Rule: Q[2, 3, 34, 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)
-0.99474612018054641349 + 1.7133136595861722966e-802j 2.22e-227, 2.22e-227j
-0.95349741828540402373 + 1.1353012941205373977e-820j 6.86e-228, 6.86e-228j
-0.90967805763906951555 - 6.5492158253577997893e-831j 8.52e-229, 8.52e-229j
-0.99805002478633812881 + 8.27330231166157457e-831j 1.61e-227, 1.61e-227j
0.89202324259832778113 + 1.5886988222704360053e-847j 3.29e-229, 3.29e-229j
0.9404305600026801178 + 4.5214677737255638649e-846j 3.77e-228, 3.77e-228j
0.99474612018054641349 - 6.1042863449071375168e-845j 2.24e-227, 2.24e-227j
-0.92582009977255146157 - 5.7492737897383600935e-845j 1.9e-228, 1.9e-228j
-0.99967606015771329434 + 8.3639030087773714081e-843j 5.94e-228, 5.94e-228j
-0.98974112479186593392 + 6.7572788490642038069e-853j 2.32e-227, 2.32e-227j
0.87289935245841923738 - 1.1032261717864405616e-864j 1.21e-229, 1.21e-229j
0.67174182748004630176 + 2.8289329302423352696e-870j 1.17e-234, 1.17e-234j
-0.89202324259832778113 - 3.8183029134023013363e-864j 3.21e-229, 3.21e-229j
-0.83040480282975221643 - 5.9506161996619613055e-866j 1.28e-230, 1.28e-230j
0.92582009977255146157 - 2.0705491869988045491e-864j 1.84e-228, 1.84e-228j
0.85235096843230253005 + 7.6644908756169962531e-865j 4.03e-230, 4.03e-230j
0.7824604929910318093 - 1.1825530253242757303e-867j 8.27e-232, 8.27e-232j
0.98310220977903727545 - 1.6369950721371830572e-860j 2.06e-227, 2.06e-227j
-0.7824604929910318093 - 3.3524959739821100606e-867j 8.22e-232, 8.22e-232j
-0.9404305600026801178 - 6.4548507958994307594e-864j 3.78e-228, 3.78e-228j
0.98974112479186593392 + 2.4281874580745166393e-861j 2.24e-227, 2.24e-227j
0.72945840244251407194 - 1.3011485047446709546e-869j 3.83e-233, 3.83e-233j
0.99967606015771329434 + 2.2838913018042824765e-862j 6.19e-228, 6.19e-228j
-0.85235096843230253005 + 1.4426815811005566693e-865j 4.32e-230, 4.32e-230j
-0.80709049477970182315 + 1.8291652214962160808e-866j 3.23e-231, 3.23e-231j
0.25466340784471960271 - 6.1177623441590570722e-884j 4.52e-247, 4.52e-247j
0.75657071273159740107 - 1.1691766042984052677e-868j 1.74e-232, 1.74e-232j
0.83040480282975221643 + 1.7084080503954797187e-866j 1.32e-230, 1.32e-230j
0.95349741828540402373 + 2.6274721671934086991e-864j 6.73e-228, 6.73e-228j
-0.64127074523328724542 + 1.7555393963595659773e-871j 1.62e-235, 1.62e-235j
-0.70116100578483626398 + 1.3716319819478152089e-869j 6.5e-234, 6.5e-234j
0.17992139718604682973 + 1.6570177794799517362e-885j 1.84e-249, 1.84e-249j
0.64127074523328724542 - 4.0760513273715567565e-871j 1.74e-235, 1.74e-235j
-0.98310220977903727545 - 6.5559226159960525816e-861j 2.08e-227, 2.08e-227j
-0.72945840244251407194 + 2.091762033585373869e-879j 3.68e-233, 3.68e-233j
-0.75657071273159740107 - 2.2623029753802443222e-879j 1.77e-232, 1.77e-232j
0.80709049477970182315 - 2.4522364840033741583e-877j 3.38e-231, 3.38e-231j
0.60979306443450752616 + 1.6578691184079397256e-883j 2.18e-236, 2.18e-236j
0.90967805763906951555 + 3.6464002157746531136e-874j 8.69e-229, 8.69e-229j
