Rule: Q[8, 25, 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)
0.99164615838979415312 + 1.0981416480608565549e-890j 3.23e-232, 3.23e-232j
-0.99947946457076465656 + 2.3399808763259474536e-891j 8.67e-233, 8.67e-233j
-0.90766894374670560038 - 2.6936988481389148788e-902j 7.46e-233, 7.46e-233j
-0.97319927986072620669 + 6.8087601347752984733e-910j 3.19e-232, 3.19e-232j
0.90766894374670560038 + 5.0997946757550752149e-923j 7.52e-233, 7.52e-233j
0.92737063192764049613 - 7.2197536963434603429e-922j 1.25e-232, 1.25e-232j
0.98369761533960530108 + 5.3889002836704596712e-921j 3.3e-232, 3.3e-232j
-0.86451492511706154927 + 6.3580927778061767442e-924j 2.48e-233, 2.48e-233j
-0.99689179723609251246 + 7.1583794125321371623e-937j 2.2e-232, 2.2e-232j
-0.99164615838979415312 - 1.8064314725728440304e-956j 3.18e-232, 3.18e-232j
0.84155259501654030938 - 1.8536872738911534067e-973j 1.3e-233, 1.3e-233j
-0.96028985649753623168 + 1.1666169922284438784e-969j 2.43e-232, 2.43e-232j
-0.92737063192764049613 - 3.8047541685080567247e-974j 1.22e-232, 1.22e-232j
-0.84155259501654030938 + 1.1442739995334184576e-977j 1.43e-233, 1.43e-233j
0.71338382202008876929 - 6.8498366254763941088e-983j 1.58e-236, 1.58e-236j
0.86451492511706154927 + 8.7892895266796834463e-979j 2.38e-233, 2.38e-233j
0.88652185748802563561 - 8.035450964950082705e-979j 4.5e-233, 4.5e-233j
-0.98369761533960530108 - 2.5982201020004790347e-976j 3.33e-232, 3.33e-232j
-0.79666647741362673959 + 1.5351723849820972153e-989j 2.56e-234, 2.56e-234j
-0.9450023899049182783 + 9.7076434558233940177e-988j 1.95e-232, 1.95e-232j
0.9450023899049182783 + 3.4841375048883340539e-988j 1.84e-232, 1.84e-232j
0.7446411919755477624 - 7.6087629356679010486e-993j 1.12e-235, 1.12e-235j
-0.3137288241483280641 + 4.4647513971631613065e-1005j 1.04e-246, 1.04e-246j
-0.81823898048729993827 + 2.7231599074625482504e-992j 6.21e-234, 6.21e-234j
-0.77309144937741596153 - 1.2684763553687435597e-992j 6.73e-235, 6.73e-235j
0.97319927986072620669 + 1.3778937049300767877e-988j 3.25e-232, 3.25e-232j
0.77309144937741596153 + 4.4670781998729693879e-993j 5.99e-235, 5.99e-235j
0.79666647741362673959 + 8.879549974440674066e-992j 2.58e-234, 2.58e-234j
0.99689179723609251246 + 2.9522631996168433288e-989j 2.28e-232, 2.28e-232j
-0.64397760905351318808 - 1.3675904292879026138e-1000j 2.53e-238, 2.53e-238j
-0.046428186322481151858 - 3.949789919506199615e-1016j 2.02e-254, 2.02e-254j
0.52553240991632898582 - 7.7492139851085453242e-1003j 2.5e-241, 2.5e-241j
0.67991977358812918431 - 1.4941583763198641999e-999j 2.15e-237, 2.15e-237j
0.96028985649753623168 - 1.1365002982378896165e-992j 2.56e-232, 2.56e-232j
-0.67991977358812918431 - 2.031156964637344651e-1003j 2.28e-237, 2.28e-237j
-0.71338382202008876929 + 4.1034497519847237176e-1002j 1.68e-236, 1.68e-236j
0.81823898048729993827 - 8.9889086686791192515e-998j 5.86e-234, 5.86e-234j
0.64397760905351318808 - 5.7315059920586020434e-1004j 2.59e-238, 2.59e-238j
0.99947946457076465656 - 2.4651310349449247034e-998j 8.48e-233, 8.48e-233j
-0.35620947444026724595 + 2.3429943559501125197e-1014j 1.43e-245, 1.43e-245j
-0.52553240991632898582 + 7.3353753531678914014e-1009j 2.65e-241, 2.65e-241j
-0.88652185748802563561 - 9.4865321704066896883e-1008j 4.57e-233, 4.57e-233j
0.56617221440839728071 + 9.9703036159649541453e-1021j 2.95e-240, 2.95e-240j
0.60582710576219683265 - 1.990219566030323455e-1019j 2.77e-239, 2.77e-239j
