Rule: Q[2, 6, 18, 47]

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.

Warning: This rule has negative weights!

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)
0.99938427483443948435 - 1.1797222071513579408e-787j 1.15e-228, 1.15e-228j
-0.98219129046748981137 + 1.2428889873031789789e-802j 2.3e-228, 2.3e-228j
-0.94737800835893597774 - 4.0826801980628428134e-802j 2.8e-228, 2.8e-228j
-0.99005569680912353749 + 1.0661964647002688067e-802j 3.44e-228, 3.44e-228j
0.95526936302604635714 - 5.1928576497799567547e-799j 2.14e-227, 2.14e-227j
0.92975579501629335971 + 7.9786488860220700982e-811j 3.04e-229, 3.04e-229j
0.99743547653621082213 - 1.0696362217393360587e-812j 4.3e-228, 4.3e-228j
-0.89266796506161021982 + 1.019441264059162756e-832j 2.88e-230, 2.88e-230j
-0.99743547653621082213 + 1.7797493662222184796e-829j 3.97e-228, 3.97e-228j
0.99517513040458488078 - 4.5584692275128131113e-829j 5.22e-228, 5.22e-228j
0.89266796506161021982 - 7.0787701053506841643e-837j 2.66e-230, 2.66e-230j
-0.99938427483443948435 + 9.1384061700243303506e-837j 1.1e-228, 1.1e-228j
-0.97179658930668721847 - 1.6385489198732293008e-835j 2.36e-228, 2.36e-228j
-0.87264705591622591191 - 1.9872175247601503267e-840j 8.38e-231, 8.38e-231j
0.64880670170968723604 - 1.8614574326151289707e-844j 7.22e-237, 7.22e-237j
0.87264705591622591191 - 8.5514829391085348807e-838j 8.51e-231, 8.51e-231j
0.94737800835893597774 + 5.0135204249333740463e-834j 2.88e-228, 2.88e-228j
0.97179658930668721847 + 1.9179517871672893177e-850j 2.21e-228, 2.21e-228j
-0.77421495376050439073 - 9.6829250121480290177e-868j 1.74e-233, 1.74e-233j
-0.95678295794889329949 - 4.3137335523578999699e-861j 1.98e-227, 1.98e-227j
0.95678295794889329949 + 2.309513685950178953e-861j 1.83e-227, 1.83e-227j
0.74508370875818926375 + 1.6835780457140289407e-876j 2.78e-234, 2.78e-234j
0.99005569680912353749 - 1.6853520993500197991e-869j 3.11e-228, 3.11e-228j
-0.85110112875893547946 - 7.6366215477464293995e-884j 2e-231, 2e-231j
-0.82747789237571241921 + 1.1312492778116259592e-884j 4.68e-232, 4.68e-232j
0.1140802956189406021 + 3.4704840613010294774e-906j 2.45e-252, 2.45e-252j
0.77421495376050439073 - 5.2203365280978401749e-888j 1.68e-233, 1.68e-233j
0.80175984712866539843 - 9.0763462590995163881e-887j 8.89e-233, 8.89e-233j
-0.99517513040458488078 - 1.3395872670392124087e-880j 4.87e-228, 4.87e-228j
-0.61375987477044822826 + 2.3768970696778972662e-892j 7.75e-238, 7.75e-238j
-0.50093357346678984413 - 3.3224503092643594977e-896j 5.65e-241, 5.65e-241j
0.82747789237571241921 - 7.2764749350806307627e-886j 4.75e-232, 4.75e-232j
0.68239011718365358647 + 4.4867611802953029329e-890j 5.95e-236, 5.95e-236j
-0.80175984712866539843 + 7.7206739991368042376e-887j 9.14e-233, 9.14e-233j
-0.71447542930649101156 - 3.5639598665311804109e-889j 4.54e-235, 4.54e-235j