-0.9748556138175737231 + 1.0380339342052193612e-872j 1.64e-227, 1.64e-227j
-0.54402022721134277203 - 4.8800117630032107788e-900j 3e-238, 3e-238j
0.9748556138175737231 - 1.0488288668062650374e-886j 1.74e-227, 1.74e-227j
0.70116100578483626398 + 2.9157875777048154422e-895j 6.68e-234, 6.68e-234j
0.57735026918962576451 + 5.6483991278911780262e-899j 2.59e-237, 2.59e-237j
-0.14272850180710537402 - 7.7902740017119798732e-913j 9.84e-251, 9.84e-251j
-0.57735026918962576451 + 1.0928547573237065092e-899j 2.54e-237, 2.54e-237j
-0.87289935245841923738 - 9.924713826735495802e-890j 1.26e-229, 1.26e-229j
0.96498579137241430502 - 5.5974003831773965669e-888j 1.11e-227, 1.11e-227j
0.47502667633647167399 + 1.9485782966771845054e-903j 2.69e-240, 2.69e-240j
0.99805002478633812881 - 1.7502749655583800127e-899j 1.66e-227, 1.66e-227j
-0.67174182748004630176 - 4.6008992632850180229e-907j 1.11e-234, 1.11e-234j
-0.47502667633647167399 - 1.904397868128074752e-912j 2.8e-240, 2.8e-240j
-0.60979306443450752616 - 1.5990719576917693453e-910j 2.14e-236, 2.14e-236j
0.54402022721134277203 + 1.3923370045362774293e-913j 2.99e-238, 2.99e-238j
0.50989487463118129875 + 1.0578178292523307485e-915j 3.18e-239, 3.18e-239j
-0.17992139718604682973 - 7.5991932817301087361e-925j 1.63e-249, 1.63e-249j
-0.50989487463118129875 - 2.5709227860841479432e-917j 3.02e-239, 3.02e-239j
-0.32963984945348778082 + 3.2520305353899210912e-923j 1.07e-244, 1.07e-244j
-0.96498579137241430502 + 2.98351875456809319e-927j 1.11e-227, 1.11e-227j
0.43945480667863374259 + 1.5381741390777234273e-951j 2.42e-241, 2.42e-241j
0.14272850180710537402 - 7.6211536369788469023e-960j 9.45e-251, 9.45e-251j
-0.40328384100232167589 - 3.9656697291805916773e-951j 2.03e-242, 2.03e-242j
-0.43945480667863374259 + 7.0675897272117358483e-951j 2.46e-241, 2.46e-241j
-0.035312898646398947311 - 3.3904117580229634388e-963j 1.7e-254, 1.7e-254j
0.40328384100232167589 + 2.4887214045938457023e-952j 2.03e-242, 2.03e-242j
0.36665714971506803423 + 4.4716878613078123553e-953j 1.56e-243, 1.56e-243j
-8.1793178144820059266e-987 - 2.5473038146226610034e-987j 6.77e-985, 6.77e-985j
-0.36665714971506803423 - 2.9890312097218496317e-952j 1.46e-243, 1.46e-243j
-0.10593036525426748417 - 6.0642412502150445115e-961j 5.53e-252, 5.53e-252j
0.10593036525426748417 + 3.1336249444632552302e-961j 5.84e-252, 5.84e-252j
0.29225074053553326977 + 1.573438623167773389e-955j 6.79e-246, 6.79e-246j
0.070250653320290839211 - 1.10052476984882964e-962j 2.95e-253, 2.95e-253j
-0.21718907274290636799 + 3.9081204359282984694e-957j 2.71e-248, 2.71e-248j
-0.25466340784471960271 - 2.5147206947824873796e-956j 4.48e-247, 4.48e-247j
0.035312898646398947311 + 2.8719443924328040658e-963j 1.7e-254, 1.7e-254j
0.32963984945348778082 + 4.8038913514220311225e-955j 1.14e-244, 1.14e-244j
0.21718907274290636799 - 8.7007065034498589483e-958j 2.78e-248, 2.78e-248j
-0.070250653320290839211 + 3.3489823887576755764e-962j 3.08e-253, 3.08e-253j
-0.29225074053553326977 + 1.5734042482237384768e-955j 6.8e-246, 6.8e-246j

