Rule: Q[1, 6, 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 + 8.2528822004109341004e-887j 3.89e-235, 3.89e-235j
-0.98930034915161930657 - 1.4208266110433195191e-892j 3.83e-235, 3.83e-235j
-0.92947183408040402369 + 2.4167076391020677771e-905j 1.49e-235, 1.49e-235j
-0.99933382637395269719 + 1.0197054830279987098e-913j 1.15e-235, 1.15e-235j
0.92947183408040402369 - 1.5806895591804842713e-936j 1.46e-235, 1.46e-235j
0.90678885812168107436 - 5.7289856972664357473e-938j 8.79e-236, 8.79e-236j
-0.97911914900063586633 + 1.7191228441752811683e-939j 4.12e-235, 4.12e-235j
-0.90678885812168107436 + 1.7615552949408426498e-953j 9.64e-236, 9.64e-236j
-0.99601971622308636806 - 1.0668625576520548115e-962j 2.96e-235, 2.96e-235j
0.99601971622308636806 + 1.0653036780085864819e-976j 3.01e-235, 3.01e-235j
0.82528599582915506023 + 2.7421771858711166409e-980j 1.14e-236, 1.14e-236j
0.96566690921802591656 + 4.0743527858518123766e-977j 3.41e-235, 3.41e-235j
-0.85393029995720000348 - 1.517228183305165377e-979j 2.37e-236, 2.37e-236j
-0.82528599582915506023 + 1.4362585127408445358e-980j 1.14e-236, 1.14e-236j
0.94910791234275852453 + 6.7184394295991748442e-978j 2.6e-235, 2.6e-235j
0.85393029995720000348 + 1.1172458017472505099e-980j 2.37e-236, 2.37e-236j
0.88136704539408034087 + 3.1613693998726408575e-980j 4.92e-236, 4.92e-236j
-0.55481194731531109975 - 4.9997819332552391471e-987j 2.09e-242, 2.09e-242j
-0.74153118559939443986 - 1.0271494421671582906e-981j 1.14e-237, 1.14e-237j
-0.96566690921802591656 + 3.9276049158941996792e-978j 3.35e-235, 3.35e-235j
0.99933382637395269719 - 3.4524083943684073617e-989j 1.2e-235, 1.2e-235j
0.71546942968709134067 + 3.2944734752911464595e-996j 2.66e-238, 2.66e-238j
0.97911914900063586633 + 3.1548406014913710606e-994j 4.08e-235, 4.08e-235j
-0.79555503612646885901 - 3.7819793882570973258e-994j 5.8e-237, 5.8e-237j
-0.76568720494642088948 + 9.2452702088755066055e-995j 2.8e-237, 2.8e-237j
0.79555503612646885901 + 8.6229476988417947975e-997j 5.41e-237, 5.41e-237j
0.74153118559939443986 + 2.456680553491432852e-998j 1.19e-237, 1.19e-237j
0.76568720494642088948 - 1.289613681545964002e-997j 2.65e-237, 2.65e-237j
-0.94910791234275852453 - 1.6623524877654383696e-997j 2.47e-235, 2.47e-235j
-0.64186222990984200115 + 2.7321192535524789812e-1009j 3.25e-240, 3.25e-240j
-0.88136704539408034087 - 3.8147699054178663355e-1009j 4.77e-236, 4.77e-236j
0.68055330812198518446 - 1.8126726246047647234e-1012j 3.2e-239, 3.2e-239j
0.64186222990984200115 + 2.4435357664263698532e-1013j 3.17e-240, 3.17e-240j
0.089917659063097209156 - 2.2919929955117439305e-1026j 2.1e-253, 2.1e-253j
-0.68055330812198518446 + 8.7444157890438877753e-1011j 3.17e-239, 3.17e-239j
-0.71546942968709134067 + 1.499183398869284143e-1017j 2.83e-238, 2.83e-238j
0.24586466432668017904 - 4.4684109929732875324e-1028j 9.62e-250, 9.62e-250j
0.60000825011073864756 + 1.2155512904308789813e-1019j 2.84e-241, 2.84e-241j
0.40584515137739716691 + 1.4357971586857781245e-1025j 6.06e-246, 6.06e-246j
