Rule: Q[1, 4, 6, 12, 46]

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)
0.99754549758686732618 + 1.3941074457875648262e-804j 5.86e-229, 5.86e-229j
0.72215859360885638236 - 3.3411570505145745965e-819j 6.36e-236, 6.36e-236j
-0.9243495664141193177 - 2.8726785006094969042e-815j 1.27e-230, 1.27e-230j
-0.97617889591282169698 + 8.7282072016021653156e-812j 4.13e-229, 4.13e-229j
0.95437314473850901745 - 2.9125297797023241463e-811j 9.23e-230, 9.23e-230j
0.9061798459386639928 + 1.3773063753562156339e-819j 3.71e-231, 3.71e-231j
0.96628155365106759407 + 1.011307545637481684e-816j 2.08e-229, 2.08e-229j
-0.9061798459386639928 - 5.9687919467000226054e-828j 3.81e-231, 3.81e-231j
-0.94040851727069687443 - 1.7957599602314425557e-827j 3.44e-230, 3.44e-230j
-0.99754549758686732618 + 8.1412913366348788789e-824j 5.92e-229, 5.92e-229j
0.88590417052124084731 - 1.999635292118207943e-828j 1.09e-231, 1.09e-231j
-0.99434386919591565811 + 3.5562140464936986176e-825j 9.13e-229, 9.13e-229j
-0.86354453105877267132 + 6.2036805334591660244e-831j 2.7e-232, 2.7e-232j
-0.88590417052124084731 + 2.4634210957073539811e-830j 1.05e-231, 1.05e-231j
0.94040851727069687443 + 1.5237222654727874835e-825j 3.39e-230, 3.39e-230j
0.86354453105877267132 + 4.9961545066958735098e-837j 2.74e-232, 2.74e-232j
0.83913703080552600731 + 4.2000132044301132244e-837j 6.51e-233, 6.51e-233j
0.97617889591282169698 - 1.8017249031579624088e-831j 3.84e-229, 3.84e-229j
-0.81273012749802516591 + 8.6516671080716059606e-849j 1.46e-233, 1.46e-233j
-0.95437314473850901745 + 8.6697838515599531986e-845j 8.85e-230, 8.85e-230j
0.99951668154894752653 + 8.8218838994183418777e-841j 1.68e-229, 1.68e-229j
0.78438345345542394474 - 4.6516830372896963128e-869j 2.68e-234, 2.68e-234j
-0.04715198318487394372 + 6.5237193875470476608e-895j 2.74e-254, 2.74e-254j
-0.78438345345542394474 + 1.1738189624627060683e-871j 2.49e-234, 2.49e-234j
-0.75416672657084922044 + 2.7322319379214290713e-872j 4.49e-235, 4.49e-235j
0.99434386919591565811 - 8.8554285408869220961e-864j 9.26e-229, 9.26e-229j
0.75416672657084922044 + 2.580850250418477605e-896j 4.56e-235, 4.56e-235j
0.61628033119598600254 + 2.8163697803093673624e-900j 1.29e-238, 1.29e-238j
-0.99951668154894752653 + 3.6205900455647538721e-888j 1.77e-229, 1.77e-229j
-0.65311997810491663606 - 7.3353752827418640851e-901j 1.11e-237, 1.11e-237j
0.9840853600948424645 + 2.6945727667455606911e-888j 6.97e-229, 6.97e-229j
0.99002914422468802988 - 2.4288020418501438804e-906j 9.64e-229, 9.64e-229j
0.68844540739164804299 - 6.2183526724705925031e-921j 9.81e-237, 9.81e-237j
-0.18767428546565773366 - 4.353432361553056471e-934j 2.11e-250, 2.11e-250j
