Rule: Q[2, 10, 13, 50]

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)
0.9993816364566942268 + 9.2368415247857529797e-772j 1.51e-229, 1.51e-229j
-0.93378479062672676698 + 2.4907765131074407719e-780j 1.61e-229, 1.61e-229j
-0.90030150467747382532 - 2.220183865473864253e-780j 4.14e-230, 4.14e-230j
-0.99678794323997871635 + 2.6516711271505624997e-778j 5.21e-229, 5.21e-229j
0.90030150467747382532 + 6.1694240290781641155e-780j 3.75e-230, 3.75e-230j
0.91770183268554596162 - 5.4109057265945634777e-780j 8.36e-230, 8.36e-230j
0.97240224221762808147 - 2.3938906126812387604e-788j 1.12e-228, 1.12e-228j
-0.91770183268554596162 - 4.8659265030913772593e-801j 9.17e-230, 9.17e-230j
-0.97240224221762808147 - 4.2323151871397254017e-799j 1.03e-228, 1.03e-228j
0.98691727581885305255 + 1.5123780341202488334e-809j 1.71e-228, 1.71e-228j
0.88131002780106247634 + 9.3432489210677578298e-832j 1.51e-230, 1.51e-230j
-0.96148624841257576536 - 1.1560983981758305135e-832j 6.01e-229, 6.01e-229j
-0.88131002780106247634 - 1.432290188410166386e-842j 1.5e-230, 1.5e-230j
-0.86044643155867989458 + 5.7048782130260811249e-843j 5.12e-231, 5.12e-231j
0.98075725178499407913 - 8.6618982995268358776e-838j 1.49e-228, 1.49e-228j
0.86044643155867989458 - 1.370058730142983158e-853j 5.11e-231, 5.11e-231j
0.83776596524493410785 - 2.3977018455349566584e-852j 1.59e-231, 1.59e-231j
-0.99238459480941147953 + 1.635693639186823953e-847j 1.14e-228, 1.14e-228j
-0.78839322059275261766 + 1.8058216963452863651e-856j 1.34e-232, 1.34e-232j
-0.94848211528487274608 + 2.9899831060840633712e-852j 3.3e-229, 3.3e-229j
0.81361060868639886683 - 6.2577405736803755706e-858j 4.21e-232, 4.21e-232j
0.73488987295705853751 + 7.5541833420931430913e-860j 7.04e-234, 7.04e-234j
-0.98075725178499407913 - 8.4623494255417222763e-851j 1.61e-228, 1.61e-228j
-0.73488987295705853751 - 2.999582608309462642e-861j 6.44e-234, 6.44e-234j
-0.7622702556366203736 + 2.3125767919819750069e-860j 3.01e-233, 3.01e-233j
0.99238459480941147953 - 1.1217771712317306183e-852j 1.08e-228, 1.08e-228j
0.7622702556366203736 + 1.4174055480169323469e-871j 3.01e-233, 3.01e-233j
0.99678794323997871635 - 1.9918784545182781018e-865j 5.57e-229, 5.57e-229j
-0.9993816364566942268 - 2.6050092637582355381e-871j 1.54e-229, 1.54e-229j
-0.64289984060031285581 - 3.2518779421272145894e-879j 2.88e-236, 2.88e-236j
-0.50838493305254074647 - 3.5367776483038754655e-883j 6.45e-240, 6.45e-240j
0.93378479062672676698 + 4.9349356781196267615e-870j 1.75e-229, 1.75e-229j
0.67496074056137039689 - 1.665639648429022083e-879j 2.09e-235, 2.09e-235j
0.94848211528487274608 - 2.2980274101626821272e-871j 3.22e-229, 3.22e-229j
-0.7057842871535886165 - 1.6003059924579920668e-881j 1.18e-234, 1.18e-234j
-0.67496074056137039689 - 2.0377788085782054954e-882j 1.79e-235, 1.79e-235j
0.7057842871535886165 - 3.143251642654145077e-882j 1.2e-234, 1.2e-234j
