Rule: Q[1, 2, 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 + 2.6232168198564653178e-840j 2.46e-226, 2.46e-226j
-0.098636293502968334058 + 1.148526054344370792e-870j 5.84e-253, 5.84e-253j
-0.95426326163001177301 - 3.5092117088536084599e-845j 4.86e-229, 4.86e-229j
-0.9848650768166890393 + 1.1188993835874797791e-841j 1.81e-227, 1.81e-227j
0.93953382446470319308 + 1.6329937615537238572e-861j 1.23e-229, 1.23e-229j
0.97688244065119801513 + 1.0712189582882147125e-859j 5.62e-228, 5.62e-228j
0.99968994604588528675 - 1.5465869289511430056e-856j 7.09e-227, 7.09e-227j
-0.93953382446470319308 - 3.7973089605514319749e-860j 1.28e-229, 1.28e-229j
-0.99491345469243912009 + 4.7238682150721015691e-855j 1.29e-226, 1.29e-226j
-0.99874976263469957675 - 1.335505859188061233e-877j 2.28e-226, 2.28e-226j
0.88175702448602086613 + 1.089012495301020655e-908j 1.65e-231, 1.65e-231j
-0.99968994604588528675 + 6.3080609806195169396e-901j 7.69e-227, 7.69e-227j
-0.9667049219241865616 - 2.2971304815376016794e-914j 1.71e-228, 1.71e-228j
-0.88175702448602086613 + 3.997037431892211689e-920j 1.62e-231, 1.62e-231j
0.9667049219241865616 - 1.8853892157181261543e-915j 1.7e-228, 1.7e-228j
0.85808729765083427457 + 1.466609450279947674e-920j 3.37e-232, 3.37e-232j
0.9225217132136291628 - 2.2605451873229590186e-918j 3.25e-230, 3.25e-230j
0.99750388282687745465 + 4.7361971642829698906e-912j 2.39e-226, 2.39e-226j
-0.80444304405680818108 + 5.486414761375680645e-922j 9.35e-234, 9.35e-234j
-0.97688244065119801513 - 1.0167255756625446244e-913j 5.59e-228, 5.59e-228j
0.99491345469243912009 + 3.8073811522292387751e-922j 1.25e-226, 1.25e-226j
0.77459666924148337704 - 1.4028257289835900765e-933j 1.55e-234, 1.55e-234j
0.04937950396814930242 + 1.2806530945136258614e-954j 2.57e-254, 2.57e-254j
-0.90325059438787057201 - 1.3707183878218051959e-927j 8.13e-231, 8.13e-231j
-0.77459666924148337704 + 3.385928249187254743e-932j 1.59e-234, 1.59e-234j
0.9848650768166890393 + 2.8900814545791244366e-923j 1.78e-227, 1.78e-227j
0.74282921459565192598 + 2.4495871939032275626e-934j 2.07e-235, 2.07e-235j
0.63680349166384192103 - 8.149024838409763065e-937j 3.45e-238, 3.45e-238j
0.99079325588510780584 - 3.6433386411439562585e-925j 4.97e-227, 4.97e-227j
-0.63680349166384192103 - 4.5796895652835248204e-937j 3.23e-238, 3.23e-238j
-0.24444966077282212532 - 1.0161245615557449547e-948j 5.47e-249, 5.47e-249j
0.90325059438787057201 - 1.7555873331443278205e-929j 7.46e-231, 7.46e-231j
0.70921858718567648513 + 8.6794341721510115803e-937j 3.13e-236, 3.13e-236j
-0.2919991541426287378 + 1.5835177717311469849e-947j 1.2e-247, 1.2e-247j
-0.74282921459565192598 - 3.8876824645301164323e-934j 2.14e-235, 2.14e-235j
-0.70921858718567648513 - 6.1068722225725118718e-935j 2.62e-236, 2.62e-236j
0.14764796060646846707 - 1.4745869737810866053e-950j 1.19e-251, 1.19e-251j
0.5981780261043510039 + 2.6008626208689447351e-941j 2.9e-239, 2.9e-239j
0.83229562803130494137 + 4.8773303591738616654e-932j 6.42e-233, 6.42e-233j
-0.99079325588510780584 - 3.5999379010254980695e-924j 4.94e-227, 4.94e-227j
-0.5981780261043510039 - 5.3313233664619048127e-952j 3.13e-239, 3.13e-239j
0.95426326163001177301 + 4.0237867032580541846e-941j 4.97e-229, 4.97e-229j
0.67384756252777542177 - 5.5190500699828793629e-950j 3.11e-237, 3.11e-237j
0.55806685067819680295 + 7.9609527025821333494e-953j 2.56e-240, 2.56e-240j
-0.99750388282687745465 - 1.2512659270008784778e-944j 2.34e-226, 2.34e-226j
-0.67384756252777542177 - 2.1905640355739953086e-966j 3.06e-237, 3.06e-237j