-0.092974291156876469802 - 2.0736318841315936501e-1031j 5.36e-253, 5.36e-253j
-0.56617221440839728071 - 2.6246069447701573728e-1018j 2.74e-240, 2.74e-240j
-0.60582710576219683265 + 5.2408862602282824236e-1016j 2.78e-239, 2.78e-239j
0.092974291156876469802 + 6.9103274486509314565e-1032j 4.61e-253, 4.61e-253j
0.44155558149113420249 - 2.4394743803058204943e-1023j 1.97e-243, 1.97e-243j
0.3137288241483280641 - 5.3164374990106326478e-1027j 1.02e-246, 1.02e-246j
-0.7446411919755477624 - 2.9621430065051144707e-1027j 1.13e-235, 1.13e-235j
-0.48398399809144638363 + 3.094191653451929861e-1034j 2.34e-242, 2.34e-242j
-0.13889763543430604999 + 1.2554625609167713662e-1044j 9.89e-252, 9.89e-252j
0.35620947444026724595 - 2.7230306867211033496e-1039j 1.37e-245, 1.37e-245j
0.48398399809144638363 - 7.8854832810495204296e-1036j 2.31e-242, 2.31e-242j
0.046428186322481151858 - 2.6970943391861874632e-1048j 2.02e-254, 2.02e-254j
-0.44155558149113420249 - 7.7264096927577767401e-1036j 2.13e-243, 2.13e-243j
-0.22707462292778445494 - 2.0853927555883706578e-1042j 3.97e-249, 3.97e-249j
0.18343464249564980494 - 4.3001489653045545099e-1045j 2.12e-250, 2.12e-250j
0.39875022894172717635 - 5.6601085459504484385e-1039j 1.65e-244, 1.65e-244j
0.13889763543430604999 + 1.7584329863476205418e-1045j 1.1e-251, 1.1e-251j
-0.27061408946948564626 - 1.2166219984197136537e-1040j 7.07e-248, 7.07e-248j
-0.39875022894172717635 - 8.4426536807039033741e-1038j 1.7e-244, 1.7e-244j
9.0844867983291684223e-1076 - 2.8260849886661986826e-1076j 6.37e-1074, 6.37e-1074j
0.27061408946948564626 + 2.41767118886541732e-1045j 6.92e-248, 6.92e-248j
0.22707462292778445494 + 2.7976725105120894864e-1044j 4.5e-249, 4.5e-249j
-0.18343464249564980494 + 2.9550110288454223359e-1043j 2.26e-250, 2.26e-250j

Weights

Weight (ball center) Error (ball radius)
0.0066154593013027582543 - 2.9469221576533342365e-891j 4.25e-31, 2.84e-141j
0.001396501098421523235 + 2.540311951573347625e-891j 1.64e-31, 1.1e-141j
0.020551003061467789103 + 2.1091540489080926868e-891j 1e-31, 6.72e-142j
0.011718611015729144348 + 1.4810375491158614932e-891j 4.36e-32, 2.91e-142j
0.020551003061467789103 - 1.1921769871715577079e-890j 4.06e-32, 2.71e-142j
0.018742983114403203329 + 9.452418294356232155e-891j 3.93e-32, 2.63e-142j
0.0092529885538122159775 + 1.4236225614836856607e-890j 1.54e-32, 1.03e-142j
0.022427281719113777887 + 3.6534674224159778243e-891j 5.53e-33, 3.7e-143j
0.0038762224126930771879 - 3.8250687525681510485e-891j 1.06e-32, 7.06e-143j
0.0066154593013027582543 + 2.1865271489012902377e-891j 5.18e-33, 3.47e-143j
0.023452436395308967092 + 3.1790007252743332421e-890j 3.76e-36, 2.52e-146j
0.014096655137910056514 - 1.4503512633388313476e-891j 7.16e-34, 4.79e-144j
0.018742983114403203329 - 1.7168764130877036945e-891j 2e-34, 1.34e-144j
0.023452436395308967092 - 4.732252719824666244e-891j 9.45e-36, 6.32e-146j
0.032318155118911873843 - 1.939504540997085214e-890j 8.29e-39, 5.55e-149j
0.022427281719113777887 - 2.2844728247116578813e-890j 1.38e-37, 9.24e-148j
0.021626355967875774329 + 1.6327587098143316067e-890j 1.75e-37, 1.17e-147j
0.0092529885538122159775 - 1.6630970801542416548e-891j 5.63e-35, 3.76e-145j
0.021364449624120539807 - 5.9573501300424681103e-891j 7.01e-39, 4.69e-149j
0.016477389802767999881 + 1.5211911053686374712e-891j 5.83e-36, 3.9e-146j
0.016477389802767999881 - 8.3485648515779306911e-891j 1.38e-40, 9.21e-151j
0.030128066173730710729 + 2.6612352575870127545e-890j 2.08e-41, 1.39e-151j