-0.14040062762858323433 + 1.7064104195391462421e-1031j 3.69e-252, 3.69e-252j
-0.60000825011073864756 + 1.7422957828028003364e-1022j 2.8e-241, 2.8e-241j
-0.19242929018355235256 - 1.143950909549743392e-1030j 6.07e-251, 6.07e-251j
0.45706389278841417784 - 6.5721438346989320579e-1024j 9.02e-245, 9.02e-245j
0.55481194731531109975 - 1.8612744737852037433e-1023j 2.15e-242, 2.15e-242j
-0.089917659063097209156 + 5.1524282708193991547e-1036j 2.1e-253, 2.1e-253j
-0.45706389278841417784 - 8.5993691182925082213e-1027j 9.67e-245, 9.67e-245j
-0.40584515137739716691 + 1.64725141898990497e-1028j 6.32e-246, 6.32e-246j
0.042133526613384323521 + 1.9898506217040285827e-1037j 1.57e-254, 1.57e-254j
0.50688844951315137419 - 1.2105515761914721947e-1027j 1.5e-243, 1.5e-243j
0.19242929018355235256 - 4.4325578351105585995e-1035j 5.86e-251, 5.86e-251j
-0.24586466432668017904 + 1.6866311679971729812e-1033j 1e-249, 1e-249j
-0.50688844951315137419 + 1.0388548257847218749e-1028j 1.64e-243, 1.64e-243j
-0.042133526613384323521 - 6.2878435629753721902e-1039j 1.78e-254, 1.78e-254j
0.3533852572415382191 - 5.674674152351370057e-1031j 3.9e-247, 3.9e-247j
0.29985799120056748494 + 2.0464707993345590924e-1032j 2.02e-248, 2.02e-248j
1.6069716862083891464e-1057 + 5.7581054794118699181e-1057j 3.53e-1055, 3.53e-1055j
-0.3533852572415382191 + 9.0053156737481514624e-1033j 3.52e-247, 3.52e-247j
-0.29985799120056748494 + 2.0315375413162735833e-1033j 1.98e-248, 1.98e-248j
0.14040062762858323433 + 2.0166325226195866583e-1037j 3.69e-252, 3.69e-252j

Weights

Weight (ball center) Error (ball radius)
0.0084736674472663880873 - 2.1680437536521686683e-887j 4.19e-39, 1.02e-151j
0.0084736674472663880873 - 3.534799340609930263e-889j 2.06e-39, 4.99e-152j
0.021178902900394285347 - 1.8878805371455855793e-888j 5.85e-40, 1.42e-152j
0.0017877227221305918329 - 6.6485241637682903216e-890j 6.99e-40, 1.69e-152j
0.021178902900394285347 - 6.0543251868621130673e-887j 3.22e-41, 7.79e-154j
0.024138559209594262841 + 6.8154415576363430631e-887j 2.73e-41, 6.61e-154j
0.011852879426584097282 + 5.497366259205868715e-889j 1.84e-40, 4.47e-153j
0.024138559209594262841 + 2.9659704222571647333e-888j 1.41e-41, 3.42e-154j
0.0049652769620799394749 + 2.0224272810227617714e-889j 5.88e-40, 1.43e-152j
0.0049652769620799394749 - 5.9785524979388748835e-887j 1.86e-43, 4.51e-156j
0.029143036936810883563 - 1.794869287993165373e-886j 3.83e-44, 9.27e-157j
0.015021920185382218547 - 6.8775371661542591874e-887j 2.28e-43, 5.53e-156j
0.028138967685276056475 + 8.8677319094759308058e-888j 1.07e-43, 2.6e-156j
0.029143036936810883563 - 1.622352597167543035e-887j 3.97e-44, 9.61e-157j
0.018093666154152023836 + 6.0168568423715359297e-887j 8.47e-44, 2.05e-156j
0.028138967685276056475 + 1.2074232263658495208e-886j 3.92e-45, 9.5e-158j
0.026580323122845455562 - 8.6156016107506187865e-887j 9.94e-45, 2.41e-157j
0.046706160204729512524 - 2.1380125019335215748e-887j 3.33e-49, 8.07e-162j
0.021675910559495714352 + 8.2663187273430207064e-887j 5.52e-48, 1.34e-160j
