Rule: Q[2, 10, 13, 26]

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)
0.99950587430119952637 - 5.8699465178076770943e-863j 3.11e-237, 3.11e-237j
-0.99950587430119952637 - 3.8266532296881435671e-874j 3.16e-237, 3.16e-237j
-0.94848211528487274608 - 2.4379587590461950859e-888j 1.73e-237, 1.73e-237j
-0.99678794323997871635 + 9.5535415821629767738e-893j 6.98e-237, 6.98e-237j
0.87072877271724792142 - 2.3513243146906854074e-914j 9.61e-239, 9.61e-239j
0.92629113327283048722 + 1.9548678143059043006e-933j 7.32e-238, 7.32e-238j
-0.99072336177415964429 - 5.4642679008395295667e-940j 6.63e-237, 6.63e-237j
-0.87072877271724792142 - 6.2318348958622966619e-950j 9.26e-239, 9.26e-239j
-0.90030150467747382532 + 1.2120315840876266578e-949j 2.89e-238, 2.89e-238j
-0.96667863061268583203 - 5.9618237116622465281e-948j 3.1e-237, 3.1e-237j
0.90030150467747382532 + 2.0725973068133583643e-951j 2.8e-238, 2.8e-238j
0.96667863061268583203 - 7.426077084472392733e-951j 2.93e-237, 2.93e-237j
-0.92629113327283048722 - 1.0065473414680609564e-953j 7.56e-238, 7.56e-238j
-0.83776596524493410785 + 2.2854921350081479815e-955j 2.71e-239, 2.71e-239j
0.99678794323997871635 - 3.6955643100991592627e-950j 7.16e-237, 7.16e-237j
0.83776596524493410785 - 2.1794594770034445357e-959j 2.74e-239, 2.74e-239j
-0.060948469882363911372 + 5.456365971795253087e-977j 2.33e-254, 2.33e-254j
0.98075725178499407913 - 4.8802542135103734586e-956j 5.72e-237, 5.72e-237j
-0.72001141805861936692 + 5.6196664306847891178e-970j 3.02e-241, 3.02e-241j
0.99072336177415964429 + 1.6251638805470472355e-965j 7.06e-237, 7.06e-237j
-0.12172613438315505292 - 2.3091482567036807579e-987j 5.33e-253, 5.33e-253j
0.80156855671329650574 - 9.5245330539923428572e-973j 7.21e-240, 7.21e-240j
-0.4159590515715079006 - 3.2419952372251532631e-983j 6.48e-247, 6.48e-247j
-0.80156855671329650574 - 1.0887960863881793199e-974j 7.12e-240, 7.12e-240j
-0.7622702556366203736 + 3.2883442199553569512e-975j 1.66e-240, 1.66e-240j
0.52529876325580441506 - 2.3688816027636229823e-980j 8.26e-245, 8.26e-245j
0.67496074056137039689 + 8.6697965151556627988e-977j 5.15e-242, 5.15e-242j
0.72001141805861936692 - 5.5763235852868529758e-976j 2.98e-241, 2.98e-241j
0.7622702556366203736 - 4.5637554064074776327e-975j 1.58e-240, 1.58e-240j
-0.67496074056137039689 + 3.9455988989508773853e-978j 4.97e-242, 4.97e-242j
-0.98075725178499407913 + 2.0005600164656915873e-977j 5.13e-237, 5.13e-237j
3.0871034088722652998e-1004 + 6.4891299410817875869e-1005j 1.61e-1002, 1.61e-1002j
0.62732557195779031686 + 2.3544684645882100907e-985j 6.85e-243, 6.85e-243j
0.24198481528492212917 - 1.8631863908203717447e-994j 1.58e-250, 1.58e-250j
-0.62732557195779031686 - 3.3729420888006381772e-987j 6.89e-243, 6.89e-243j
-0.57735026918962576451 + 2.6854360533000424035e-988j 7.68e-244, 7.68e-244j
0.12172613438315505292 - 4.539527167822507036e-996j 5.33e-253, 5.33e-253j
0.57735026918962576451 - 1.4151526645821867077e-986j 8.04e-244, 8.04e-244j
0.30104038245057791574 + 3.1792157738696522623e-992j 2.79e-249, 2.79e-249j
-0.18214172801840361769 - 3.5975018571769565809e-995j 9.71e-252, 9.71e-252j
-0.47142619912599849039 - 2.0074887791209511631e-990j 7.6e-246, 7.6e-246j
-0.24198481528492212917 + 2.2281302459265499993e-994j 1.63e-250, 1.63e-250j
0.35909882564439703209 - 4.9367101215604890186e-991j 4.73e-248, 4.73e-248j
0.47142619912599849039 - 2.8008316480226195805e-988j 7.43e-246, 7.43e-246j
0.060948469882363911372 + 2.642225769067598177e-997j 2.15e-254, 2.15e-254j
-0.52529876325580441506 - 1.931081133057974522e-988j 8.47e-245, 8.47e-245j
-0.35909882564439703209 + 3.1211112867991803081e-992j 4.99e-248, 4.99e-248j
0.94848211528487274608 + 1.8638646979956730409e-993j 1.68e-237, 1.68e-237j
0.4159590515715079006 + 2.5117771894112954435e-1007j 6.45e-247, 6.45e-247j
0.18214172801840361769 + 1.4608615543036885457e-1012j 9.98e-252, 9.98e-252j
-0.30104038245057791574 + 2.1697400058750140676e-1010j 3.14e-249, 3.14e-249j