0.042733157626777570018 - 3.675365154660395864e-891j 3.87e-44, 2.59e-154j
0.02261307478075938891 + 5.9421000845477391168e-891j 1.76e-38, 1.18e-148j
0.026294495191058715755 + 4.2484355623838728835e-891j 6.92e-40, 4.63e-150j
0.011718611015729144348 - 9.3011004589292606517e-891j 3.35e-42, 2.24e-152j
0.026294495191058715755 - 3.8325160898129723009e-890j 1.1e-42, 7.34e-153j
0.021364449624120539807 + 4.7784369295878210231e-890j 1.29e-42, 8.66e-153j
0.0038762224126930771879 - 7.9193572072883499208e-891j 8.85e-44, 5.92e-154j
0.037149311211859247373 + 2.6889636710843791313e-892j 1.36e-46, 9.1e-157j
0.046537088418119260225 - 6.6036525646555412662e-891j 2.84e-49, 1.9e-159j
0.041079575536662184648 + 8.8346186422354052377e-891j 3.6e-48, 2.41e-158j
0.03468355040609101004 + 1.4732200271368225895e-890j 1.66e-45, 1.11e-155j
0.014096655137910056514 + 8.2213233345140281492e-891j 4.71e-43, 3.15e-153j
0.03468355040609101004 - 7.3008673625425942751e-892j 7.12e-47, 4.76e-157j
0.032318155118911873843 + 1.4116900005772499852e-891j 1.94e-46, 1.3e-156j
0.02261307478075938891 - 4.3477875017269519833e-890j 1.17e-43, 7.83e-154j
0.037149311211859247373 - 1.1669766367587376944e-890j 2.2e-47, 1.47e-157j
0.001396501098421523235 + 1.7418848721545896349e-891j 4.9e-45, 3.28e-155j
0.042381805076813736556 + 2.8837578395728085248e-891j 7.14e-52, 4.78e-162j
0.041079575536662184648 + 6.8133141154289006002e-892j 2.94e-51, 1.97e-161j
0.021626355967875774329 - 2.7656278400062295753e-891j 1.71e-46, 1.14e-156j
0.040195231177443527371 - 9.0949151628769145849e-891j 1.12e-49, 7.48e-160j
0.039022578407318607689 + 9.9130653079515832534e-891j 7.7e-49, 5.15e-159j
0.046414225554595425118 + 6.2243953182600842774e-891j 3.94e-54, 2.64e-164j
0.040195231177443527371 - 3.6715407853981237845e-892j 1.36e-51, 9.09e-162j
0.039022578407318607689 + 6.9137332344600509315e-893j 4.96e-51, 3.32e-161j
0.046414225554595425118 + 8.4563492400604091505e-891j 1.97e-56, 1.32e-166j
0.042742968708399483493 + 9.3193871086787388312e-891j 7.33e-55, 4.9e-165j
0.042733157626777570018 - 1.1406211324197910149e-890j 1.88e-56, 1.26e-166j
0.030128066173730710729 - 2.4816771689442159043e-891j 4.96e-51, 3.32e-161j
0.042024431654255075561 - 1.0480817655731683345e-891j 1.72e-54, 1.15e-164j
0.04527427291552222689 - 5.9980972383537977614e-891j 5.59e-57, 3.74e-167j
0.042381805076813736556 + 1.0908951702770430118e-890j 7.69e-57, 5.15e-167j
0.042024431654255075561 - 8.9118688398902965156e-891j 2.64e-55, 1.76e-165j
0.046537088418119260225 - 7.6887912012987989671e-891j 4.14e-58, 2.77e-168j
0.042742968708399483493 + 1.5127496040780854091e-891j 1.26e-56, 8.41e-167j
0.043549429543495909032 - 5.169057896935931369e-891j 3.7e-58, 2.47e-168j
0.043901536797371462044 + 1.0609501805214621838e-890j 2.9e-59, 1.94e-169j
0.042737960419665833276 - 1.0072743449502741201e-890j 6.48e-58, 4.34e-168j
0.04527427291552222689 - 9.5230673263948903379e-891j 3.95e-59, 2.65e-169j
0.043441324994962136235 + 4.4426492710063426909e-891j 3.85e-59, 2.57e-169j
0.042737960419665833276 - 2.1284859574509722139e-891j 8.92e-59, 5.97e-169j
0.046358846162519576502 + 7.1120353140692909451e-891j 1.3e-59, 8.67e-170j
0.043441324994962136235 + 1.148834061418540229e-890j 2.44e-60, 1.64e-170j
0.043549429543495909032 - 1.1271442688300630403e-890j 2.2e-60, 1.47e-170j
0.043901536797371462044 + 5.7141628773549525938e-891j 1.91e-60, 1.27e-170j

Download

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