Rule: Q[7, 22, 30]

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)
0.98930034915161930657 - 1.2827192652915415237e-890j 3.35e-235, 3.35e-235j
-0.98930034915161930657 + 1.3060751990069520999e-889j 3.44e-235, 3.44e-235j
-0.92947183408040402369 + 4.4667933388363775798e-904j 1.43e-235, 1.43e-235j
-0.99933382637395269719 - 1.9935221824950224406e-910j 1.01e-235, 1.01e-235j
0.92947183408040402369 - 2.3824483590985120199e-936j 1.52e-235, 1.52e-235j
0.90678885812168107436 - 1.3617150544479074025e-938j 8.34e-236, 8.34e-236j
-0.97911914900063586633 + 2.7666547322266184953e-936j 3.68e-235, 3.68e-235j
-0.90678885812168107436 + 1.6687545632560134048e-952j 7.64e-236, 7.64e-236j
-0.99601971622308636806 + 5.4344932187948657045e-961j 2.56e-235, 2.56e-235j
0.99601971622308636806 + 3.5711742185395080197e-977j 2.66e-235, 2.66e-235j
0.82528599582915506023 + 5.9744826288511340759e-980j 1.18e-236, 1.18e-236j
0.96566690921802591656 - 3.1457827285190442843e-978j 2.93e-235, 2.93e-235j
-0.85393029995720000348 - 2.0859390141037746928e-979j 2.38e-236, 2.38e-236j
-0.82528599582915506023 + 2.7223856945353574846e-980j 1.17e-236, 1.17e-236j
0.94910791234275852453 + 4.9505363748441094037e-979j 2.28e-235, 2.28e-235j
0.85393029995720000348 + 4.0372232451478297642e-981j 2.45e-236, 2.45e-236j
0.88136704539408034087 + 1.0720562907665226422e-980j 4.89e-236, 4.89e-236j
-0.55481194731531109975 - 3.2477694629519345494e-987j 2.17e-242, 2.17e-242j
-0.74153118559939443986 + 8.1316663145697458967e-982j 1.12e-237, 1.12e-237j
-0.96566690921802591656 + 9.4852278520603117693e-980j 3.17e-235, 3.17e-235j
0.99933382637395269719 - 9.5308507451682575367e-990j 9.88e-236, 9.88e-236j
0.71546942968709134067 - 2.1176316227083380565e-996j 2.9e-238, 2.9e-238j
0.97911914900063586633 + 1.818531690164958308e-995j 3.86e-235, 3.86e-235j
-0.79555503612646885901 - 2.8474849331845658464e-995j 5.45e-237, 5.45e-237j
-0.76568720494642088948 + 7.8314453564435510104e-996j 2.75e-237, 2.75e-237j
0.79555503612646885901 - 8.9075801196270768317e-997j 5.28e-237, 5.28e-237j
0.74153118559939443986 + 1.9459092734521634568e-997j 1.15e-237, 1.15e-237j
0.76568720494642088948 - 2.752326967964838459e-999j 2.71e-237, 2.71e-237j
-0.94910791234275852453 + 9.6050393258019323364e-996j 2.22e-235, 2.22e-235j
