Rule: Q[1, 2, 8, 22, 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)
-0.99970410104391670461 - 4.0148550998459166566e-845j 1.09e-229, 1.09e-229j
-0.98468195927199447623 + 1.7721582996053246653e-847j 2.26e-229, 2.26e-229j
-0.9225217132136291628 + 4.2538253718099908048e-850j 2.58e-231, 2.58e-231j
-0.99823057474573572479 + 6.1788476649887390474e-848j 2.77e-229, 2.77e-229j
0.95417744289591430055 - 7.3991109177650088492e-850j 2.12e-230, 2.12e-230j
0.93950036120944049357 - 1.6293602065233834156e-852j 7.77e-231, 7.77e-231j
0.99527136786624958644 + 5.1282062482105852921e-853j 3.72e-229, 3.72e-229j
-0.93950036120944049357 - 7.6373053359110006252e-885j 7.8e-231, 7.8e-231j
0.99079325588510780584 + 3.0878569855523570786e-879j 3.23e-229, 3.23e-229j
0.99823057474573572479 - 1.380155031146304939e-897j 2.83e-229, 2.83e-229j
0.88177827725295929029 + 6.6764064414858741945e-921j 2.06e-232, 2.06e-232j
0.99970410104391670461 - 3.9172853290849624949e-916j 1.12e-229, 1.12e-229j
-0.88177827725295929029 - 7.7454040090762281574e-930j 2.08e-232, 2.08e-232j
-0.85810591605597981957 + 4.4575244728591152836e-930j 4.54e-233, 4.54e-233j
0.70921295863303400043 + 1.6731290664949966429e-934j 9.02e-237, 9.02e-237j
0.85810591605597981957 + 5.8274596227889762328e-930j 4.97e-233, 4.97e-233j
0.90326723171240018946 - 1.9484339083065046309e-928j 7.61e-232, 7.61e-232j
-0.99527136786624958644 - 3.8410310688784347943e-925j 3.75e-229, 3.75e-229j
-0.77459666924148337704 + 6.4040908696711345907e-933j 4.21e-235, 4.21e-235j
-0.95417744289591430055 - 9.7072000489953640423e-928j 2.32e-230, 2.32e-230j
0.9225217132136291628 + 3.0074029611237091238e-928j 2.6e-231, 2.6e-231j
0.77459666924148337704 - 4.0232105744484004399e-932j 3.87e-235, 3.87e-235j
-0.96655433101153010644 + 5.6004523323385025409e-927j 5.29e-230, 5.29e-230j
-0.83230817570307920397 - 4.5394305527350235454e-932j 1.11e-233, 1.11e-233j
-0.80444880898222963771 - 8.1222458940987642592e-933j 2.04e-234, 2.04e-234j
-0.97667972251506854616 + 6.1378254605284848229e-927j 1.16e-229, 1.16e-229j
0.74282534743536069472 - 2.6737567163574158066e-933j 6.03e-236, 6.03e-236j
0.96655433101153010644 + 3.1067174629104427918e-925j 5.52e-230, 5.52e-230j
-0.99079325588510780584 + 8.7683107191728471068e-937j 3.27e-229, 3.27e-229j
-0.6367993325216061138 + 1.7495090786477115648e-947j 1.33e-238, 1.33e-238j
-0.24444856241006580723 - 1.0059739053980797446e-958j 5.17e-249, 5.17e-249j
0.80444880898222963771 - 1.6847879487418159313e-942j 2.2e-234, 2.2e-234j
0.67384201563671628051 - 4.7790723882792816146e-945j 1.17e-237, 1.17e-237j
0.98468195927199447623 + 2.1107793693076944332e-939j 2.19e-229, 2.19e-229j
-0.5981759193301111904 + 1.790804940361734326e-967j 1.42e-239, 1.42e-239j
-0.74282534743536069472 + 4.7136526679647994741e-964j 6.07e-236, 6.07e-236j
0.97667972251506854616 - 1.6479557166563028939e-961j 1.09e-229, 1.09e-229j
0.6367993325216061138 + 8.3184307163565398298e-972j 1.32e-238, 1.32e-238j
0.83230817570307920397 - 6.6765299979684466627e-967j 1.12e-233, 1.12e-233j
-0.70921295863303400043 - 1.5012154089531038351e-967j 9.12e-237, 9.12e-237j
-0.55806685067819680295 - 2.304257382423477909e-972j 1.29e-240, 1.29e-240j
-0.90326723171240018946 + 8.9365422616522686624e-974j 7.35e-232, 7.35e-232j
0.55806685067819680295 + 9.4710043624653042651e-985j 1.31e-240, 1.31e-240j
0.51657109968341089508 - 1.2310401988171842238e-985j 1.21e-241, 1.21e-241j