-0.74508370875818926375 + 3.9108606224525566429e-888j 2.8e-234, 2.8e-234j
0.91170554006328717675 + 3.7600959649245932679e-882j 8.39e-230, 8.39e-230j
0.57735026918962576451 - 6.9245484536486308096e-894j 7.26e-239, 7.26e-239j
0.2925799740003368291 - 8.0501354641250752546e-903j 4.86e-247, 4.86e-247j
-0.2925799740003368291 + 4.1745365738206104945e-903j 4.7e-247, 4.7e-247j
-0.57735026918962576451 + 2.2764203212128654069e-895j 7.62e-239, 7.62e-239j
-0.91170554006328717675 - 2.4356845266933843629e-882j 8.65e-230, 8.65e-230j
0.71447542930649101156 - 8.8350865724023622457e-889j 4.53e-235, 4.53e-235j
0.61375987477044822826 - 5.210712864922691324e-893j 7.9e-238, 7.9e-238j
0.98219129046748981137 + 2.0246240936786459693e-881j 2.43e-228, 2.43e-228j
-0.64880670170968723604 + 1.2201271355281485651e-903j 7.13e-237, 7.13e-237j
-0.68239011718365358647 - 2.4182953653124454067e-902j 5.96e-236, 5.96e-236j
-0.068509439373879866294 - 8.8245356579211006959e-920j 1.09e-253, 1.09e-253j
0.46111006295702354451 + 8.6591694745515856609e-909j 3.85e-242, 3.85e-242j
0.85110112875893547946 + 4.7644846869996011896e-899j 2.06e-231, 2.06e-231j
-0.92975579501629335971 - 4.3723205960953263907e-893j 2.96e-229, 2.96e-229j
-0.46111006295702354451 + 2.6699456832329276919e-910j 4.35e-242, 4.35e-242j
-0.95526936302604635714 - 5.6783861823487085635e-915j 2.16e-227, 2.16e-227j
0.53970495345071090898 - 2.4128991844485551843e-932j 7.3e-240, 7.3e-240j
0.50093357346678984413 + 2.7585868855426521998e-934j 5.57e-241, 5.57e-241j
-0.02255064885557926965 + 1.0337109401440471363e-947j 5.83e-255, 5.83e-255j
-0.42028669872369888199 - 8.0338204777458419761e-935j 2.7e-243, 2.7e-243j
-0.2486390713361216634 - 2.0030528926757670736e-941j 2.27e-248, 2.27e-248j
0.068509439373879866294 + 1.6005099932737380328e-946j 1.09e-253, 1.09e-253j
0.42028669872369888199 - 1.6979763132598125098e-936j 2.77e-243, 2.77e-243j
0.15932622241604883463 - 9.280775873352927779e-944j 4.86e-251, 4.86e-251j
-0.53970495345071090898 + 1.3643031529603935155e-932j 6.65e-240, 6.65e-240j
-0.33591637530927440701 + 3.6393499521604133134e-938j 1e-245, 1e-245j
-2.5921592962793658926e-983 - 3.866383214977224686e-984j 1.91e-981, 1.91e-981j
0.33591637530927440701 + 9.9517155193641999475e-939j 9.56e-246, 9.56e-246j
0.2041968861768067152 + 1.8395093526674477399e-942j 1.16e-249, 1.16e-249j
-0.1140802956189406021 - 5.4864260693344703045e-945j 2.15e-252, 2.15e-252j
-0.37852488518370962071 + 1.1294747357918676112e-936j 1.75e-244, 1.75e-244j
-0.15932622241604883463 + 3.3735668878383722684e-943j 5.23e-251, 5.23e-251j
0.2486390713361216634 - 5.5999526137338975586e-941j 2.27e-248, 2.27e-248j
0.37852488518370962071 - 7.0242901630905200351e-938j 1.68e-244, 1.68e-244j
0.02255064885557926965 - 1.8281411867063042754e-947j 5.83e-255, 5.83e-255j
-0.2041968861768067152 - 4.3676160999846664795e-942j 1.13e-249, 1.13e-249j