0.64289984060031285581 + 5.3847615937003319143e-886j 3.06e-236, 3.06e-236j
0.78839322059275261766 + 3.1467196554836193021e-879j 1.25e-232, 1.25e-232j
-0.83776596524493410785 + 1.0933004375193314413e-878j 1.47e-231, 1.47e-231j
-0.57735026918962576451 - 9.7448307608840807215e-885j 5.5e-238, 5.5e-238j
0.083362927250312611764 - 1.0303671348881415738e-900j 5.63e-253, 5.63e-253j
0.57735026918962576451 + 4.2221388022819752095e-886j 5.75e-238, 5.75e-238j
0.54367583472569205306 + 2.4268841510302631092e-888j 6.66e-239, 6.66e-239j
-0.042566506554882905263 - 4.1521725770348882172e-903j 2.42e-254, 2.42e-254j
-0.61025140088655062983 + 1.220010570922328292e-884j 4.14e-237, 4.14e-237j
-0.81361060868639886683 - 1.348543983578935779e-878j 4.27e-232, 4.27e-232j
0.24198481528492212917 + 4.8356481010389404607e-896j 6.24e-248, 6.24e-248j
0.50838493305254074647 - 1.4655210398385692226e-888j 6.71e-240, 6.71e-240j
0.61025140088655062983 - 1.2125804076545311412e-884j 4.32e-237, 4.32e-237j
-0.54367583472569205306 + 2.1662534797808982132e-886j 7.08e-239, 7.08e-239j
-0.47142619912599849039 - 1.9893406314813285301e-888j 5.81e-241, 5.81e-241j
0.96148624841257576536 - 9.1437067192308857467e-881j 6.12e-229, 6.12e-229j
0.43356046489100499419 - 1.319076981597584283e-895j 4.5e-242, 4.5e-242j
0.47142619912599849039 + 2.8546821951060045034e-894j 5.49e-241, 5.49e-241j
-2.0605837765039174387e-937 + 5.5571742642272427002e-938j 1.6e-935, 1.6e-935j
-0.43356046489100499419 - 2.1710415767685444153e-894j 4.83e-242, 4.83e-242j
-0.24198481528492212917 + 5.029950884163421535e-900j 6.65e-248, 6.65e-248j
-0.98691727581885305255 - 3.5958297271497490046e-901j 1.68e-228, 1.68e-228j
0.39589965299795110178 + 9.9239163741863130774e-921j 3.85e-243, 3.85e-243j
0.12172613438315505292 + 4.9658398202815865659e-929j 8.7e-252, 8.7e-252j
-0.28293120964392343734 + 6.6106903358241152734e-924j 1.28e-246, 1.28e-246j
-0.39589965299795110178 - 3.4209700136248172262e-920j 3.82e-243, 3.82e-243j
0.16008051458594357061 - 9.677406627903678816e-928j 1.67e-250, 1.67e-250j
0.32201015564044991657 + 1.9115896303743486515e-922j 2.39e-245, 2.39e-245j
0.28293120964392343734 - 3.9649293162875894993e-925j 1.35e-246, 1.35e-246j
-0.12172613438315505292 - 1.1880832597338237641e-928j 1.01e-251, 1.01e-251j
-0.35909882564439703209 + 7.4929525552144936951e-921j 3.25e-244, 3.25e-244j
-0.16008051458594357061 - 1.0026806428437861527e-927j 1.59e-250, 1.59e-250j
0.042566506554882905263 + 5.8798285634944991636e-933j 2.2e-254, 2.2e-254j
0.35909882564439703209 - 2.2113183879146793538e-921j 3.3e-244, 3.3e-244j
0.20048341069941011949 - 8.7423628414852280356e-927j 3.21e-249, 3.21e-249j
-0.20048341069941011949 + 3.0394639915967352039e-926j 3.5e-249, 3.5e-249j
-0.32201015564044991657 - 3.2860813587140964182e-922j 2.27e-245, 2.27e-245j
-0.083362927250312611764 - 9.3485480016903535334e-930j 5.16e-253, 5.16e-253j