Weights

Weight (ball center) Error (ball radius)
0.0013662909978619135409 + 5.4059527798625129441e-863j 1.14e-57, 2.77e-170j
0.0013662909978619135409 + 4.0120099445989117422e-866j 5.63e-58, 1.37e-170j
0.020222144909165150148 - 1.3295325393380290163e-865j 1.05e-58, 2.57e-171j
0.0042593183193332413087 - 9.9954558303466133365e-866j 3.38e-58, 8.23e-171j
0.031296733419970432297 + 2.2889931647407128153e-864j 3.34e-60, 8.14e-173j
0.024126283830794153084 + 3.626022752284808241e-864j 3.21e-60, 7.81e-173j
0.007957723011833967584 + 1.2479119484514078226e-865j 1.15e-58, 2.81e-171j
0.031296733419970432297 + 1.5761118838373366924e-865j 8.61e-61, 2.1e-173j
0.027816294102448523941 - 1.4618126273336802457e-865j 1.43e-60, 3.5e-173j
0.016149414097051913193 + 1.311208349083476702e-865j 4.74e-60, 1.16e-172j
0.027816294102448523941 - 2.7994355762473441303e-864j 7.12e-63, 1.74e-175j
0.016149414097051913193 + 7.8534694053222434783e-864j 7.81e-64, 1.9e-176j
0.024126283830794153084 + 1.3785373831298996275e-865j 9.25e-61, 2.25e-173j
0.034603287825073078945 - 1.7156943528257686996e-865j 1.31e-62, 3.2e-175j
0.0042593183193332413087 - 7.3415647136417271271e-863j 5.39e-64, 1.31e-176j
0.034603287825073078945 - 1.948929573621906607e-864j 1.75e-65, 4.25e-178j
0.060892865950984973186 + 7.3825378656145296406e-865j 3.79e-68, 9.23e-181j
0.012007541927954426792 - 1.3772098854448533983e-863j 1.15e-64, 2.81e-177j
0.043685926644401175513 + 2.2558378357734027811e-865j 3.37e-67, 8.2e-180j
0.007957723011833967584 + 2.8279274750569125012e-863j 1.87e-64, 4.55e-177j
0.060630529540363643751 - 6.8539362665539702114e-865j 4.47e-69, 1.09e-181j
0.037769772901049200737 + 1.7067555220958453036e-864j 5.37e-68, 1.31e-180j
0.056196081019788710409 + 4.26905490583817481e-865j 2e-69, 4.86e-182j
0.037769772901049200737 + 1.875717094112008993e-865j 1.72e-66, 4.19e-179j
0.040803801158881575375 - 2.0547911040806520525e-865j 4.7e-67, 1.15e-179j
0.053002473612383805099 + 1.0996437578058908347e-864j 1.37e-71, 3.33e-184j
0.046380859584712301566 - 1.2822865715105818047e-864j 5.64e-71, 1.38e-183j
0.043685926644401175513 + 1.3878458341072564779e-864j 1.11e-70, 2.71e-183j
0.040803801158881575375 - 1.5259436756283562747e-864j 3.49e-70, 8.51e-183j
0.046380859584712301566 - 2.4853279434560304819e-865j 7.69e-72, 1.88e-184j
0.012007541927954426792 - 1.3039069358952849116e-865j 8.12e-69, 1.98e-181j
0.060976017098349043973 - 7.8826572900217384478e-865j 1.55e-74, 3.77e-187j
0.04884845357576347125 + 1.2027015886010423826e-864j 5.21e-73, 1.27e-185j
0.05948489185636207216 - 9.466416382219903448e-865j 5.32e-76, 1.3e-188j
0.04884845357576347125 + 2.7514948883714043407e-865j 2.53e-73, 6.17e-186j
0.051057634969407886403 - 3.0617533364715270554e-865j 3.71e-74, 9.04e-187j
0.060630529540363643751 - 8.7548759422097584873e-865j 2.24e-76, 5.47e-189j
0.051057634969407886403 - 1.1436409940125731353e-864j 3.88e-75, 9.46e-188j
0.058591267739547938197 + 9.7783686518255161518e-865j 9.17e-77, 2.23e-189j
0.060165284836743219772 + 6.3136478723008048627e-865j 8.22e-77, 2e-189j
0.054704998832886353378 - 3.8242128653597179352e-865j 6.39e-77, 1.55e-189j
0.05948489185636207216 - 5.7761285066831894761e-865j 2.16e-77, 5.28e-190j
0.057492116786062350386 - 1.007078090083291335e-864j 7.23e-78, 1.77e-190j
0.054704998832886353378 - 1.0652099718651841421e-864j 7.63e-78, 1.86e-190j
0.060892865950984973186 + 8.3413591047750308888e-865j 1.03e-77, 2.5e-190j
0.053002473612383805099 + 3.4198406583667386452e-865j 1.15e-77, 2.78e-190j
0.057492116786062350386 - 4.7470754919076764779e-865j 1.69e-78, 4.11e-191j
0.020222144909165150148 - 5.0758969330538163818e-864j 1.25e-78, 3.16e-191j
0.056196081019788710409 + 1.0355120190101930232e-864j 1e-78, 2.51e-191j
0.060165284836743219772 + 9.1275191163694062966e-865j 7.37e-79, 1.88e-191j
0.058591267739547938197 + 5.2515264523486794059e-865j 5.48e-79, 1.25e-191j

Download

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