0.098634553014592439996 - 1.8829497158483957579e-996j 4.64e-253, 4.64e-253j
-0.51657109968341089508 + 2.8645455688631088948e-983j 1.14e-241, 1.14e-241j
-0.67384201563671628051 + 7.5006295290150953183e-986j 1.15e-237, 1.15e-237j
0.049378511602724708577 - 2.9697510862827490062e-1002j 2.17e-254, 2.17e-254j
0.47379132949741309452 + 2.5655461547294822695e-989j 8.52e-243, 8.52e-243j
0.5981759193301111904 - 2.7986368132498220218e-991j 1.42e-239, 1.42e-239j
-0.33882426570083056354 - 9.1674257023603355645e-998j 2.15e-246, 2.15e-246j
-0.47379132949741309452 + 1.0222145140621716883e-993j 9.26e-243, 9.26e-243j
-0.1476459082052927976 + 6.0502151582485825956e-1004j 1.12e-251, 1.12e-251j
0.33882426570083056354 - 7.6208054824076974658e-999j 2.01e-246, 2.01e-246j
0.38480726695303768366 + 7.4235393988106332293e-997j 3.65e-245, 3.65e-245j
-8.5888067967421873318e-1049 - 2.0706700204479491766e-1048j 1.5e-1046, 1.5e-1046j
-0.42983363895728045028 - 5.4302071400462979512e-995j 5.81e-244, 5.81e-244j
-0.2919991541426287378 + 3.5045821819590476262e-999j 1.04e-247, 1.04e-247j
0.1476459082052927976 + 4.3807189209004668657e-1004j 1.08e-251, 1.08e-251j
0.42983363895728045028 - 8.8343417026597510971e-996j 5.89e-244, 5.89e-244j
0.19629087859904982233 - 1.2664431050402015958e-1003j 2.3e-250, 2.3e-250j
-0.19629087859904982233 - 1.3234117775538533256e-1002j 2.24e-250, 2.24e-250j
-0.38480726695303768366 + 3.1155331763079662239e-996j 3.79e-245, 3.79e-245j
-0.049378511602724708577 - 1.4624111158019613899e-1006j 2.35e-254, 2.35e-254j
0.24444856241006580723 - 2.7846554917036973745e-1001j 4.95e-249, 4.95e-249j
0.2919991541426287378 + 9.2941673281790257701e-1000j 1.03e-247, 1.03e-247j
-0.098634553014592439996 - 7.1514879376889152972e-1005j 5.72e-253, 5.72e-253j

Weights

Weight (ball center) Error (ball radius)
0.0007953830760179075773 - 4.1671499779819735527e-845j 1.88e-23, 1.88e-130j
0.0070104091656751119795 - 8.357142033893110725e-846j 3.96e-24, 3.97e-131j
0.018122426792585656544 + 3.7901617504121508124e-847j 1e-24, 1e-131j
0.0022009833498934978465 + 6.0194221034401196075e-845j 1.35e-23, 1.35e-130j
0.013523670782711931926 + 2.7268762209567688322e-848j 1.22e-25, 1.23e-132j
0.015830396101133155688 - 2.0831629937875717881e-848j 1.01e-25, 1.01e-132j
0.0037153368653435579011 - 6.1955899545037290249e-848j 1.01e-26, 1.01e-133j
0.015830396101133155688 - 6.5200455053362753836e-847j 3.22e-26, 3.23e-133j
0.0052591624859932865213 + 6.7561375954329849782e-848j 6.29e-27, 6.3e-134j
0.0022009833498934978465 + 4.3601647895088612897e-848j 2.93e-27, 2.93e-134j
0.022589806317219724164 + 9.2608828385784723256e-849j 1.06e-30, 1.06e-137j
0.0007953830760179075773 - 1.5710774394448303666e-848j 1.44e-27, 1.45e-134j
0.022589806317219724164 + 1.4692052538197059557e-847j 1.68e-31, 1.68e-138j
0.024745226231400873948 - 9.7200879826456937266e-848j 7.09e-32, 7.1e-139j
0.034505779650501820651 + 3.3329479924530931761e-849j 8.21e-34, 8.23e-141j
0.024745226231400873948 - 7.44074135692670072e-849j 2.84e-32, 2.84e-139j
0.020379549844067645494 - 1.1802556375383023348e-848j 1.78e-31, 1.78e-138j
0.0037153368653435579011 - 2.8553910900691085077e-845j 5.75e-32, 5.76e-139j
0.030824378168674219199 + 3.4322305743830059259e-848j 5.12e-36, 5.13e-143j
0.013523670782711931926 + 1.1764847698595802099e-846j 3.13e-33, 3.14e-140j
0.018122426792585656544 + 1.5435037798686789958e-848j 1.83e-33, 1.84e-140j
0.030824378168674219199 + 4.3645453596661856121e-849j 6.72e-37, 6.73e-144j
