Rule: Q[1, 10, 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 - 8.1299501731743462268e-875j 1.63e-230, 1.63e-230j
-0.98739148159008519489 - 1.9798848744027206345e-885j 2.06e-230, 2.06e-230j
-0.90649922253643841743 + 4.4688099547654043432e-905j 8.88e-232, 8.88e-232j
-0.99586270351285081861 - 3.2031539820334904101e-912j 1.64e-230, 1.64e-230j
0.9420442432437725123 + 7.7543643294719957339e-928j 4.27e-231, 4.27e-231j
0.925196002776519573 + 2.6449299713479736545e-927j 1.97e-231, 1.97e-231j
0.99269927422948553157 - 1.3761278203332148317e-926j 2.63e-230, 2.63e-230j
-0.925196002776519573 - 6.2017999306208593423e-929j 1.95e-231, 1.95e-231j
-0.9420442432437725123 + 2.392798948794012703e-934j 4.22e-231, 4.22e-231j
-0.99914652732514104357 + 7.5196712805053883517e-946j 2.86e-231, 2.86e-231j
0.84158444565058652392 - 1.0491535879647972693e-962j 3.8e-233, 3.8e-233j
0.95566886457188528153 + 1.235825968587239563e-959j 7.98e-231, 7.98e-231j
-0.88706259976809529908 - 3.8132684928709217471e-962j 4.21e-232, 4.21e-232j
-0.81571552547096518165 + 4.7782915847442008574e-964j 1.1e-233, 1.1e-233j
0.98739148159008519489 + 1.0028472447425060321e-958j 2.09e-230, 2.09e-230j
0.86574605855438217586 + 1.975575575493980319e-964j 1.32e-232, 1.32e-232j
0.88706259976809529908 + 4.3694014974479792785e-964j 4.11e-232, 4.11e-232j
-0.99269927422948553157 - 1.7477268892445924495e-959j 2.62e-230, 2.62e-230j
-0.76089690057994266014 - 4.0070705445746710909e-969j 6.31e-235, 6.31e-235j
-0.96723206344327922166 + 8.7052114704332450602e-964j 1.26e-230, 1.26e-230j
0.90649922253643841743 - 1.797832921529736031e-970j 8.8e-232, 8.8e-232j
0.73015200557404932409 + 1.7840913655696497393e-974j 1.16e-235, 1.16e-235j
-0.04509637928695960757 - 6.6565826806559493519e-993j 2.07e-254, 2.07e-254j
-0.84158444565058652392 - 1.5793444545622303017e-971j 3.99e-233, 3.99e-233j
-0.78913679525560244035 + 1.7631535710302386123e-973j 2.99e-234, 2.99e-234j
0.96723206344327922166 + 8.2172195090450609059e-968j 1.15e-230, 1.15e-230j
0.76089690057994266014 + 4.9999075271839293156e-976j 6.68e-235, 6.68e-235j
0.78913679525560244035 - 1.1218859130085858659e-974j 2.76e-234, 2.76e-234j
-0.95566886457188528153 + 7.8666050867586797249e-968j 8.01e-231, 8.01e-231j
-0.66511705212951455584 - 2.7081804652520702665e-980j 3.31e-237, 3.31e-237j
0.99914652732514104357 - 2.6615581518488206625e-973j 2.92e-231, 2.92e-231j
0.81571552547096518165 + 7.1337508400045051811e-980j 1.06e-233, 1.06e-233j
0.69791593237073278724 + 6.1512496937739754173e-983j 2.05e-236, 2.05e-236j
-0.13641636860467846244 + 6.7271243361572551618e-999j 9.49e-252, 9.49e-252j
-0.73015200557404932409 + 5.6861380147183459171e-980j 1.18e-235, 1.18e-235j
-0.69791593237073278724 - 1.6276099796729313309e-980j 2.06e-236, 2.06e-236j
0.22509811712194158674 - 5.703012596141859772e-996j 4.16e-249, 4.16e-249j
0.59457013709158187507 + 9.827170189285861822e-986j 5.83e-239, 5.83e-239j
0.26954315595234497233 + 5.2669656198265031758e-994j 8.01e-248, 8.01e-248j
-0.9782286581460569928 + 7.1972999344257759789e-980j 1.36e-230, 1.36e-230j
-0.55699940786554051754 - 2.5149808505241642276e-994j 6.61e-240, 6.61e-240j
0.04509637928695960757 - 1.7522722391951378465e-1008j 2.07e-254, 2.07e-254j
0.66511705212951455584 - 1.5611551536414513703e-991j 3.43e-237, 3.43e-237j
0.51909612920681181593 + 8.2904330239947058052e-997j 7.11e-241, 7.11e-241j
0.9782286581460569928 + 4.6508251554516378443e-991j 1.36e-230, 1.36e-230j
-0.63092262908088092039 - 1.2096616286213644357e-996j 4.73e-238, 4.73e-238j
