988e-1029j 5.77e-253, 5.77e-253j
0.434243749346802558 + 2.8916199832962101885e-1022j 3.23e-245, 3.23e-245j
0.38329527196567593336 + 1.1366331432215707232e-1022j 2.22e-246, 2.22e-246j
-0.056296706472299648031 - 2.023388054954569625e-1030j 2.34e-254, 2.34e-254j
-0.38329527196567593336 + 7.1020106845396326861e-1024j 2.05e-246, 2.05e-246j
-0.33102621368690377904 - 3.0448011361030786012e-1024j 1.16e-247, 1.16e-247j
0.22325031359655868096 + 1.4092733914613711305e-1026j 2.42e-250, 2.42e-250j

Weights

Weight (ball center) Error (ball radius)
0.0066475572213666425173 - 6.3614356089272982257e-876j 2.26e-48, 5.12e-158j
0.0014102324109764631359 - 5.3305256859663076137e-876j 1.06e-48, 2.4e-158j
0.013862449765309275396 + 5.298450295374602244e-876j 2e-49, 4.51e-159j
0.011577651007627054651 - 7.6996941123510901709e-878j 2.71e-50, 6.12e-160j
0.01612264546911842944 - 1.1395041494270204171e-877j 1.7e-50, 3.83e-160j
0.018342802560367865164 + 1.2259817655840857798e-877j 1.06e-50, 2.39e-160j
0.011577651007627054651 - 6.8759027682349509026e-876j 2.08e-49, 4.69e-159j
0.025482116557460684495 - 1.5284841925522851341e-876j 2.19e-51, 4.96e-161j
0.003921998510825978996 + 5.0053057711376550024e-876j 7.39e-49, 1.67e-158j
0.0014102324109764631359 - 7.7526624007199325994e-879j 3.54e-53, 7.99e-163j
0.022959039409962665881 + 1.2047666185425342145e-877j 4.3e-53, 9.72e-163j
0.055457320963503618953 - 2.2111525704110803961e-878j 1.92e-54, 4.33e-164j
0.02058428433227298575 - 2.7002946960543959858e-876j 7.18e-52, 1.62e-161j
0.022959039409962665881 + 2.064050634729778381e-876j 5.65e-52, 1.28e-161j
0.0066475572213666425173 - 3.747757301695080486e-878j 3.72e-53, 8.4e-163j
0.025482116557460684495 - 1.1024203988146773476e-877j 3.83e-54, 8.67e-164j
0.028091445681040511422 + 9.7112079368892965838e-878j 8.06e-55, 1.82e-164j
0.0092095454170422906246 + 5.0561538822601494498e-878j 2.07e-53, 4.68e-163j
0.035914627175558491625 - 4.0703298485595586687e-877j 2.69e-57, 6.07e-167j
0.018342802560367865164 + 3.4233885027435099588e-876j 3.77e-54, 8.51e-164j
0.055941101737597970176 + 2.2488431015384748706e-878j 1.29e-58, 2.92e-168j
0.033354330689242991342 + 7.0992213127151413865e-878j 2.35e-57, 5.32e-167j
0.003921998510825978996 + 2.2912195786449782437e-878j 8.34e-54, 1.89e-163j
0.030731049702470223351 - 7.916515124241041163e-877j 4.99e-57, 1.13e-166j
0.028091445681040511422 + 1.1063645440608345894e-876j 2.57e-56, 5.81e-166j
0.02058428433227298575 - 1.2508014167734360723e-877j 2.04e-55, 4.62e-165j
0.035914627175558491625 - 6.0215562553341656946e-878j 3.75e-59, 8.48e-169j
0.013862449765309275396 + 1.0293068089535320359e-877j 7.37e-55, 1.66e-164j
0.01612264546911842944 - 4.2580578162188348279e-876j 2.76e-56, 6.23e-166j
0.038376019066380633516 + 2.9665435965804289321e-877j 5.57e-61, 1.26e-170j
0.0092095454170422906246 + 1.0619179288077866494e-875j 3.39e-56, 7.67e-166j
0.030731049702470223351 - 8.3522552129221724971e-878j 2.08e-58, 4.7e-168j
0.04292541257054711338 + 3.8491143693078315156e-878j 1.11e-62, 2.5e-172j
0.056329063064400513107 + 2.4390720289516365068e-878j 4.02e-65, 9.09e-175j
0.04292541257054711338 + 1.6589757914919827648e-877j 1.29e-63, 2.91e-173j
0.033354330689242991342 + 5.6569646177676516599e-877j 2.83e-60, 6.4e-170j
0.052869703586261000081 + 2.3095293267730005279e-878j 8.58e-66, 1.94e-175j
0.044989071488969107957 - 3.4012641740112060419e-878j 2.31e-64, 5.22e-174j
0.038376019066380633516 + 5.1329265188054579753e-878j 7.19e-63, 1.62e-172j
0.040717378398402533218 - 2.1980414838631167494e-877j 2.24e-63, 5.06e-173j
0.044989071488969107957 - 1.2766310361869777708e-877j 2.64e-65, 5.97e-175j
0.054782428441525641638 + 3.4831984228594085955e-878j 1.4e-68, 3.16e-178j
0.040717378398402533218 - 4.4175074133614525997e-878j 9.53e-64, 2.15e-173j
0.046898936091260446881 + 3.0509317589657852492e-878j 6.7e-66, 1.51e-175j
0.055457320963503618953 - 3.1082312673757325462e-878j 4.87e-69, 1.1e-178j
0.050229343351646245811 + 6.542539423389262119e-878j 5.13e-69, 1.16e-178j
0.046898936091260446881 + 1.0019337169747997348e-877j 1.03e-67, 2.32e-177j
0.05623200209202099408 - 2.3235251786900284838e-878j 2.16e-69, 4.87e-179j
0.048647681291824948688 - 2.7794075632975291029e-878j 8.83e-69, 1.99e-178j
0.05391889651971129967 - 2.2407920025379084853e-878j 3.88e-70, 8.76e-180j
0.05391889651971129967 - 3.97059744243447506e-878j 1.89e-70, 4.28e-180j
0.048647681291824948688 - 8.0188920704919434096e-878j 2.36e-69, 5.33e-179j
0.055941101737597970176 + 2.8204171160548495482e-878j 1.4e-70, 3.17e-180j
0.050229343351646245811 + 2.5721271310883890637e-878j 3.27e-70, 7.39e-180j
0.051638396957505635606 - 2.4181474180491782112e-878j 1.7e-70, 3.85e-180j
0.05623200209202099408 - 2.6016696829640246861e-878j 2.93e-71, 6.66e-181j
0.051638396957505635606 - 5.4393484669361247905e-878j 5.78e-72, 1.31e-181j
0.052869703586261000081 + 4.6059170635025089385e-878j 4.68e-72, 1.07e-181j
0.054782428441525641638 + 2.2085240038797480544e-878j 3.51e-72, 7.22e-182j

Download

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