Weights

Weight (ball center) Error (ball radius)
0.0015822196259029200327 - 1.290161444219848944e-771j 2.76e-17, 2.72e-125j
0.0154296435952305709 - 3.1780878950913229588e-773j 1.31e-17, 1.29e-125j
0.018132216381886124184 - 4.5948425932230301261e-773j 1.07e-17, 1.06e-125j
0.0035699334680701486814 + 3.058303595293515887e-774j 1.53e-18, 1.51e-126j
0.018132216381886124184 - 8.8097568988377841486e-772j 6.88e-19, 6.78e-127j
0.016721393866466023042 + 9.1030754977474644023e-772j 5.51e-19, 5.43e-127j
0.0097115907216029798838 + 1.6785611660725980825e-771j 1.01e-19, 9.95e-128j
0.016721393866466023042 + 3.8784963459358339957e-773j 8.26e-19, 8.13e-127j
0.0097115907216029798838 + 2.2967594334907513179e-773j 3.35e-20, 3.3e-128j
0.00568220651387750841 + 2.5955193695056710192e-771j 1.51e-20, 1.49e-128j
0.019904595755353496947 + 8.3119284728582919244e-772j 2.4e-20, 2.36e-128j
0.012033398521583527122 - 2.3576802042823233716e-773j 3.52e-20, 3.47e-128j
0.019904595755353496947 + 5.2183208293815864831e-773j 1.11e-20, 1.09e-128j
0.021811335704462792181 - 5.8368561808102312602e-773j 2.18e-21, 2.15e-129j
0.0070120882074912339791 - 2.351670703017944474e-771j 7.95e-22, 7.83e-130j
0.021811335704462792181 - 7.813373230644909564e-772j 9.19e-23, 9.05e-131j
0.023489142477903995089 + 7.5762143972490479418e-772j 1.75e-23, 1.73e-131j
0.0051118464048900706694 - 8.0878893191889143958e-774j 1.5e-23, 1.47e-131j
0.025654752983053766633 + 9.4020083889734192761e-773j 1.06e-25, 1.05e-133j
0.013910636698395762284 + 2.6480402603594936404e-773j 1.62e-22, 1.6e-130j
0.024747280329408868139 - 7.6764016109491977699e-772j 1.11e-25, 1.1e-133j
0.028193900739770606853 + 8.0309643648029863431e-772j 1.7e-27, 1.68e-135j
0.0070120882074912339791 - 2.211928655096247607e-773j 2.24e-23, 2.2e-131j
0.028193900739770606853 + 1.2247944125623398169e-772j 1.2e-27, 1.18e-135j
0.026657779869171220639 - 1.0963623219150442071e-772j 6.81e-27, 6.71e-135j
0.0051118464048900706694 - 2.3021236035364285059e-771j 7.2e-27, 7.09e-135j
0.026657779869171220639 - 8.1455666380208579305e-772j 1.58e-29, 1.56e-137j
0.0035699334680701486814 + 2.3535740027864679224e-771j 3.9e-27, 3.84e-135j
0.0015822196259029200327 - 7.3110036740325802936e-775j 2.86e-27, 2.82e-135j
0.032458470959040329716 - 1.7414014731901348216e-772j 1.22e-32, 1.2e-140j
0.036200213764642973019 - 2.8647626325433751202e-772j 9.22e-35, 9.08e-143j
0.0154296435952305709 - 9.3659134297354820595e-772j 3.28e-28, 3.23e-136j
0.031547725839451772142 + 7.7238950138165392608e-772j 3.39e-33, 3.34e-141j
0.013910636698395762284 + 1.0133669085568120173e-771j 1.92e-28, 1.89e-136j
0.030014091813163033413 - 1.3403747648892012268e-772j 7.84e-32, 7.73e-140j
0.031547725839451772142 + 1.4965845201303449415e-772j 1.83e-32, 1.81e-140j
0.030014091813163033413 - 7.7846730133466667606e-772j 9.16e-33, 9.02e-141j
0.032458470959040329716 - 8.0224837810446078967e-772j 9.42e-35, 9.28e-143j