-0.51656941841567041201 + 2.3851591436283577614e-971j 1.86e-241, 1.86e-241j
0.80444304405680818108 + 3.3165850217957210089e-963j 1.06e-233, 1.06e-233j
0.51656941841567041201 - 2.764540565749904904e-971j 1.86e-241, 1.86e-241j
0.1962927094566443174 - 4.2071508627415481677e-980j 2.78e-250, 2.78e-250j
-0.85808729765083427457 - 6.7071710423489126988e-960j 3.66e-232, 3.66e-232j
-0.42983083445732339603 + 1.4111213739673982929e-974j 8.54e-244, 8.54e-244j
-0.04937950396814930242 - 3.2479528426111122529e-984j 2.25e-254, 2.25e-254j
0.47378868408257621959 + 1.4135541995396393029e-973j 1.33e-242, 1.33e-242j
0.42983083445732339603 - 6.9617973978121618406e-974j 8.14e-244, 8.14e-244j
-0.1962927094566443174 + 6.0329884457364777497e-980j 2.85e-250, 2.85e-250j
-0.47378868408257621959 - 3.8780539614697130329e-972j 1.28e-242, 1.28e-242j
-0.83229562803130494137 + 7.8280702251229573507e-961j 5.85e-233, 5.85e-233j
0.24444966077282212532 + 2.438841765351306062e-979j 5.5e-249, 5.5e-249j
0.38480501431708872328 + 2.9352221459981613418e-975j 4.8e-245, 4.8e-245j
0.098636293502968334058 - 3.0469707714828421405e-983j 5.52e-253, 5.52e-253j
-0.55806685067819680295 - 6.857026562253796264e-970j 2.54e-240, 2.54e-240j
-0.33882304766713233616 + 4.0446645344233450395e-977j 2.81e-246, 2.81e-246j
-0.9225217132136291628 - 2.8217970806875605207e-977j 3.26e-230, 3.26e-230j
0.33882304766713233616 - 8.0828296633566016965e-994j 2.61e-246, 2.61e-246j
0.2919991541426287378 + 4.8196234812874493068e-996j 1.21e-247, 1.21e-247j
-1.9782924159425918793e-1065 + 4.1723955804387335859e-1065j 3.19e-1063, 3.19e-1063j
-0.38480501431708872328 - 1.4041074118155999074e-993j 4.71e-245, 4.71e-245j
-0.14764796060646846707 - 1.0808111338471328273e-999j 1.11e-251, 1.11e-251j

Weights

Weight (ball center) Error (ball radius)
0.00095063915331301178794 - 1.0568320418016204081e-840j 1.7e-29, 3.17e-134j
0.049154588810721586619 - 2.2624044440609944207e-847j 8.33e-30, 1.55e-134j
0.013584441653769678635 - 3.0115880591027476617e-843j 2.38e-30, 4.44e-135j
0.0069243961108118510063 - 1.0205051668339351772e-841j 2.11e-30, 3.92e-135j
0.015873418796724825159 - 3.838067590022461679e-844j 5.21e-31, 9.7e-136j
0.0090636294388291057223 + 7.6952535452553972383e-843j 5.7e-31, 1.06e-135j
0.00075662968348838281542 - 8.2354256908288367916e-841j 2.96e-30, 5.51e-135j
0.015873418796724825159 + 1.1443866994599635817e-843j 9.39e-32, 1.75e-136j
0.0033236128749914560581 - 3.3130364072282327499e-841j 2.84e-32, 5.29e-137j
0.00095063915331301178794 - 3.8311475272613349286e-841j 8.62e-33, 1.61e-137j
0.022590069714468911841 + 4.1478495204544258641e-845j 1.71e-36, 3.19e-141j
0.00075662968348838281542 + 1.1132954922257502041e-841j 5.9e-33, 1.1e-137j
0.011302539058165400601 + 9.7939634428889226989e-843j 4.14e-34, 7.71e-139j
0.022590069714468911841 - 1.1318768588462263946e-844j 6.49e-37, 1.21e-141j
0.011302539058165400601 - 2.5531227853442550615e-843j 1.86e-36, 3.46e-141j
0.024740330557037568242 - 2.2330679998915880176e-845j 4.17e-38, 7.76e-143j
0.018146769562951203773 + 1.7028462998856904294e-844j 2.87e-37, 5.35e-142j
0.0018410604291256375081 + 2.2094947857316594662e-840j 5.51e-36, 1.03e-140j
0.0288611467690400163 + 2.1117203778682203023e-845j 8.15e-42, 1.52e-146j
0.0090636294388291057223 - 4.5669301604275298838e-842j 5.59e-37, 1.04e-141j
0.0033236128749914560581 - 4.0562667291327263828e-841j 9.87e-37, 1.84e-141j
0.030819477952933378867 + 4.4954522665512098364e-846j 1.42e-42, 2.64e-147j
0.049338583828620159476 + 1.4992914396184189929e-847j 9.31e-45, 1.73e-149j
