Rule: Q[11, 24, 34]

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)
0.99586270351285081861 + 3.7357518270391485482e-875j 1.6e-230, 1.6e-230j
-0.98739148159008519489 + 4.1915831129116348289e-884j 1.97e-230, 1.97e-230j
-0.90649922253643841743 - 1.9904667675412158498e-904j 9.84e-232, 9.84e-232j
-0.99586270351285081861 - 2.0551583443725624327e-912j 1.65e-230, 1.65e-230j
0.9420442432437725123 - 5.5515385653887487489e-929j 4.29e-231, 4.29e-231j
0.925196002776519573 - 7.6614614628971997547e-930j 2.05e-231, 2.05e-231j
0.99269927422948553157 - 9.0467025858645817634e-929j 2.55e-230, 2.55e-230j
-0.925196002776519573 + 1.4051144250957996816e-929j 2.02e-231, 2.02e-231j
-0.9420442432437725123 + 1.192648826462613999e-933j 4.52e-231, 4.52e-231j
-0.99914652732514104357 + 2.645966187630996157e-946j 2.99e-231, 2.99e-231j
0.84158444565058652392 - 2.9391684468344373146e-965j 3.71e-233, 3.71e-233j
0.95566886457188528153 - 7.1686287789574756823e-962j 8.53e-231, 8.53e-231j
-0.88706259976809529908 + 4.3412630108964765078e-962j 3.8e-232, 3.8e-232j
-0.81571552547096518165 + 9.7814537965762282429e-964j 1.09e-233, 1.09e-233j
0.98739148159008519489 - 1.1761032578765405796e-961j 2.11e-230, 2.11e-230j
0.86574605855438217586 + 9.3676936089032924713e-964j 1.33e-232, 1.33e-232j
0.88706259976809529908 + 8.40414769285942699e-964j 3.78e-232, 3.78e-232j
-0.99269927422948553157 + 5.503013322841548295e-959j 2.61e-230, 2.61e-230j
-0.76089690057994266014 - 3.7327151084731768277e-971j 6.09e-235, 6.09e-235j
-0.96723206344327922166 - 1.8840791769574704132e-965j 1.12e-230, 1.12e-230j
0.90649922253643841743 + 6.0127838019627983673e-971j 9.11e-232, 9.11e-232j
0.73015200557404932409 - 8.9382730112527521354e-976j 1.15e-235, 1.15e-235j
-0.04509637928695960757 + 1.4901411682626024826e-997j 2.16e-254, 2.16e-254j
-0.84158444565058652392 + 5.3502026699869088668e-974j 3.86e-233, 3.86e-233j
-0.78913679525560244035 - 6.5302827911825828741e-976j 2.72e-234, 2.72e-234j
0.96723206344327922166 - 3.4415779689837946815e-969j 1.12e-230, 1.12e-230j
0.76089690057994266014 + 6.4200862378883568309e-979j 5.89e-235, 5.89e-235j
0.78913679525560244035 + 2.0112499486555617771e-977j 2.71e-234, 2.71e-234j
-0.95566886457188528153 - 5.4866525767282801759e-972j 8.74e-231, 8.74e-231j
-0.66511705212951455584 - 4.3260577173137002171e-982j 3.33e-237, 3.33e-237j
0.99914652732514104357 - 2.4954306348892057253e-975j 2.88e-231, 2.88e-231j
0.81571552547096518165 - 4.9896627631436850666e-980j 1.03e-233, 1.03e-233j
0.69791593237073278724 + 3.3851453009963905369e-983j 1.89e-236, 1.89e-236j
-0.13641636860467846244 - 4.0179449313696410893e-999j 9.62e-252, 9.62e-252j
