Rule: Q[3, 8, 24, 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)
0.99874976263469957675 - 5.2690344186833614799e-840j 2.32e-226, 2.32e-226j
-0.098636293502968334058 + 2.4571931221435224357e-871j 4.84e-253, 4.84e-253j
-0.95426326163001177301 - 1.672530864585545132e-845j 5.05e-229, 5.05e-229j
-0.9848650768166890393 - 2.5070806009328975967e-842j 1.75e-227, 1.75e-227j
0.93953382446470319308 + 1.8464445081816207411e-859j 1.28e-229, 1.28e-229j
0.97688244065119801513 - 2.7320291833300784613e-857j 5.6e-228, 5.6e-228j
0.99968994604588528675 - 4.9273400677043782882e-855j 7.66e-227, 7.66e-227j
-0.93953382446470319308 - 7.2600118935622468734e-860j 1.32e-229, 1.32e-229j
-0.99491345469243912009 - 2.2694580043698229993e-856j 1.31e-226, 1.31e-226j
-0.99874976263469957675 - 4.5637439534950559923e-877j 2.28e-226, 2.28e-226j
0.88175702448602086613 + 9.290988610318506082e-906j 1.66e-231, 1.66e-231j
-0.99968994604588528675 - 2.7780273030143009251e-898j 7.44e-227, 7.44e-227j
-0.9667049219241865616 + 1.689495550642310762e-912j 1.64e-228, 1.64e-228j
-0.88175702448602086613 + 3.5511583335956102725e-917j 1.56e-231, 1.56e-231j
0.9667049219241865616 + 1.6337828057551527967e-914j 1.8e-228, 1.8e-228j
0.85808729765083427457 - 6.4081387333558073691e-920j 3.26e-232, 3.26e-232j
0.9225217132136291628 - 4.0852531092288360155e-917j 3.07e-230, 3.07e-230j
0.99750388282687745465 - 7.4212022911664247371e-912j 2.37e-226, 2.37e-226j
-0.80444304405680818108 - 1.0168143038617874955e-919j 1.04e-233, 1.04e-233j
-0.97688244065119801513 + 4.4916773023052265525e-912j 5.65e-228, 5.65e-228j
0.99491345469243912009 - 4.7158613661905248565e-921j 1.19e-226, 1.19e-226j
0.77459666924148337704 + 7.992665874392068743e-933j 1.52e-234, 1.52e-234j
0.04937950396814930242 + 2.0658631687187639176e-952j 2.22e-254, 2.22e-254j
-0.90325059438787057201 - 7.2777985653449221017e-927j 7.65e-231, 7.65e-231j
-0.77459666924148337704 + 8.1084480534919189641e-932j 1.49e-234, 1.49e-234j
0.9848650768166890393 - 4.7781471972177257848e-923j 1.65e-227, 1.65e-227j
0.74282921459565192598 - 9.9722289951880977836e-934j 2.16e-235, 2.16e-235j
0.63680349166384192103 + 1.6426926500828188502e-937j 3.19e-238, 3.19e-238j
0.99079325588510780584 + 2.8363114850803167932e-924j 4.68e-227, 4.68e-227j
-0.63680349166384192103 + 1.2340118426923049848e-936j 3.06e-238, 3.06e-238j
-0.24444966077282212532 - 1.9986680830527321458e-947j 6.66e-249, 6.66e-249j
0.90325059438787057201 - 5.4861507736071334579e-929j 8e-231, 8e-231j
0.70921858718567648513 + 1.7322265930625639932e-935j 2.85e-236, 2.85e-236j
-0.2919991541426287378 - 3.214808725291766378e-946j 1.38e-247, 1.38e-247j
-0.74282921459565192598 - 3.2683191079072080243e-933j 2.26e-235, 2.26e-235j
-0.70921858718567648513 + 2.9805100875483920461e-934j 2.82e-236, 2.82e-236j
0.14764796060646846707 + 2.1950357800215932868e-950j 1.24e-251, 1.24e-251j
0.5981780261043510039 - 4.4437686394733209369e-938j 2.98e-239, 2.98e-239j
0.83229562803130494137 + 2.3713901242922700295e-931j 6e-233, 6e-233j
-0.99079325588510780584 - 8.0533271141326168836e-924j 5.14e-227, 5.14e-227j
-0.5981780261043510039 + 7.155370097307359179e-952j 3e-239, 3e-239j
0.95426326163001177301 - 1.8324716821775437578e-941j 4.79e-229, 4.79e-229j
0.67384756252777542177 + 4.8684941281486028611e-951j 3.32e-237, 3.32e-237j
0.55806685067819680295 + 4.923215749657962364e-955j 2.57e-240, 2.57e-240j
-0.99750388282687745465 + 3.0503356113106084463e-944j 2.56e-226, 2.56e-226j
-0.67384756252777542177 + 4.4869310126168641164e-964j 3.24e-237, 3.24e-237j