Weights

Weight (ball center) Error (ball radius)
0.0015282784979043083813 + 2.0630043944590795078e-787j 1.3e-23, 1.51e-130j
0.0091235932504872246129 + 4.8349100931127876815e-790j 6.2e-24, 7.22e-131j
0.020684349058424575263 + 3.5021837004081514089e-789j 2.23e-24, 2.6e-131j
0.0065791540081857160106 - 4.3282189830288407652e-790j 3.91e-24, 4.56e-131j
-0.046635095964010155155 - 7.8117289543344456776e-787j 1.59e-25, 1.85e-132j
0.017512712135255850148 - 2.7136853288854039373e-788j 1.1e-25, 1.28e-132j
0.0018676906571449896074 - 3.8575874709831953856e-787j 2.3e-25, 2.68e-132j
0.019485551956403766348 - 6.4701416230983678481e-790j 1.19e-26, 1.39e-133j
0.0018676906571449896074 - 3.7648164755814953325e-790j 3.23e-26, 3.76e-133j
0.0034793995166256890238 + 2.40637986455014788e-787j 4.62e-26, 5.38e-133j
0.019485551956403766348 - 1.1471391745548400871e-788j 5.29e-28, 6.17e-135j
0.0015282784979043083813 + 9.0202744234181637519e-791j 1.72e-26, 2e-133j
0.011723385686473123852 - 7.8272544505181767082e-790j 6.12e-27, 7.13e-134j
0.020659650036966942347 + 5.8498304759384543125e-790j 5.4e-29, 6.29e-136j
0.034327219172102105046 + 1.1092884254604010722e-789j 2.55e-31, 2.97e-138j
0.020659650036966942347 + 8.6407655336101539905e-789j 1.87e-29, 2.18e-136j
0.020684349058424575263 + 1.3109803104216885873e-787j 1.94e-28, 2.26e-135j
0.011723385686473123852 - 5.5926888741975410624e-788j 2.75e-29, 3.21e-136j
0.028368112166980766963 + 3.2017730931986457451e-790j 3.91e-34, 4.55e-141j
0.053224767475278252169 + 1.5226676303202296999e-788j 2.01e-30, 2.34e-137j
0.053224767475278252169 + 6.9917850962041681948e-787j 3.89e-28, 4.54e-135j
0.029876600751384466489 - 1.9914681423812674974e-789j 1.82e-34, 2.11e-141j
0.0065791540081857160106 - 9.2304870340258590437e-788j 3.15e-29, 3.67e-136j
0.0225359700940587831 - 5.0639713258085221758e-790j 8.58e-34, 1e-140j
0.024705929561752095879 + 4.2627002985011113865e-790j 2.03e-34, 2.36e-141j
0.045416577055449806415 - 1.0507589923355979209e-789j 4.17e-39, 4.85e-146j
0.028368112166980766963 + 2.5219520408686050316e-789j 6e-35, 6.99e-142j
0.026680155004116236219 - 3.3128573637350775409e-789j 7.2e-35, 8.39e-142j
0.0034793995166256890238 + 5.0782144549771580315e-790j 1.99e-32, 2.32e-139j
0.035748878153310489798 - 2.2595142160523276558e-790j 1.3e-39, 1.52e-146j
0.039307031915486032258 + 2.2218828674765175478e-790j 1.85e-40, 2.15e-147j
0.024705929561752095879 + 4.5300039440703313177e-789j 4.43e-35, 5.16e-142j
0.032833927327429702605 - 1.326933909260255436e-789j 1.9e-37, 2.21e-144j
0.026680155004116236219 - 3.6349203408847881317e-790j 3.99e-37, 4.64e-144j
0.031341650534268805441 + 2.6800425258377668549e-790j 1.47e-39, 1.72e-146j
0.029876600751384466489 - 2.903071198173209009e-790j 8.87e-39, 1.03e-145j
0.018576470805815883584 + 1.5876227834667593701e-788j 8.42e-36, 9.81e-143j