-0.31343442429678087989 + 1.8857294045838180214e-1006j 1.41e-246, 1.41e-246j
-0.26954315595234497233 + 8.9834144679082705246e-1008j 8.05e-248, 8.05e-248j
0.48010624132914006699 - 1.350979366092505785e-1002j 5.97e-242, 5.97e-242j
0.63092262908088092039 + 1.3184092723841027053e-999j 4.81e-238, 4.81e-238j
-0.22509811712194158674 - 3.5029416652616981144e-1009j 4.36e-249, 4.36e-249j
-0.48010624132914006699 + 2.830365333980749427e-1001j 6.05e-242, 6.05e-242j
-0.59457013709158187507 + 8.7776447345732343449e-998j 5.56e-239, 5.56e-239j
0.55699940786554051754 + 2.1798602504774973912e-1000j 6.3e-240, 6.3e-240j
0.43932109076235962814 + 5.0210557514890731711e-1004j 4.77e-243, 4.77e-243j
-8.9480570758118852106e-1037 - 2.7305558824476728127e-1036j 1.98e-1034, 1.98e-1034j
-0.51909612920681181593 + 5.0577611063830410623e-1000j 6.78e-241, 6.78e-241j
-0.18094636520965929953 - 2.805996018464612766e-1010j 2.07e-250, 2.07e-250j
0.18094636520965929953 - 9.6882452448701482709e-1011j 2.09e-250, 2.09e-250j
0.39763440686059364642 - 1.0838188569042511372e-1004j 3.24e-244, 3.24e-244j
0.090849783728614288704 + 2.5931220329690072031e-1013j 4.46e-253, 4.46e-253j
-0.43932109076235962814 + 1.7719777102844532975e-1002j 4.78e-243, 4.78e-243j
-0.39763440686059364642 - 1.7960086571363196598e-1004j 3.36e-244, 3.36e-244j
0.13641636860467846244 - 6.0993191873813078141e-1013j 1.07e-251, 1.07e-251j
0.35590643072768674405 - 2.9421411267460506767e-1006j 2.27e-245, 2.27e-245j
0.31343442429678087989 - 3.2846660538881348747e-1008j 1.45e-246, 1.45e-246j
-0.86574605855438217586 + 1.593775579367062784e-1009j 1.35e-232, 1.35e-232j
-0.35590643072768674405 + 4.7502168715508176361e-1024j 2.26e-245, 2.26e-245j
-0.090849783728614288704 - 2.5080414186908094443e-1031j 4.52e-253, 4.52e-253j

Weights

Weight (ball center) Error (ball radius)
0.0039129417771850287726 + 1.2280142516532150953e-874j 6.7e-36, 2.65e-144j
0.0076674140045796827626 + 3.1468247781098821694e-877j 3.07e-36, 1.22e-144j
0.019089307581895921698 + 8.2295901720303336387e-877j 1.01e-36, 3.98e-145j
0.0039129417771850287726 + 1.5972092211489027202e-877j 1.96e-36, 7.77e-145j
0.015346773098313543356 + 2.3325989119414406864e-875j 1.98e-37, 7.81e-146j
0.0180677014829205956 - 1.8873759261968063643e-875j 1.57e-37, 6.22e-146j
0.0030000469092167390355 - 1.9021100489086948812e-874j 1.69e-37, 6.7e-146j
0.0180677014829205956 - 6.9427669865977253551e-877j 6.38e-38, 2.52e-146j
0.015346773098313543356 + 6.4779623162872381771e-877j 3.4e-38, 1.34e-146j
0.0021655579602971421903 - 2.5037114167327886566e-878j 2.55e-38, 1.01e-146j
0.025286742504245821939 - 1.2657245200428554219e-875j 2.53e-40, 9.99e-149j
0.012125313526707984287 - 2.9324819461477093798e-875j 2.83e-39, 1.12e-147j
0.020036656901794148325 - 9.5169553354246403969e-877j 1.44e-39, 5.69e-148j
0.026240426015410318112 + 1.1920507178716752625e-876j 2.12e-41, 8.37e-150j
0.0076674140045796827626 + 7.3672410572173205709e-875j 1.69e-39, 6.68e-148j
0.022796894675524919841 + 1.4397518470701166666e-875j 8.29e-41, 3.28e-149j
0.020036656901794148325 - 1.6470311518691517622e-875j 1.27e-40, 5.01e-149j
0.0030000469092167390355 - 3.0259005005052541298e-877j 9.15e-40, 3.62e-148j
0.029532701345042322622 + 1.384658238890072307e-876j 8.3e-44, 3.28e-152j
0.011341651747598429719 + 4.7142178044393572211e-877j 5.57e-41, 2.2e-149j
0.019089307581895921698 + 1.7519079212379723908e-875j 2.64e-41, 1.04e-149j
0.031743001218084707253 - 9.4114606769687641037e-876j 1.6e-45, 6.34e-154j
0.045447880788063070922 + 3.6016666612041608987e-876j 5.83e-48, 2.31e-156j