-0.73015200557404932409 + 7.2955584176560898424e-982j 1.15e-235, 1.15e-235j
-0.69791593237073278724 - 1.0757165782451103613e-982j 2.08e-236, 2.08e-236j
0.22509811712194158674 - 3.6927848744744375016e-996j 4.21e-249, 4.21e-249j
0.59457013709158187507 - 1.4502123169875660117e-985j 5.52e-239, 5.52e-239j
0.26954315595234497233 + 6.6820086552337005688e-995j 7.39e-248, 7.39e-248j
-0.9782286581460569928 - 4.2331359288058727368e-979j 1.39e-230, 1.39e-230j
-0.55699940786554051754 + 1.0396684235031393722e-994j 6.15e-240, 6.15e-240j
0.04509637928695960757 - 1.0321262588015017668e-1009j 2.16e-254, 2.16e-254j
0.66511705212951455584 - 2.7346347780990555821e-992j 3.07e-237, 3.07e-237j
0.51909612920681181593 - 1.4467884845629404235e-995j 6.41e-241, 6.41e-241j
0.9782286581460569928 - 6.1481027957909166411e-992j 1.38e-230, 1.38e-230j
-0.63092262908088092039 - 1.4730158749367724956e-999j 4.34e-238, 4.34e-238j
-0.31343442429678087989 + 7.3370487099423866052e-1008j 1.32e-246, 1.32e-246j
-0.26954315595234497233 - 7.4297108321283489791e-1009j 7.9e-248, 7.9e-248j
0.48010624132914006699 - 1.4839870613780500211e-1004j 5.66e-242, 5.66e-242j
0.63092262908088092039 - 7.2835705605961533609e-1001j 4.28e-238, 4.28e-238j
-0.22509811712194158674 + 4.5767183628336234123e-1011j 4.15e-249, 4.15e-249j
-0.48010624132914006699 - 8.2692982181647115869e-1003j 5.79e-242, 5.79e-242j
-0.59457013709158187507 + 5.0791503623600436292e-1001j 5.32e-239, 5.32e-239j
0.55699940786554051754 + 2.7809412778042799753e-1002j 5.97e-240, 5.97e-240j
0.43932109076235962814 - 1.1185048591007113043e-1005j 4.32e-243, 4.32e-243j
1.8942569045492894235e-1039 + 5.7804440559124131502e-1039j 4.2e-1037, 4.2e-1037j
-0.51909612920681181593 + 1.9128007136218930562e-1001j 5.96e-241, 5.96e-241j
-0.18094636520965929953 - 1.065515256201824173e-1011j 2.07e-250, 2.07e-250j
0.18094636520965929953 + 5.6179140399656285012e-1012j 2.26e-250, 2.26e-250j
0.39763440686059364642 - 2.3788667786898406166e-1006j 3.39e-244, 3.39e-244j
0.090849783728614288704 + 5.3868241076774390336e-1016j 3.92e-253, 3.92e-253j
-0.43932109076235962814 - 8.1082677679383540678e-1004j 4.82e-243, 4.82e-243j
-0.39763440686059364642 + 1.8227300661234383011e-1005j 3.33e-244, 3.33e-244j
0.13641636860467846244 + 6.0544263938510254761e-1014j 9.21e-252, 9.21e-252j
0.35590643072768674405 + 2.1561348755659754274e-1007j 2.23e-245, 2.23e-245j
0.31343442429678087989 - 1.2187418985036488098e-1008j 1.41e-246, 1.41e-246j
-0.86574605855438217586 - 4.8755741982727738956e-1010j 1.27e-232, 1.27e-232j
-0.35590643072768674405 + 1.4811382082165306267e-1023j 2.14e-245, 2.14e-245j
-0.090849783728614288704 + 3.1008502154706903905e-1031j 5.02e-253, 5.02e-253j