Weights

Weight (ball center) Error (ball radius)
0.004165009829648469399 + 3.1964861531893532927e-803j 3.18e-18, 1.49e-123j
0.012285399502430094622 - 5.662913919720848139e-803j 1.09e-18, 5.11e-124j
0.016903863779222295049 + 4.2507260400251546204e-803j 4.87e-19, 2.29e-124j
0.0024413857023741850276 + 1.317052865814556086e-802j 8.62e-19, 4.05e-124j
0.018397916213608041655 - 2.1858503601864963635e-804j 2.5e-21, 1.17e-126j
0.013842133165335812861 + 1.4100439133255706171e-804j 1.82e-21, 8.54e-127j
0.004165009829648469399 + 3.5868288846164190017e-805j 3.54e-22, 1.66e-127j
0.015377486782490852297 - 4.5767880677817055523e-803j 1.62e-19, 7.62e-125j
0.00087227467234834569923 - 2.9938216178894563108e-803j 4.08e-19, 1.92e-124j
0.0058317420310675685634 - 2.0032999835637851239e-802j 1.64e-19, 7.7e-125j
0.019842002709388456097 + 2.5119729729414290249e-804j 5.95e-23, 2.8e-128j
0.029955148970233651982 + 7.7698002580240499046e-804j 2.29e-24, 1.08e-129j
0.018397916213608041655 - 4.0148753503503372733e-803j 2.22e-21, 1.04e-126j
0.022637054950916630718 + 3.6689478758696394395e-803j 6.78e-23, 3.19e-128j
0.015377486782490852297 - 1.6425353340365085678e-804j 1.39e-23, 6.54e-129j
0.02125080293532130688 - 2.8823782967718036679e-804j 1.36e-23, 6.37e-129j
0.025267788224909559925 + 4.3531238644877388371e-804j 9.18e-25, 4.31e-130j
0.0074418074408794428722 + 6.6404603359550371196e-805j 1.04e-25, 4.89e-131j
0.025267788224909559925 + 3.6443355220728525978e-803j 3.45e-26, 1.62e-131j
0.013842133165335812861 + 5.023761312902536225e-803j 2.73e-23, 1.28e-128j
0.0058317420310675685634 - 5.052442239314977342e-805j 8.72e-26, 4.09e-131j
0.027712999641795219276 + 5.7792241162279917795e-804j 8.19e-27, 3.85e-132j
0.00087227467234834569923 + 7.4003192624123497842e-806j 8.7e-27, 4.09e-132j
0.02125080293532130688 - 3.7389142080209346314e-803j 2.71e-25, 1.27e-130j
0.023982370497407704745 - 3.6377149353703995512e-803j 4.83e-26, 2.27e-131j
0.037578029567345168381 + 7.9226681661766963417e-803j 2.47e-31, 1.16e-136j
0.02650599485491486156 - 5.0110854877950015035e-804j 1.21e-26, 5.7e-132j
0.022637054950916630718 + 3.3036157153367224225e-804j 3.04e-26, 1.43e-131j
0.012285399502430094622 - 1.1989663690420600638e-804j 1.66e-26, 7.79e-132j
0.030979910052646833516 - 4.1965089470660046208e-803j 2.07e-31, 9.71e-137j
0.028870812582419464435 - 3.8623654741006715578e-803j 1.15e-30, 5.42e-136j
0.03722057066243500751 + 1.321775299789177678e-802j 4.51e-34, 2.12e-139j
0.030979910052646833516 - 9.0669149254672524553e-804j 7.12e-31, 3.34e-136j
0.0074418074408794428722 + 1.1279564109261167364e-802j 5.35e-28, 2.51e-133j
0.027712999641795219276 + 3.7561348272792718006e-803j 1.82e-30, 8.55e-136j
0.02650599485491486156 - 3.6846786408114835134e-803j 6.1e-30, 2.87e-135j
0.023982370497407704745 - 3.7885658752804593486e-804j 1.4e-29, 6.57e-135j
0.031969503386918427907 + 1.062347192616243599e-803j 3.26e-33, 1.53e-138j
0.016903863779222295049 + 1.8987420598363909629e-804j 1.21e-29, 5.7e-135j
0.0090553864509132565459 - 8.2360679080760085061e-803j 4.57e-30, 2.14e-135j