0.025286742504245821939 - 1.0627449824350640511e-876j 7.07e-43, 2.8e-151j
0.027126819975264023504 - 1.3222775360384598166e-876j 1.43e-43, 5.68e-152j
0.011341651747598429719 + 3.2323609607104671784e-875j 1.02e-42, 4.02e-151j
0.029532701345042322622 + 1.0352619954240333592e-875j 6.98e-46, 2.76e-154j
0.027126819975264023504 - 1.1417363016901419863e-875j 1.38e-45, 5.47e-154j
0.012125313526707984287 - 6.0397540471308290926e-877j 9.38e-44, 3.71e-152j
0.033247452784367530266 - 1.7187094285783762637e-876j 3.49e-49, 1.38e-157j
0.0021655579602971421903 + 1.5210704509853205857e-875j 7.29e-45, 2.88e-153j
0.026240426015410318112 + 1.1987382496703885078e-875j 2.03e-45, 8.05e-154j
0.03253396647925993122 + 8.9982537264216829398e-876j 2.37e-48, 9.36e-157j
0.045072833028331743114 + 3.2838878609786700438e-876j 2.62e-53, 1.03e-161j
0.031743001218084707253 - 1.448843843297930731e-876j 5.32e-49, 2.11e-157j
0.03253396647925993122 + 1.5828518476596821232e-876j 9.93e-50, 3.93e-158j
0.04431977510500346149 + 4.7434832009878596717e-876j 2.14e-54, 8.47e-163j
0.037200844596980833492 - 7.3770692474457131325e-876j 1.56e-52, 6.18e-161j
0.044393268402467960445 - 4.9073133980056600566e-876j 1.54e-54, 6.11e-163j
0.010362848183689348351 - 3.3741571733536329316e-877j 1.13e-47, 4.46e-156j
0.037754960542669295071 + 2.0045004546787319158e-876j 7.57e-54, 2.99e-162j
0.045447880788063070922 + 3.9433323716708982682e-876j 3.83e-55, 1.52e-163j
0.033247452784367530266 - 8.6312293301648410868e-876j 1.39e-51, 5.51e-160j
0.038218175212731961711 - 6.8336325655493386341e-876j 3.03e-54, 1.2e-162j
0.010362848183689348351 - 3.7772924052044249434e-875j 1.51e-48, 5.99e-157j
0.0353060871825559946 + 1.7889327643993597618e-876j 2.43e-53, 9.61e-162j
0.043207881879951101072 + 2.7221793758896288022e-876j 3.72e-57, 1.47e-165j
0.044393268402467960445 - 2.8167070827226416926e-876j 2.71e-57, 1.07e-165j
0.039916147929935121749 + 6.3819800380075050488e-876j 3.15e-56, 1.25e-164j
0.0353060871825559946 + 7.9744861864186118496e-876j 5.99e-54, 2.37e-162j
0.04431977510500346149 + 2.9944522425173885526e-876j 1.73e-57, 6.83e-166j
0.039916147929935121749 + 2.2300926163980897691e-876j 7.47e-58, 2.96e-166j
0.037200844596980833492 - 1.8613568426923121427e-876j 5.2e-56, 2.06e-164j
0.037754960542669295071 + 7.0926706321426695161e-876j 7.1e-56, 2.81e-164j
0.041466364454989378096 - 5.9630618423182078155e-876j 6.36e-58, 2.52e-166j
0.044890239395832021227 - 3.8175589539644279176e-876j 1.58e-59, 6.27e-168j
0.038218175212731961711 - 2.1505848989064517314e-876j 1.63e-58, 6.45e-167j
0.044132418486227516264 - 3.1781986751076669182e-876j 2.26e-59, 8.95e-168j
0.044132418486227516264 - 4.5895914063099136014e-876j 2.02e-60, 7.98e-169j
0.041727026986845841518 + 5.7528590311048627189e-876j 5.09e-60, 2.01e-168j
0.045882584504387727569 - 4.0759755269443047065e-876j 1.45e-60, 5.75e-169j
0.041466364454989378096 - 2.3123812209367817797e-876j 5.1e-61, 2.02e-169j
0.041727026986845841518 + 2.4697023289660640452e-876j 2.26e-61, 8.93e-170j
0.045072833028331743114 + 4.3263637870017793066e-876j 2.65e-61, 1.05e-169j
0.041884413029544843418 - 5.5579389691191267258e-876j 9.03e-62, 3.57e-170j
0.043207881879951101072 + 5.222734383827273685e-876j 6.97e-62, 2.75e-170j
0.022796894675524919841 + 1.0063106903089500774e-876j 2.26e-62, 9.06e-171j
0.041884413029544843418 - 2.631246576656925632e-876j 1.44e-62, 5.85e-171j
0.045882584504387727569 - 3.3944677694274656263e-876j 1.51e-62, 5.82e-171j

Download

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