0.020389325479130724295 + 2.2390127807761442441e-844j 1.58e-40, 2.94e-145j
0.030819477952933378867 - 1.3273870351370741312e-845j 5.48e-43, 1.02e-147j
0.0069243961108118510063 - 2.5890902854567758092e-842j 3.74e-38, 6.96e-143j
0.03270244143293630063 - 2.8086466784349712103e-846j 3.5e-44, 6.51e-149j
0.037850388413374299049 + 7.6509363924443531958e-847j 5.05e-46, 9.41e-151j
0.0049728900330703774979 + 9.6580309729492735282e-842j 8.44e-38, 1.57e-142j
0.037850388413374299049 - 2.9194282680299996849e-846j 1.96e-47, 3.66e-152j
0.047873049139775959673 + 3.5687944615623657721e-847j 1.86e-48, 3.46e-153j
0.020389325479130724295 - 8.1393593302226401272e-845j 1.08e-41, 2.01e-146j
0.034505012623629483184 + 1.7946302604789860654e-846j 2.01e-45, 3.75e-150j
0.047206242342776417571 - 4.2369045720382543736e-847j 8.97e-49, 1.67e-153j
0.03270244143293630063 + 8.6679710256807913899e-846j 2.4e-47, 4.47e-152j
0.034505012623629483184 - 5.8556951605228180856e-846j 6.1e-48, 1.14e-152j
0.048848441018277381216 + 1.10503780564722667e-847j 9.99e-51, 1.86e-155j
0.039384590823161643946 - 5.0288376335858207104e-847j 7.68e-49, 1.43e-153j
0.026832825681762094254 + 1.2600230393105782702e-845j 1.25e-45, 2.32e-150j
0.0049728900330703774979 + 2.7817180153118013555e-841j 1.42e-44, 2.64e-149j
0.039384590823161643946 + 2.1428078669939806719e-846j 1.48e-50, 2.75e-155j
0.013584441653769678635 + 9.4275131646009452712e-844j 8.03e-43, 1.5e-147j
0.036222473623630778384 - 1.1659332871054768309e-846j 5.44e-48, 1.01e-152j
0.040821180087314348966 + 3.2716607140138926163e-847j 1.9e-50, 3.55e-155j
0.0018410604291256375081 + 4.650408294206247831e-841j 1.59e-44, 2.96e-149j
0.036222473623630778384 + 4.0781677930162725326e-846j 9.77e-51, 1.82e-155j
0.042156520817076445891 + 1.2338036093437216479e-846j 2.29e-53, 4.27e-158j
0.0288611467690400163 - 7.4000529582424153568e-846j 2.39e-47, 4.45e-152j
0.042156520817076445891 - 2.0661125035418733577e-847j 1.81e-52, 3.38e-157j
0.048420905094973508228 - 9.1106569176392476642e-848j 2.17e-55, 4.04e-160j
0.024740330557037568242 + 6.1228089862724281161e-845j 2.14e-51, 3.99e-156j
0.044510258321383732516 + 7.6726249405213174897e-847j 2.12e-55, 3.96e-160j
0.049338583828620159476 + 1.9700447109040478936e-847j 9.87e-56, 1.84e-160j
0.043387245486861209128 + 1.2190181193456031829e-847j 3.93e-54, 7.32e-159j
0.044510258321383732516 - 6.0834690590744740609e-848j 4.23e-55, 7.87e-160j
0.048420905094973508228 - 3.0389867345482230664e-847j 7.23e-57, 1.35e-161j
0.043387245486861209128 - 9.6440099610082802945e-847j 2.2e-56, 4.09e-161j
0.026832825681762094254 - 3.5078738304256020807e-845j 1.67e-54, 3.11e-159j
0.047873049139775959673 + 7.0434632605863533416e-848j 3.58e-57, 6.67e-162j
0.045522739897745318427 + 1.5518176286951652875e-848j 1.18e-56, 2.19e-161j
0.049154588810721586619 - 1.2977048662383059142e-847j 2.21e-57, 4.12e-162j
0.040821180087314348966 - 1.6090723780312170615e-846j 8.88e-57, 1.66e-161j
0.046422151991524369007 + 5.0922986371260876482e-847j 3.54e-58, 6.59e-163j
0.018146769562951203773 - 4.8063648611439000413e-844j 7.93e-55, 1.47e-159j
0.046422151991524369007 + 1.9274345484176526298e-848j 5.67e-58, 1.05e-162j
0.047206242342776417571 - 4.7095363537595409247e-848j 3.61e-58, 6.71e-163j
0.049399966593206867455 - 1.7198215220683589671e-847j 3.63e-59, 6.77e-164j
0.045522739897745318427 - 6.2042595398695992203e-847j 2.18e-59, 4.27e-164j
0.048848441018277381216 + 2.6121830614735470436e-847j 1.57e-59, 2.85e-164j

Download

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