-0.64186222990984200115 - 5.2221327907958738676e-1009j 3.38e-240, 3.38e-240j
-0.88136704539408034087 - 3.1685349936724637346e-1008j 4.63e-236, 4.63e-236j
0.68055330812198518446 - 3.0597957398220847406e-1011j 3.23e-239, 3.23e-239j
0.64186222990984200115 - 2.9816339190526654613e-1013j 3.46e-240, 3.46e-240j
0.089917659063097209156 - 8.316619637254043164e-1028j 2.11e-253, 2.11e-253j
-0.68055330812198518446 + 2.3565202555795719348e-1010j 3.03e-239, 3.03e-239j
-0.71546942968709134067 + 1.9927088721077530269e-1015j 2.79e-238, 2.79e-238j
0.24586466432668017904 + 8.8469503086042995979e-1028j 9.63e-250, 9.63e-250j
0.60000825011073864756 - 1.5842803399189719294e-1019j 2.81e-241, 2.81e-241j
0.40584515137739716691 + 6.6538770430282490515e-1025j 6.62e-246, 6.62e-246j
-0.14040062762858323433 - 9.7993777211982825186e-1031j 3.76e-252, 3.76e-252j
-0.60000825011073864756 + 2.7969691203950260844e-1021j 3.1e-241, 3.1e-241j
-0.19242929018355235256 - 3.5971715311866289706e-1031j 5.78e-251, 5.78e-251j
0.45706389278841417784 + 1.8294213357911643594e-1023j 9.91e-245, 9.91e-245j
0.55481194731531109975 + 1.9903359733062772359e-1022j 2.15e-242, 2.15e-242j
-0.089917659063097209156 - 9.3438551921056272813e-1036j 1.89e-253, 1.89e-253j
-0.45706389278841417784 - 2.70612450655335208e-1025j 1.02e-244, 1.02e-244j
-0.40584515137739716691 + 5.2340891077809846429e-1027j 6.2e-246, 6.2e-246j
0.042133526613384323521 - 1.8430366344822152724e-1036j 1.09e-254, 1.09e-254j
0.50688844951315137419 - 1.0969444768382495836e-1027j 1.68e-243, 1.68e-243j
0.19242929018355235256 + 2.0414857832223746239e-1034j 5.58e-251, 5.58e-251j
-0.24586466432668017904 - 3.9119591987531673161e-1032j 1.01e-249, 1.01e-249j
-0.50688844951315137419 - 1.7588695001687721659e-1027j 1.63e-243, 1.63e-243j
-0.042133526613384323521 - 1.1713094685872162697e-1038j 1.09e-254, 1.09e-254j
0.3533852572415382191 + 3.1305738969686664901e-1031j 3.74e-247, 3.74e-247j
0.29985799120056748494 + 9.4854083648281581257e-1033j 1.86e-248, 1.86e-248j
-8.8152041195459406635e-1055 + 5.3171640985796786885e-1055j 6.07e-1053, 6.07e-1053j
-0.3533852572415382191 - 3.6586292935611492952e-1032j 3.64e-247, 3.64e-247j
-0.29985799120056748494 + 1.8166004152019559644e-1032j 1.88e-248, 1.88e-248j
0.14040062762858323433 - 2.2320777701091877389e-1036j 3.62e-252, 3.62e-252j