0.037048353553942702102 + 8.2361501116619375095e-790j 4.08e-42, 4.75e-149j
0.043658219762451732134 - 5.8259502610640387455e-790j 6.49e-45, 7.56e-152j
0.043658219762451732134 - 3.1872450841262703555e-790j 1.81e-45, 2.11e-152j
0.037048353553942702102 + 2.20451529770212731e-790j 1.63e-42, 1.9e-149j
0.018576470805815883584 + 7.283841704507525596e-790j 1.04e-38, 1.22e-145j
0.031341650534268805441 + 1.6121706863493593447e-789j 5.99e-40, 6.98e-147j
0.035748878153310489798 - 9.4520008017369102033e-790j 8.09e-42, 9.42e-149j
0.0091235932504872246129 + 5.5724704312248111895e-788j 5.62e-37, 6.54e-144j
0.034327219172102105046 + 2.3595059651926182745e-790j 1.42e-42, 1.66e-149j
0.032833927327429702605 - 2.5011101299944851686e-790j 4.29e-42, 5e-149j
0.04572106474182267294 + 1.4260149223503005531e-789j 5.18e-49, 6.03e-156j
0.04033186357068243478 - 6.2116108386835520824e-790j 9e-47, 1.05e-153j
0.0225359700940587831 - 6.319534802596752878e-789j 1.25e-40, 1.46e-147j
0.017512712135255850148 - 9.794508294541192659e-790j 8.26e-41, 9.63e-148j
0.04033186357068243478 - 2.289327553119804527e-790j 1.16e-47, 1.35e-154j
-0.046635095964010155155 - 1.763042450195602805e-788j 2.1e-39, 2.45e-146j
0.038223681478745527349 - 7.3431663209313646547e-790j 1.73e-46, 2.02e-153j
0.039307031915486032258 + 6.6877837943920122386e-790j 3.03e-47, 3.53e-154j
0.046501237181930804323 - 4.5442808309202323119e-789j 1.3e-51, 1.51e-158j
0.041305023876400478303 + 2.4006656388892192725e-790j 6.63e-50, 7.72e-157j
0.044206191394021330456 + 3.729143236214744598e-790j 1.38e-51, 1.61e-158j
0.04572106474182267294 + 1.6359152852077278208e-789j 3.35e-52, 3.91e-159j
0.041305023876400478303 + 5.8852868071715352401e-790j 6.65e-51, 7.74e-158j
0.045066598658740041377 + 8.1209718479642795028e-790j 1.5e-52, 1.75e-159j
0.038223681478745527349 - 2.1931812978604004932e-790j 5.67e-50, 6.6e-157j
0.042993561595404753794 + 2.8199685873737186611e-790j 3.31e-52, 3.86e-159j
-0.0017544974534622175865 + 7.3408791811856182287e-789j 9.3e-53, 1.08e-159j
0.042993561595404753794 + 5.675490691863165902e-790j 2.42e-53, 2.81e-160j
0.044666255997889129982 - 6.8897988782254193042e-790j 1.3e-53, 1.52e-160j
0.045416577055449806415 - 8.3544743299051695539e-790j 2.7e-54, 3.14e-161j
0.042203238057404044848 - 2.5697163784389406113e-790j 1.04e-53, 1.21e-160j
0.045066598658740041377 + 5.8876551222531838529e-790j 8.73e-55, 1.02e-161j
0.044206191394021330456 + 6.1992508221473548381e-790j 6.04e-55, 7.07e-162j
0.042203238057404044848 - 5.7031202161438269144e-790j 5.93e-55, 6.94e-162j
0.046501237181930804323 - 4.7540944134871445121e-789j 2.15e-54, 2.56e-161j
0.044666255997889129982 - 4.5519831614422237731e-790j 2.37e-55, 2.69e-162j

Download

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