0.025654752983053766633 + 7.9666232464150778182e-772j 2.6e-31, 2.56e-139j
0.023489142477903995089 + 6.6648817378048705186e-773j 2.39e-32, 2.35e-140j
0.033129424422954030791 - 2.4182694039683841089e-772j 2.62e-36, 2.58e-144j
0.039456115990421070953 + 1.0635288722965293552e-771j 2.29e-41, 2.26e-149j
0.033129424422954030791 - 9.034779784280618782e-772j 1.95e-37, 1.92e-145j
0.034386026822256512376 + 9.0463593170748615076e-772j 2.4e-38, 2.37e-146j
0.041960519183496559702 - 8.417866201374535737e-772j 7.9e-43, 7.78e-151j
0.032769180812992145051 + 2.0754681284832766175e-772j 5.43e-37, 5.35e-145j
0.024747280329408868139 - 7.8657544386315884411e-773j 1.94e-34, 1.91e-142j
0.041482507977861577211 + 9.4228995783279496635e-772j 9.07e-43, 8.94e-151j
0.036200213764642973019 - 8.797190390708985787e-772j 6.96e-40, 6.85e-148j
0.032769180812992145051 + 8.5851463959355039691e-772j 1.3e-37, 1.28e-145j
0.034386026822256512376 + 2.6716311521506310279e-772j 9.94e-40, 9.79e-148j
0.037582543048004683074 + 3.1511022228727872852e-772j 1.17e-41, 1.15e-149j
0.012033398521583527122 - 1.2199530522050093984e-771j 3.08e-36, 3.04e-144j
0.037953982552339703429 - 9.310906500419828039e-772j 1.02e-42, 1.01e-150j
0.037582543048004683074 + 8.7785137949660760543e-772j 1.03e-41, 1.01e-149j
0.042868277955689881526 + 8.3393113455837309661e-772j 2.9e-46, 2.85e-154j
0.037953982552339703429 - 3.6765684890519187295e-772j 1.56e-44, 1.54e-152j
0.041482507977861577211 + 5.7492091220840373398e-772j 2.23e-47, 2.2e-155j
0.00568220651387750841 + 1.6287830240316275087e-773j 1.72e-40, 1.7e-148j
0.037223933620477842119 + 1.028348794418172939e-771j 7.72e-45, 7.61e-153j
0.037761059081368351226 - 1.1522329626871935479e-771j 4.43e-47, 4.37e-155j
0.040179731391772665572 - 5.4934786714078208105e-772j 1.38e-47, 1.36e-155j
0.037223933620477842119 + 4.4477780663742434043e-772j 2.81e-46, 2.77e-154j
0.039346126620249883326 + 1.0963375428790023047e-771j 1.37e-47, 1.35e-155j
0.037929952551370921382 + 1.0660848254679983554e-771j 1.43e-47, 1.41e-155j
0.040179731391772665572 - 9.8323019406772574877e-772j 1.07e-47, 1.06e-155j
0.037761059081368351226 - 9.0202182465721736395e-772j 2.42e-50, 2.39e-158j
0.036591422187433018672 - 5.1654712024373173604e-772j 1.8e-49, 1.78e-157j
0.039346126620249883326 + 7.9360712455835231441e-772j 1.49e-50, 1.47e-158j
0.041960519183496559702 - 9.1668490076223774151e-772j 4.88e-50, 4.82e-158j
0.036591422187433018672 - 1.0959516305354997482e-771j 1.61e-49, 1.59e-157j
0.041236870518336370393 - 9.8744379661164355321e-772j 6e-50, 5.93e-158j
0.041236870518336370393 - 6.5746327182923219752e-772j 2.45e-51, 2.42e-159j
0.037929952551370921382 + 5.4649621913391468413e-772j 2.2e-51, 2.22e-159j
0.039456115990421070953 + 8.9976198295048055337e-772j 2.99e-51, 2.9e-159j

Download

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