0.03374082544445200478 + 5.0699937323984490992e-803j 1.9e-36, 8.94e-142j
0.0090553864509132565459 - 8.3173952532485624812e-805j 6e-31, 2.82e-136j
0.028870812582419464435 - 6.6862919094487788505e-804j 1.06e-31, 4.99e-137j
0.032902649856635145303 - 1.251611164435757311e-803j 1.1e-34, 5.18e-140j
0.037114868889389345415 - 2.2711434123641272222e-802j 1.13e-40, 5.31e-146j
0.032902649856635145303 - 4.7141182353239348707e-803j 4.07e-37, 1.91e-142j
0.019842002709388456097 + 3.8503072654372419718e-803j 2.69e-32, 1.26e-137j
0.010683729791621924117 + 1.0080154328539992855e-804j 9.44e-32, 4.43e-137j
0.035230113472160926863 + 2.1325844419130266316e-803j 8.54e-39, 4.01e-144j
0.0024413857023741850276 - 2.1835735885108307995e-805j 2.54e-32, 1.19e-137j
0.029955148970233651982 + 4.0087016731177934166e-803j 8.89e-36, 4.17e-141j
0.035230113472160926863 + 6.0309742806920548973e-803j 1.63e-40, 7.66e-146j
0.031969503386918427907 + 4.4280144624779979283e-803j 4.19e-37, 1.97e-142j
0.03374082544445200478 + 1.4850711131399427131e-803j 3.37e-38, 1.58e-143j
0.034501624078766030553 - 1.7740110265151108722e-803j 5.55e-39, 2.61e-144j
0.03722057066243500751 + 1.9054975457958936894e-802j 2.86e-44, 1.34e-149j
0.034501624078766030553 - 5.5052961918624196098e-803j 1.47e-40, 6.92e-146j
0.037212800798181663288 + 9.7493249738832543619e-803j 2.41e-44, 1.13e-149j
0.010683729791621924117 + 6.6378299239827539027e-803j 2.45e-37, 1.15e-142j
0.035895765622490353747 - 2.5854161704846287006e-803j 1.36e-42, 6.4e-148j
0.037114868889389345415 - 1.7011845044996706476e-802j 1.42e-45, 6.66e-151j
0.036419510700514719851 + 7.490737494943180438e-803j 8.29e-44, 3.89e-149j
0.035895765622490353747 - 6.6775873813718402293e-803j 4.98e-43, 2.34e-148j
0.035032953818180192408 + 3.3510931397592008559e-802j 1.81e-47, 8.49e-153j
0.036419510700514719851 + 3.169094221511718372e-803j 4.12e-45, 1.94e-150j
0.036823331496326386503 - 3.9233447472098791581e-803j 6.31e-46, 2.96e-151j
0.035487817966014644252 - 3.3163368630742170986e-802j 2.3e-48, 1.08e-153j
0.036823331496326386503 - 8.5039773327350339678e-803j 1.39e-46, 6.51e-152j
0.036325629042548790563 + 2.7153323016172094403e-802j 2.74e-48, 1.29e-153j
0.036325629042548790563 + 2.1926789219851492119e-802j 7.97e-49, 3.74e-154j
0.03753680956361839737 - 6.1796293271397252431e-803j 7.83e-49, 3.68e-154j
0.035095252856908651074 - 2.7277234236338377346e-802j 3.59e-49, 1.68e-154j
0.037352830978227488517 - 1.59767287082497435e-802j 6.09e-50, 2.86e-155j
0.037578029567345168381 + 1.3375068663557593478e-802j 3.33e-50, 1.56e-155j
0.035032953818180192408 + 3.1213260871223060578e-802j 6.6e-50, 3.1e-155j
0.037212800798181663288 + 4.8961083280559653151e-803j 1.8e-50, 8.47e-156j
0.037352830978227488517 - 1.0250397937642438628e-802j 1.75e-50, 8.23e-156j
0.035095252856908651074 - 3.1422724602843398117e-802j 1.21e-50, 5.71e-156j
0.03753680956361839737 - 1.1321303705138616273e-802j 2.99e-51, 1.38e-156j

Download

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