-0.51656941841567041201 + 2.3359717983986039342e-969j 1.67e-241, 1.67e-241j
0.80444304405680818108 + 9.4131880927649109986e-962j 1e-233, 1e-233j
0.51656941841567041201 - 1.7688850535535753362e-969j 1.84e-241, 1.84e-241j
0.1962927094566443174 + 1.9320840053005343466e-978j 3.06e-250, 3.06e-250j
-0.85808729765083427457 - 6.3425148315025426029e-957j 3.12e-232, 3.12e-232j
-0.42983083445732339603 - 8.5851880479576842101e-973j 7.59e-244, 7.59e-244j
-0.04937950396814930242 - 5.3731389180044897393e-982j 2.45e-254, 2.45e-254j
0.47378868408257621959 + 6.2911434898780135164e-971j 1.33e-242, 1.33e-242j
0.42983083445732339603 - 1.8432419626996039034e-972j 7.89e-244, 7.89e-244j
-0.1962927094566443174 - 8.5941642055072208043e-978j 3.08e-250, 3.08e-250j
-0.47378868408257621959 + 6.9918423749800627779e-970j 1.19e-242, 1.19e-242j
-0.83229562803130494137 + 3.1875723753972618802e-958j 5.88e-233, 5.88e-233j
0.24444966077282212532 - 3.2591232274164631487e-977j 6.52e-249, 6.52e-249j
0.38480501431708872328 - 1.4448490601292428381e-973j 4.48e-245, 4.48e-245j
0.098636293502968334058 + 5.1792340771637009397e-981j 4.68e-253, 4.68e-253j
-0.55806685067819680295 - 4.6348517472041858982e-967j 2.52e-240, 2.52e-240j
-0.33882304766713233616 - 3.851473178783716864e-975j 2.54e-246, 2.54e-246j
-0.9225217132136291628 - 8.981288699754159368e-976j 3.18e-230, 3.18e-230j
0.33882304766713233616 + 9.9718032191998294341e-995j 2.54e-246, 2.54e-246j
0.2919991541426287378 - 3.7378628703460641551e-996j 1.41e-247, 1.41e-247j
6.8628639776920744027e-1067 - 1.447439372405982458e-1066j 1.11e-1064, 1.11e-1064j
-0.38480501431708872328 - 7.0702270838184300229e-994j 4.43e-245, 4.43e-245j
-0.14764796060646846707 - 1.3481692706807516424e-1000j 1.1e-251, 1.1e-251j

Weights

Weight (ball center) Error (ball radius)
0.00095063915331301178794 + 2.1275661392494517354e-840j 1.7e-29, 3.01e-134j
0.049154588810721586619 - 1.9645980623309844919e-847j 8.33e-30, 1.48e-134j
0.013584441653769678635 + 6.519217831795928015e-844j 2.38e-30, 4.22e-135j
0.0069243961108118510063 + 2.3104132114797892893e-842j 2.11e-30, 3.73e-135j
0.015873418796724825159 + 8.1914895597914030759e-844j 5.21e-31, 9.22e-136j
0.0090636294388291057223 - 1.5792068414451098171e-842j 5.7e-31, 1.01e-135j
0.00075662968348838281542 + 1.652693378326271924e-840j 2.96e-30, 5.24e-135j
0.015873418796724825159 - 2.2151507896163015685e-844j 9.39e-32, 1.66e-136j
0.0033236128749914560581 + 7.5341621753186012034e-842j 2.84e-32, 5.03e-137j
0.00095063915331301178794 + 8.7646537757826156257e-842j 8.62e-33, 1.53e-137j
0.022590069714468911841 - 9.4765062165360814668e-845j 1.71e-36, 3.04e-141j
0.00075662968348838281542 - 2.5506981794093221526e-842j 5.9e-33, 1.05e-137j
0.011302539058165400601 - 2.1691360209572953745e-843j 4.14e-34, 7.33e-139j
0.022590069714468911841 + 1.946037679984744096e-845j 6.49e-37, 1.15e-141j
0.011302539058165400601 + 5.2940059637410129305e-843j 1.86e-36, 3.29e-141j
0.024740330557037568242 + 5.2622037876464735974e-845j 4.17e-38, 7.38e-143j
0.018146769562951203773 - 3.70423183632703469e-844j 2.87e-37, 5.09e-142j
0.0018410604291256375081 - 4.4433312885834297482e-840j 5.51e-36, 9.75e-141j
0.0288611467690400163 - 2.7848474788060357896e-846j 8.15e-42, 1.44e-146j
0.0090636294388291057223 + 1.0134988189551351104e-842j 5.59e-37, 9.91e-142j
0.0033236128749914560581 + 8.1775954607454891538e-841j 9.87e-37, 1.75e-141j
0.030819477952933378867 - 1.2030681408425970692e-845j 1.42e-42, 2.51e-147j
0.049338583828620159476 + 2.4657496409522910644e-847j 9.31e-45, 1.65e-149j