0.015021920185382218547 - 8.3153825277339525092e-889j 2.02e-45, 4.89e-158j
0.0017877227221305918329 + 1.3181866047686059095e-887j 4.05e-46, 9.82e-159j
0.031599522729074786625 - 4.3178242421634988369e-886j 3.57e-50, 8.65e-163j
0.011852879426584097282 + 1.0624997260285021747e-886j 1.39e-45, 3.36e-158j
0.030284129837680108613 + 3.0333628000121233067e-887j 1.58e-48, 3.82e-161j
0.028181136431434341505 - 5.9928331805207860683e-887j 7.08e-49, 1.72e-161j
0.030284129837680108613 + 2.7944051853704744153e-886j 2.85e-49, 6.9e-162j
0.021675910559495714352 + 5.7745025170624606106e-886j 1.13e-50, 2.74e-163j
0.028181136431434341505 - 4.7033048455230560849e-886j 3.06e-50, 7.41e-163j
0.018093666154152023836 + 1.2476845769746679491e-888j 4.39e-50, 1.06e-162j
0.040189724882380855628 - 3.3355948277839868799e-887j 4.71e-54, 1.14e-166j
0.026580323122845455562 - 4.9711563003997549688e-888j 1.74e-50, 4.22e-163j
0.037190055574145053472 + 2.4749805741001606649e-886j 3.29e-53, 7.97e-166j
0.040189724882380855628 - 1.5659926701156674755e-886j 1.91e-54, 4.63e-167j
0.049587818298354684024 + 1.4106114496328877241e-886j 1.15e-59, 2.78e-172j
0.037190055574145053472 + 4.576148319733304075e-887j 1.02e-54, 2.48e-167j
0.031599522729074786625 - 6.9356351962550669891e-887j 6.14e-54, 1.49e-166j
0.053900333448397188326 - 6.1682674817244245107e-887j 1.83e-60, 4.44e-173j
0.043568006538830918063 + 1.0551483433829963102e-886j 3.72e-57, 9e-170j
0.051849590944456372528 + 4.865008659109659964e-887j 4.46e-60, 1.08e-172j
0.05125108120887498412 - 7.7941382575546439154e-887j 3.3e-62, 8e-175j
0.043568006538830918063 + 2.5845429102705741503e-887j 1.24e-58, 3e-171j
0.052812256572344932318 + 5.2715431241054912888e-887j 2.34e-62, 5.67e-175j
0.050569689147191013501 - 5.1974499794198778626e-887j 6.67e-61, 1.62e-173j
0.046706160204729512524 - 7.598160919576225695e-887j 6.39e-60, 1.55e-172j
0.049587818298354684024 + 1.1755551809522422433e-886j 9.97e-63, 2.42e-175j
0.050569689147191013501 - 1.9125773913059570144e-887j 1.83e-62, 4.44e-175j
0.051849590944456372528 + 2.034572186103674581e-887j 5.37e-63, 1.3e-175j
0.045219572602376098953 - 1.9111229616453203234e-886j 7.72e-64, 1.87e-176j
0.048994342288802738438 + 5.9987940489628878534e-887j 7.25e-62, 1.76e-174j
0.052812256572344932318 + 7.8174881772904156101e-887j 4.11e-64, 9.95e-177j
0.053900333448397188326 - 3.7126363475778486288e-887j 1.41e-64, 3.42e-177j
0.048994342288802738438 + 1.9341833603693880914e-887j 2.02e-63, 4.9e-176j
0.045219572602376098953 - 1.7549867591653934723e-886j 2.03e-64, 4.93e-177j
0.053049263817200055124 - 4.8729581370386031166e-887j 8.08e-65, 1.96e-177j
0.053905325297675887296 + 5.255708779774574033e-887j 4.68e-65, 1.13e-177j
0.040182313728077103482 + 2.1413424845836299792e-886j 5.19e-65, 1.26e-177j
0.053049263817200055124 - 2.307909122128682701e-887j 1.57e-66, 3.81e-179j
0.053905325297675887296 + 2.8107614626186937221e-887j 1.56e-66, 3.78e-179j
0.05125108120887498412 - 1.0372293213527431951e-886j 3.56e-66, 8.55e-179j

Download

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