-0.72215859360885638236 + 3.6634561315313442207e-919j 6.59e-236, 6.59e-236j
-0.68844540739164804299 - 8.4797038481890711497e-920j 9.31e-237, 9.31e-237j
0.23388907474754617648 - 8.2051695518175665576e-934j 4.97e-249, 4.97e-249j
0.57802849163039593306 + 1.9322385397499126512e-924j 1.29e-239, 1.29e-239j
0.18767428546565773366 + 4.5751696225493312199e-934j 2.3e-250, 2.3e-250j
-0.96628155365106759407 + 1.3301318510629143194e-911j 1.92e-229, 1.92e-229j
-0.57802849163039593306 - 9.1394807572731562493e-923j 1.41e-239, 1.41e-239j
0.9243495664141193177 + 5.9270097197730374528e-914j 1.23e-230, 1.23e-230j
0.81273012749802516591 + 1.5552431566804770598e-917j 1.42e-233, 1.42e-233j
0.49770935108051503356 - 1.6729624735024747232e-925j 9.09e-242, 9.09e-242j
0.65311997810491663606 + 1.5606189821455371898e-921j 1.13e-237, 1.13e-237j
-0.53846931010568309104 + 5.043445284560584544e-924j 1.15e-240, 1.15e-240j
-0.4130159172460903685 + 2.4225091719251066613e-927j 4.75e-244, 4.75e-244j
-0.99002914422468802988 - 2.1001601722907908421e-910j 9.6e-229, 9.6e-229j
0.53846931010568309104 + 2.4866692843361946931e-928j 1.15e-240, 1.15e-240j
0.04715198318487394372 - 6.7824453803599277572e-942j 1.86e-254, 1.86e-254j
-0.61628033119598600254 - 1.2288822935428457548e-925j 1.25e-238, 1.25e-238j
-0.49770935108051503356 + 4.9709994120229957839e-929j 9.11e-242, 9.11e-242j
-0.83913703080552600731 + 5.9225416744617421811e-918j 6.25e-233, 6.25e-233j
0.45585587046042572039 + 1.3044067626047636245e-930j 6.56e-243, 6.56e-243j
0.36929559432339203192 - 8.3376439101511058089e-933j 2.8e-245, 2.8e-245j
-0.9840853600948424645 - 5.0859109739629557509e-936j 6.65e-229, 6.65e-229j
-0.45585587046042572039 + 2.7457841377029080839e-954j 7.26e-243, 7.26e-243j
-0.094210839673839223415 + 1.195284838724517664e-963j 4.32e-253, 4.32e-253j
0.14108304540169852469 + 3.411905426229454295e-962j 1.12e-251, 1.12e-251j
0.4130159172460903685 + 2.376683661295201015e-955j 4.55e-244, 4.55e-244j
0.094210839673839223415 + 1.8379709717280174824e-963j 4.74e-253, 4.74e-253j
-0.27963041316178319341 + 3.4015230131803093428e-958j 9.56e-248, 9.56e-248j
-0.32479950687148398694 - 7.0082367606659909751e-957j 1.64e-246, 1.64e-246j
4.6433930204854373219e-1011 - 7.2001953891544755022e-1011j 5.91e-1009, 5.91e-1009j
0.32479950687148398694 + 4.7522430917539399826e-958j 1.71e-246, 1.71e-246j
0.27963041316178319341 + 1.1507423826453121451e-958j 9.69e-248, 9.69e-248j
-0.14108304540169852469 + 1.1851605062680055034e-962j 1.02e-251, 1.02e-251j
-0.36929559432339203192 + 1.1263073302794804291e-955j 3.04e-245, 3.04e-245j
-0.23388907474754617648 - 7.3102264420837737486e-960j 4.81e-249, 4.81e-249j