0.020389325479130724295 - 4.0699696207748087782e-845j 1.58e-40, 2.79e-145j
0.030819477952933378867 + 1.5232865802446035778e-846j 5.48e-43, 9.71e-148j
0.0069243961108118510063 + 5.2711861223552286949e-842j 3.74e-38, 6.62e-143j
0.03270244143293630063 + 7.9625611986307987938e-846j 3.5e-44, 6.19e-149j
0.037850388413374299049 - 2.7808341446488177076e-846j 5.05e-46, 8.95e-151j
0.0049728900330703774979 - 1.954896515173264377e-841j 8.44e-38, 1.5e-142j
0.037850388413374299049 + 6.4630307487043583759e-848j 1.96e-47, 3.48e-152j
0.047873049139775959673 + 1.6840823998472334517e-847j 1.86e-48, 3.29e-153j
0.020389325479130724295 + 1.8109666797386465889e-844j 1.08e-41, 1.91e-146j
0.034505012623629483184 - 5.4467926805844453945e-846j 2.01e-45, 3.56e-150j
0.047206242342776417571 - 1.6126166614683494734e-847j 8.97e-49, 1.59e-153j
0.03270244143293630063 - 8.2764223989302980947e-847j 2.4e-47, 4.25e-152j
0.034505012623629483184 + 4.3225440568519493494e-847j 6.1e-48, 1.08e-152j
0.048848441018277381216 + 3.0298188988165342875e-847j 9.99e-51, 1.77e-155j
0.039384590823161643946 + 2.0654719336315681955e-846j 7.68e-49, 1.36e-153j
0.026832825681762094254 - 3.0782816103092696783e-845j 1.25e-45, 2.21e-150j
0.0049728900330703774979 - 6.2863553783825524385e-842j 1.42e-44, 2.51e-149j
0.039384590823161643946 + 1.8482539450313115025e-848j 1.48e-50, 2.62e-155j
0.013584441653769678635 - 1.9803953162809997938e-843j 8.03e-43, 1.42e-147j
0.036222473623630778384 + 3.839066330927348038e-846j 5.44e-48, 9.63e-153j
0.040821180087314348966 - 1.5700816215502455367e-846j 1.9e-50, 3.37e-155j
0.0018410604291256375081 - 1.0618144237852675736e-841j 1.59e-44, 2.82e-149j
0.036222473623630778384 - 2.0179780813935163391e-847j 9.77e-51, 1.73e-155j
0.042156520817076445891 + 1.0180281729636084214e-847j 2.29e-53, 4.06e-158j
0.0288611467690400163 + 1.8854790680032056979e-845j 2.39e-47, 4.23e-152j
0.042156520817076445891 + 1.219435917126478584e-846j 1.81e-52, 3.21e-157j
0.048420905094973508228 - 3.4217371520203019188e-847j 2.17e-55, 3.84e-160j
0.024740330557037568242 - 9.8175780697668160287e-846j 2.14e-51, 3.79e-156j
0.044510258321383732516 + 1.3633488773147417961e-847j 2.12e-55, 3.76e-160j
0.049338583828620159476 + 2.0985611942353177039e-847j 9.87e-56, 1.75e-160j
0.043387245486861209128 - 9.6626688401099187242e-847j 3.93e-54, 6.95e-159j
0.044510258321383732516 + 7.8015538286109467852e-847j 4.23e-55, 7.48e-160j
0.048420905094973508228 - 1.7628568171758707512e-847j 7.23e-57, 1.28e-161j
0.043387245486861209128 - 1.2247330409485074394e-847j 2.2e-56, 3.89e-161j
0.026832825681762094254 + 5.1573827318399667595e-846j 1.67e-54, 2.96e-159j
0.047873049139775959673 + 3.9163847115431711461e-847j 3.58e-57, 6.34e-162j
0.045522739897745318427 - 6.4109090327837465122e-847j 1.18e-56, 2.08e-161j
0.049154588810721586619 - 2.7169853884838817259e-847j 2.21e-57, 3.91e-162j
0.040821180087314348966 - 6.968171021868323223e-848j 8.88e-57, 1.57e-161j
0.046422151991524369007 + 1.5417846817273150496e-847j 3.54e-58, 6.26e-163j
0.018146769562951203773 + 9.1127626820521978798e-845j 7.93e-55, 1.4e-159j
0.046422151991524369007 + 5.3564145751914603712e-847j 5.67e-58, 1e-162j
0.047206242342776417571 - 4.5462117412811738713e-847j 3.61e-58, 6.37e-163j
0.049399966593206867455 - 2.2629671090035136788e-847j 3.63e-59, 6.43e-164j
0.045522739897745318427 - 1.4628332649374949606e-847j 2.18e-59, 4.06e-164j
0.048848441018277381216 + 1.8545795481103311769e-847j 1.57e-59, 2.71e-164j

Download

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