0.011237673675994406662 - 2.2075591360630095559e-846j 2.08e-33, 2.09e-140j
0.026839619292757064696 + 6.6635393068725123906e-848j 4.72e-36, 4.73e-143j
0.028867632734499652369 - 4.7151813058257839265e-848j 9.88e-37, 9.9e-144j
0.0090338343941237849284 + 4.2111802373826296953e-846j 1.31e-33, 1.31e-140j
0.032705244305957020794 - 3.784923615400032835e-849j 1.85e-39, 1.85e-146j
0.011237673675994406662 - 3.6436582618742010262e-848j 1.21e-36, 1.21e-143j
0.0052591624859932865213 + 1.5623411979702413911e-845j 1.49e-33, 1.49e-140j
0.037848560108731145407 + 1.2136729016231046639e-848j 3.54e-42, 3.54e-149j
0.047873998297058339519 - 3.0025920355752372747e-849j 4.44e-45, 4.45e-152j
0.028867632734499652369 - 5.1172882163103984217e-849j 1.88e-39, 1.88e-146j
0.03622163560819422054 - 2.9769705044910396455e-849j 7.2e-42, 7.21e-149j
0.0070104091656751119795 - 6.1486732596477001525e-848j 4.35e-37, 4.36e-144j
0.039382417757958066764 - 9.8183311088707600997e-849j 2.26e-44, 2.27e-151j
0.032705244305957020794 - 2.5625513127374121864e-848j 4.53e-42, 4.54e-149j
0.0090338343941237849284 + 4.9199380412039558676e-848j 2.44e-37, 2.45e-144j
0.037848560108731145407 + 2.6946000556111829746e-849j 2.21e-44, 2.21e-151j
0.026839619292757064696 + 6.1096610351565473895e-849j 2e-40, 2e-147j
0.034505779650501820651 + 1.9575343776174443271e-848j 2.38e-43, 2.39e-150j
0.040819220562245432564 + 8.0729648958373813136e-849j 4.48e-46, 4.49e-153j
0.020379549844067645494 - 2.3113697079739620607e-847j 4.56e-40, 4.57e-147j
0.040819220562245432564 + 2.290758096651575169e-849j 3.39e-47, 3.39e-154j
0.042155166650439025395 - 2.1490162951794913148e-849j 4.16e-48, 4.16e-155j
0.04915403352337792146 + 1.9148331121962115413e-849j 4.58e-52, 4.59e-159j
0.042155166650439025395 - 6.739372116737117455e-849j 1.7e-48, 1.7e-155j
0.03622163560819422054 - 1.5267768509046414743e-848j 1.63e-45, 1.63e-152j
0.049337675590295678703 - 1.983385983320079052e-849j 1.17e-52, 1.17e-159j
0.043386685628243512325 + 2.0381997806220439083e-849j 5.67e-50, 5.68e-157j
0.039382417757958066764 - 2.4697590965103124657e-849j 1.48e-47, 1.49e-154j
0.046423330721986493672 - 3.7465671933091334457e-849j 3.72e-52, 3.73e-159j
0.043386685628243512325 + 5.7068433894958690411e-849j 2.39e-50, 2.39e-157j
0.048848389116050906697 - 2.5124565980630532921e-849j 1.24e-53, 1.24e-160j
0.046423330721986493672 - 1.8505694080916655546e-849j 1.33e-53, 1.33e-160j
0.045523579339177354529 + 1.8919027823594182721e-849j 4.66e-53, 4.67e-160j
0.04939893170347493219 + 2.0739130738690275001e-849j 1.21e-54, 1.21e-161j
0.044510483497866468382 - 4.8979824950591892945e-849j 9.17e-53, 9.18e-160j
0.047207448126030162956 + 3.3353236897203406493e-849j 9.12e-54, 9.13e-161j
0.048848389116050906697 - 1.8661266124968501006e-849j 1.8e-55, 1.8e-162j
0.044510483497866468382 - 1.9536343151239940677e-849j 3.49e-54, 3.5e-161j
0.048421396386057486106 + 1.8358487408920102241e-849j 6.23e-56, 6.23e-163j
0.048421396386057486106 + 2.7323324831627203386e-849j 7.86e-56, 7.84e-163j
0.045523579339177354529 + 4.2577836609802362093e-849j 4.56e-55, 4.57e-162j
0.049337675590295678703 - 2.1893835134694453776e-849j 1.22e-56, 1.23e-163j
0.047873998297058339519 - 1.8232077097945273969e-849j 4.58e-57, 4.7e-164j
0.047207448126030162956 + 1.8279933579208636532e-849j 4.74e-57, 4.9e-164j
0.04915403352337792146 + 2.3337979729403965657e-849j 3.86e-57, 3.65e-164j

Download

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