Weights

Weight (ball center) Error (ball radius)
0.0026527033705377011179 - 9.1920061182515551273e-805j 5.42e-28, 6.36e-135j
0.032875631530076450181 - 2.2736119199146032519e-807j 2.57e-28, 3.02e-135j
0.017113499713216417119 - 1.4973095670723679651e-807j 6.75e-29, 7.92e-136j
0.0089019734148769157111 - 3.691158702322653649e-807j 2.02e-29, 2.37e-136j
0.012928714468898631517 - 1.0828862447741476125e-805j 7.56e-29, 8.87e-136j
0.019225061484252564365 + 2.4802219795120588878e-806j 3.1e-29, 3.64e-136j
0.010896277175279819421 + 1.8850135117978691587e-805j 5.11e-29, 6e-136j
0.019225061484252564365 + 1.1903324467304728067e-807j 2.14e-29, 2.52e-136j
0.015007105836977173352 + 1.8945939863910227516e-807j 1.63e-29, 1.92e-136j
0.0026527033705377011179 - 1.8536434154689791754e-807j 3.39e-31, 3.98e-138j
0.021322573894401964258 - 1.6139109836109866485e-806j 2.02e-31, 2.37e-138j
0.0037135726677625262165 + 3.5353916281224726894e-807j 4.9e-31, 5.75e-138j
0.023390660633872511781 + 7.7981163832806015087e-808j 4.47e-32, 5.25e-139j
0.021322573894401964258 - 9.5664278620025784081e-808j 2.24e-31, 2.63e-138j
0.015007105836977173352 + 6.4260452792935113765e-806j 7.08e-33, 8.3e-140j
0.023390660633872511781 + 1.0830531396414633459e-806j 1.41e-33, 1.65e-140j
0.025416245049078088462 - 7.4910728129958606591e-807j 2.97e-34, 3.48e-141j
0.0089019734148769157111 - 3.4096618017468963216e-805j 4.17e-34, 4.9e-141j
0.027387604990926406576 + 5.4472526888652303352e-808j 8.14e-37, 9.56e-144j
0.012928714468898631517 - 2.3950907011870811394e-807j 5.63e-35, 6.61e-142j
0.0012301474295006923569 - 5.0816222425182840466e-805j 3.54e-35, 4.16e-142j
0.029294104115671104979 - 3.90943417172661362e-807j 2.07e-36, 2.42e-143j
0.047120960844977465215 - 3.1330913179044087736e-808j 5.54e-41, 6.5e-148j
0.029294104115671104979 - 4.6766304547503484919e-808j 7.05e-38, 8.28e-145j
0.031126221368056144955 + 4.089157678759081181e-808j 1.15e-38, 1.35e-145j
0.0037135726677625262165 + 2.1995160152655946481e-804j 1.58e-35, 1.86e-142j
0.031126221368056144955 + 2.9431623275707572572e-807j 6.98e-39, 8.19e-146j
0.037563021140622062253 + 1.2058840432586207528e-807j 8.73e-42, 1.02e-148j
0.0012301474295006923569 + 5.0158156550090863787e-808j 7.7e-39, 9.03e-146j
0.03609924890741923462 - 3.0413538291719489381e-808j 1.72e-42, 2.02e-149j
0.0069100833964938368063 + 6.4051679907262448733e-805j 4.43e-36, 5.2e-143j
0.005029183188188600791 - 1.1919592717749847327e-804j 5.87e-36, 6.9e-143j
0.034535251795564218745 + 1.79972509936541248e-807j 1.04e-41, 1.22e-148j
0.046419044455611851845 + 2.7844071012629399734e-808j 3.43e-47, 4.03e-154j
0.032875631530076450181 - 3.6408739799823983485e-808j 1.43e-43, 1.68e-150j
0.034535251795564218745 + 3.2995131462387563839e-808j 3.09e-44, 3.62e-151j
0.045994372168714570597 - 4.3496553044015144474e-808j 2.39e-48, 2.8e-155j
0.038923164274471313739 - 1.0174672428224603911e-807j 7.3e-46, 8.57e-153j
0.046419044455611851845 + 4.0748881618903669432e-808j 1.53e-48, 1.8e-155j
0.010896277175279819421 + 3.0008516316951458888e-807j 2.33e-43, 2.73e-150j
0.038923164274471313739 - 2.7091375999766220522e-808j 1.04e-47, 1.22e-154j
0.017113499713216417119 - 3.9314753238149584214e-806j 1.35e-40, 1.58e-147j
0.027387604990926406576 + 5.3356157807479268171e-807j 2.76e-42, 3.24e-149j
0.041324606097373182933 - 7.6323118843739211179e-808j 2.58e-48, 3.02e-155j
0.03609924890741923462 - 1.4575748972747356148e-807j 5.9e-45, 6.92e-152j
0.040177420909217213557 + 2.6123906528931409996e-808j 2.91e-50, 3.41e-157j
0.043297712132498946324 - 2.5153716095747308788e-808j 4.05e-52, 4.75e-159j
0.005029183188188600791 - 4.5076622889003683774e-807j 3.19e-46, 3.74e-153j
0.040177420909217213557 + 8.7407536336717189094e-808j 1.39e-48, 1.64e-155j
0.047120960844977465215 - 3.4439762200125560502e-808j 5e-53, 5.86e-160j
0.037563021140622062253 + 2.8488911353807596331e-808j 1.13e-49, 1.33e-156j
0.041324606097373182933 - 2.5513406174923448173e-808j 1.65e-51, 1.93e-158j
0.025416245049078088462 - 6.460822677892809072e-808j 3.85e-48, 4.51e-155j
0.042364501251766216461 + 6.7625290487960786934e-808j 8.01e-52, 9.41e-159j
0.044125493703590979851 + 5.5105646661114550718e-808j 3.12e-53, 3.66e-160j
0.0069100833964938368063 + 4.350792336221126123e-807j 1.9e-47, 2.23e-154j
0.042364501251766216461 + 2.5204263204898143996e-808j 6.1e-53, 7.16e-160j
0.046981171369106697398 + 3.0021844007423219227e-808j 1.58e-55, 1.85e-162j
0.046747527307811790794 - 3.8369042838235626133e-808j 3.2e-55, 3.76e-162j
0.043297712132498946324 - 6.0699867128360760985e-808j 4.69e-54, 5.51e-161j
0.046981171369106697398 + 3.6283938959718699778e-808j 1.76e-55, 2.06e-162j
0.045471842018438197281 + 2.6256361620063961851e-808j 2.43e-57, 2.86e-164j
0.044849552375636132885 - 2.5702838506666287492e-808j 3.5e-57, 4.11e-164j
0.047167491038224751072 + 3.2797730554992234638e-808j 9.63e-57, 1.13e-163j
0.044849552375636132885 - 5.0521333593999598267e-808j 8.96e-57, 1.05e-163j
0.045471842018438197281 + 4.6710254477876761313e-808j 6.58e-57, 7.72e-164j
0.046747527307811790794 - 2.8860722834658422761e-808j 2.12e-58, 2.49e-165j
0.044125493703590979851 + 2.5328556448169628946e-808j 8.66e-59, 1.04e-165j
0.045994372168714570597 - 2.6973758773564991554e-808j 8.78e-59, 1.02e-165j

Download

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