Weights

Weight (ball center) Error (ball radius)
0.0084736674472663880873 + 3.9290686084771049493e-891j 4.19e-39, 8.86e-152j
0.0084736674472663880873 + 3.4365712548598225686e-890j 2.06e-39, 4.35e-152j
0.021178902900394285347 + 9.6107253521239793542e-890j 5.85e-40, 1.24e-152j
0.0017877227221305918329 - 2.0850869977475488033e-890j 7e-40, 1.48e-152j
0.021178902900394285347 + 1.2397580267810977514e-890j 3.22e-41, 6.8e-154j
0.024138559209594262841 - 1.5286689409402614025e-890j 2.73e-41, 5.77e-154j
0.011852879426584097282 - 1.6823328119424683791e-889j 1.85e-40, 3.9e-153j
0.024138559209594262841 - 1.0832000110580396693e-889j 1.41e-41, 2.99e-154j
0.0049652769620799394749 + 9.4583243438538587998e-890j 5.89e-40, 1.24e-152j
0.0049652769620799394749 + 8.9720484190980526431e-891j 1.86e-43, 3.94e-156j
0.029143036936810883563 + 5.3571432153516269855e-890j 3.83e-44, 8.09e-157j
0.015021920185382218547 + 1.2005316252324893887e-890j 2.28e-43, 4.82e-156j
0.028138967685276056475 - 1.9246123192090148213e-889j 1.07e-43, 2.27e-156j
0.029143036936810883563 + 2.8657185129178817389e-889j 3.97e-44, 8.39e-157j
0.018093666154152023836 - 1.1326191596487178036e-890j 8.48e-44, 1.79e-156j
0.028138967685276056475 - 3.2800058143591063358e-890j 3.92e-45, 8.29e-158j
0.026580323122845455562 + 2.1257915564715027242e-890j 9.95e-45, 2.1e-157j
0.046706160204729512524 + 1.2356907301833076162e-889j 3.33e-49, 7.04e-162j
0.021675910559495714352 - 9.267023165178539102e-889j 5.53e-48, 1.17e-160j
0.015021920185382218547 + 1.0897096432727632311e-889j 2.02e-45, 4.27e-158j
0.0017877227221305918329 - 1.9435622168848849616e-891j 4.06e-46, 8.57e-159j
0.031599522729074786625 + 1.7687055847915426765e-889j 3.57e-50, 7.55e-163j
0.011852879426584097282 - 1.7383802014647613836e-890j 1.39e-45, 2.93e-158j
0.030284129837680108613 - 4.4694828411197815745e-889j 1.58e-48, 3.33e-161j
0.028181136431434341505 + 7.5364442393044808156e-889j 7.09e-49, 1.5e-161j
0.030284129837680108613 - 9.1436829002770538137e-890j 2.85e-49, 6.02e-162j
0.021675910559495714352 - 2.2056982509386098977e-889j 1.13e-50, 2.39e-163j
0.028181136431434341505 + 1.6794137015866092955e-889j 3.06e-50, 6.47e-163j
0.018093666154152023836 - 9.5414789497275386905e-890j 4.4e-50, 9.29e-163j
0.040189724882380855628 + 2.5301335450816049752e-889j 4.72e-54, 9.96e-167j
0.026580323122845455562 + 1.3712041772453831407e-889j 1.75e-50, 3.69e-163j
0.037190055574145053472 - 1.1088783538784218593e-889j 3.29e-53, 6.96e-166j
0.040189724882380855628 + 7.7127366444653729388e-890j 1.91e-54, 4.04e-167j
0.049587818298354684024 - 2.0796393817575255471e-889j 1.15e-59, 2.43e-172j
0.037190055574145053472 - 3.9879501809367843682e-889j 1.02e-54, 2.16e-167j
0.031599522729074786625 + 6.9410482702446147024e-889j 6.14e-54, 1.3e-166j
0.053900333448397188326 + 6.8341980210217215503e-890j 1.84e-60, 3.88e-173j
0.043568006538830918063 - 5.7301704937665090789e-890j 3.72e-57, 7.86e-170j
0.051849590944456372528 - 3.9759890398589301583e-890j 4.46e-60, 9.42e-173j
0.05125108120887498412 + 1.7626259388692839113e-889j 3.3e-62, 6.98e-175j
0.043568006538830918063 - 1.7100143488870228881e-889j 1.24e-58, 2.62e-171j
0.052812256572344932318 - 1.3191033841438708027e-889j 2.34e-62, 4.94e-175j
0.050569689147191013501 + 3.8345933370997240054e-890j 6.67e-61, 1.41e-173j
0.046706160204729512524 + 4.5644881323575144452e-890j 6.4e-60, 1.35e-172j
0.049587818298354684024 - 2.4150985733161382111e-889j 9.98e-63, 2.11e-175j
0.050569689147191013501 + 8.522580213462819042e-890j 1.84e-62, 3.88e-175j
0.051849590944456372528 - 8.0154300482696126504e-890j 5.37e-63, 1.13e-175j
0.045219572602376098953 + 3.0744209821741771257e-889j 7.73e-64, 1.63e-176j
0.048994342288802738438 - 3.9933344388606663103e-890j 7.26e-62, 1.53e-174j
0.052812256572344932318 - 9.557603114030980965e-890j 4.11e-64, 8.69e-177j
0.053900333448397188326 + 1.0338737762296012293e-889j 1.41e-64, 2.99e-177j
0.048994342288802738438 - 9.7941200262834743875e-890j 2.03e-63, 4.28e-176j
0.045219572602376098953 + 3.297249858642515538e-889j 2.04e-64, 4.3e-177j
0.053049263817200055124 + 4.4097989513948152375e-890j 8.09e-65, 1.71e-177j
0.053905325297675887296 - 5.2650858004962208318e-890j 4.68e-65, 9.89e-178j
0.040182313728077103482 - 3.7216369689574650643e-889j 5.2e-65, 1.1e-177j
0.053049263817200055124 + 8.0704937870597052322e-890j 1.57e-66, 3.33e-179j
0.053905325297675887296 - 8.7543781942712274455e-890j 1.56e-66, 3.3e-179j
0.05125108120887498412 + 1.3946860485196694659e-889j 3.56e-66, 7.46e-179j

Download

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