Weights

Weight (ball center) Error (ball radius)
0.0039129417771850287726 - 5.6427854864033266717e-875j 6.7e-36, 2.6e-144j
0.0076674140045796827626 - 1.4459815231516134348e-877j 3.07e-36, 1.19e-144j
0.019089307581895921698 - 3.781536795847426014e-877j 1.01e-36, 3.9e-145j
0.0039129417771850287726 - 7.3392563017663352286e-878j 1.96e-36, 7.61e-145j
0.015346773098313543356 - 1.0718405969474579839e-875j 1.98e-37, 7.65e-146j
0.0180677014829205956 + 8.6725845966173095917e-876j 1.57e-37, 6.1e-146j
0.0030000469092167390355 + 8.7402886107151435601e-875j 1.69e-37, 6.57e-146j
0.0180677014829205956 + 3.1902352442649167299e-877j 6.38e-38, 2.47e-146j
0.015346773098313543356 - 2.9766551958171360345e-877j 3.4e-38, 1.32e-146j
0.0021655579602971421903 + 1.1504678430452345848e-878j 2.55e-38, 9.9e-147j
0.025286742504245821939 + 5.8160660116257950992e-876j 2.53e-40, 9.79e-149j
0.012125313526707984287 + 1.3474897821612075434e-875j 2.83e-39, 1.1e-147j
0.020036656901794148325 + 4.373087385938942529e-877j 1.44e-39, 5.58e-148j
0.026240426015410318112 - 5.4775312281571200284e-877j 2.12e-41, 8.2e-150j
0.0076674140045796827626 - 3.3852832616884210734e-875j 1.69e-39, 6.54e-148j
0.022796894675524919841 - 6.6157300822190292244e-876j 8.29e-41, 3.21e-149j
0.020036656901794148325 + 7.5681886153450054962e-876j 1.27e-40, 4.9e-149j
0.0030000469092167390355 + 1.3904166354747534683e-877j 9.15e-40, 3.55e-148j
0.029532701345042322622 - 6.3625722071935112651e-877j 8.3e-44, 3.22e-152j
0.011341651747598429719 - 2.1662058832651288026e-877j 5.57e-41, 2.16e-149j
0.019089307581895921698 - 8.0501024948780951402e-876j 2.64e-41, 1.02e-149j
0.031743001218084707253 + 4.3246121641852534112e-876j 1.6e-45, 6.21e-154j
0.045447880788063070922 - 1.6549834263535006016e-876j 5.83e-48, 2.26e-156j
0.025286742504245821939 + 4.8833650519231355456e-877j 7.07e-43, 2.74e-151j
0.027126819975264023504 + 6.0759298238342665568e-877j 1.43e-43, 5.56e-152j
0.011341651747598429719 - 1.4852856545509939693e-875j 1.02e-42, 3.94e-151j
0.029532701345042322622 - 4.7570794505737979572e-876j 6.98e-46, 2.7e-154j
0.027126819975264023504 + 5.2463340901711153457e-876j 1.38e-45, 5.35e-154j
0.012125313526707984287 + 2.7752963073596115518e-877j 9.38e-44, 3.63e-152j
0.033247452784367530266 + 7.8975537548386801763e-877j 3.49e-49, 1.35e-157j
0.0021655579602971421903 - 6.9893930409112163132e-876j 7.29e-45, 2.82e-153j
0.026240426015410318112 - 5.5082608262884637706e-876j 2.03e-45, 7.88e-154j
0.03253396647925993122 - 4.1347415514357288807e-876j 2.37e-48, 9.17e-157j
0.045072833028331743114 - 1.5089625148042768953e-876j 2.62e-53, 1.01e-161j
0.031743001218084707253 + 6.65750820064977737e-877j 5.32e-49, 2.06e-157j
0.03253396647925993122 - 7.2732815305619542163e-877j 9.93e-50, 3.85e-158j
0.04431977510500346149 - 2.1796537057189244698e-876j 2.14e-54, 8.3e-163j
0.037200844596980833492 + 3.3897993621915099186e-876j 1.56e-52, 6.05e-161j
0.044393268402467960445 + 2.2549344818039765545e-876j 1.54e-54, 5.98e-163j
0.010362848183689348351 + 1.5504413408663510354e-877j 1.13e-47, 4.37e-156j
0.037754960542669295071 - 9.2107774915445046315e-877j 7.57e-54, 2.93e-162j
0.045447880788063070922 - 1.8119804898469320576e-876j 3.83e-55, 1.49e-163j
0.033247452784367530266 + 3.9660920480268999859e-876j 1.39e-51, 5.4e-160j
0.038218175212731961711 + 3.1400875515132022128e-876j 3.03e-54, 1.17e-162j
0.010362848183689348351 + 1.7356843158062153969e-875j 1.51e-48, 5.86e-157j
0.0353060871825559946 - 8.2202334175044502523e-877j 2.43e-53, 9.41e-162j
0.043207881879951101072 - 1.2508547209677931558e-876j 3.72e-57, 1.44e-165j
0.044393268402467960445 + 1.2942906642772636694e-876j 2.71e-57, 1.05e-165j
0.039916147929935121749 - 2.9325510083191986982e-876j 3.15e-56, 1.22e-164j
0.0353060871825559946 - 3.6643153646308992978e-876j 5.99e-54, 2.32e-162j
0.04431977510500346149 - 1.3759654337406564745e-876j 1.73e-57, 6.69e-166j
0.039916147929935121749 - 1.0247384500694030741e-876j 7.47e-58, 2.89e-166j
0.037200844596980833492 + 8.5530255990220311857e-877j 5.2e-56, 2.01e-164j
0.037754960542669295071 - 3.2591168088319722208e-876j 7.1e-56, 2.75e-164j
0.041466364454989378096 + 2.7400560505480451707e-876j 6.36e-58, 2.46e-166j
0.044890239395832021227 + 1.7541869897788001563e-876j 1.58e-59, 6.14e-168j
0.038218175212731961711 + 9.8820426517577159899e-877j 1.63e-58, 6.31e-167j
0.044132418486227516264 + 1.4603978173701104838e-876j 2.26e-59, 8.77e-168j
0.044132418486227516264 + 2.1089396740643768345e-876j 2.02e-60, 7.82e-169j
0.041727026986845841518 - 2.6434668316768065291e-876j 5.09e-60, 1.97e-168j
0.045882584504387727569 + 1.8729306678876699821e-876j 1.45e-60, 5.63e-169j
0.041466364454989378096 + 1.0625504661305889506e-876j 5.1e-61, 1.98e-169j
0.041727026986845841518 - 1.1348402840425639706e-876j 2.26e-61, 8.75e-170j
0.045072833028331743114 - 1.9879852968232852182e-876j 2.65e-61, 1.02e-169j
0.041884413029544843418 + 2.5539001107440973498e-876j 9.03e-62, 3.49e-170j
0.043207881879951101072 - 2.3998719659659253267e-876j 6.97e-62, 2.7e-170j
0.022796894675524919841 - 4.6240467121431925119e-877j 2.26e-62, 8.87e-171j
0.041884413029544843418 + 1.2090706552546161454e-876j 1.44e-62, 5.73e-171j
0.045882584504387727569 + 1.5597745231519614078e-876j 1.51e-62, 5.7e-171j

Download

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