Rule: Q[12, 26, 39]

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)
0.99381937293232952854 - 9.2029580177155852832e-783j 4.47e-226, 4.47e-226j
-0.97284885228713460901 - 2.7285480584222566101e-789j 7.37e-227, 7.37e-227j
-0.93655622336835242944 - 1.0080099834210887371e-790j 7.1e-228, 7.1e-228j
-0.99981909887392141229 + 4.4723028532574467687e-787j 7.56e-226, 7.56e-226j
0.97284885228713460901 - 2.9062446138461529869e-792j 7.43e-227, 7.43e-227j
0.95032654598470294068 - 2.7600006630969124578e-797j 1.63e-227, 1.63e-227j
0.76990267419430468704 + 3.3311496707702864813e-805j 2.59e-232, 2.59e-232j
-0.88550550394625872589 + 7.7267510484105115001e-802j 3.18e-229, 3.18e-229j
-0.95032654598470294068 + 4.5363101890176355817e-799j 1.75e-227, 1.75e-227j
-0.99927796258795845889 - 2.7151050016275328142e-795j 1.25e-225, 1.25e-225j
0.88550550394625872589 - 7.8247982524267243688e-807j 3.24e-229, 3.24e-229j
-0.99738453741357650427 + 4.2114695634598909e-803j 7.96e-226, 7.96e-226j
-0.92114412261476900694 - 4.2032393685280794204e-806j 3e-228, 3e-228j
-0.90411725637047485668 + 2.5335465344317048087e-807j 1.01e-228, 1.01e-228j
0.65290189927931623274 + 7.0631485352368662785e-813j 1.51e-235, 1.51e-235j
0.82049893693481308376 - 3.3815238332237922095e-808j 6.09e-231, 6.09e-231j
0.92114412261476900694 - 1.5761868435922433197e-803j 2.92e-228, 2.92e-228j
-0.7425558144209943417 + 3.4865955495816937039e-812j 4.43e-233, 4.43e-233j
-0.82049893693481308376 - 3.3235772630205373477e-809j 5.92e-231, 5.92e-231j
-0.99381937293232952854 - 2.0269650914097703309e-803j 5.02e-226, 5.02e-226j
0.86534135474544746183 - 2.0395916400518410838e-807j 9.51e-230, 9.51e-230j
0.79589886862336672061 - 7.324616810661920207e-810j 1.25e-231, 1.25e-231j
0.98156063424671925069 + 6.7194326630863205378e-803j 1.51e-226, 1.51e-226j
-0.86534135474544746183 + 4.4723964689989008022e-818j 8.94e-230, 8.94e-230j
-0.79589886862336672061 - 3.3503764590862161487e-820j 1.29e-231, 1.29e-231j
0.99927796258795845889 - 5.8566552055789957358e-811j 1.23e-225, 1.23e-225j
0.71390619053787702443 - 1.4382529853322778693e-842j 7.54e-234, 7.54e-234j
0.8436599064839882039 + 9.8998566957658570782e-839j 2.49e-230, 2.49e-230j
-0.9885517410050013161 + 9.4635528880211722137e-836j 2.76e-226, 2.76e-226j
-0.65290189927931623274 + 2.7214226247030016653e-846j 1.48e-235, 1.48e-235j
-0.98156063424671925069 + 1.716162316006589994e-835j 1.56e-226, 1.56e-226j
0.90411725637047485668 + 2.2789305743118394795e-836j 9.15e-229, 9.15e-229j
0.7425558144209943417 + 1.6880118880663482705e-841j 4.4e-233, 4.4e-233j
0.96243116182708369602 - 1.2873746721483981362e-832j 3.62e-227, 3.62e-227j
-0.71390619053787702443 + 8.2831285990478555048e-845j 7.52e-234, 7.52e-234j
-0.55295131338298778661 - 1.2266131645596794811e-848j 2.1e-238, 2.1e-238j
-2.0467510274301565955e-903 - 1.9158522291978319341e-903j 2.16e-901, 2.16e-901j
0.5873179542866174473 - 4.918524390643379815e-847j 2.08e-237, 2.08e-237j
0.12523340851146891547 + 2.2065742493369559294e-861j 9.85e-252, 9.85e-252j
0.99738453741357650427 - 5.1049716073886703409e-833j 7.79e-226, 7.79e-226j
-0.5873179542866174473 - 8.297670458960642211e-869j 2.15e-237, 2.15e-237j
0.9885517410050013161 - 7.3663515477029286568e-855j 2.9e-226, 2.9e-226j
0.93655622336835242944 + 8.9944607453735539029e-870j 7.13e-228, 7.13e-228j
0.68400405653487613553 + 1.9145159928009456169e-886j 1.13e-234, 1.13e-234j
-0.8436599064839882039 - 3.1727955453143100492e-880j 2.56e-230, 2.56e-230j
-0.62065432472342213376 + 6.0172216286150061558e-887j 1.8e-236, 1.8e-236j
-0.96243116182708369602 - 1.0132333665909397962e-881j 3.67e-227, 3.67e-227j
-0.68400405653487613553 - 1.073790631264112266e-889j 1.05e-234, 1.05e-234j
0.44428116303155462665 - 7.1147803324810064188e-898j 1.23e-241, 1.23e-241j
-0.12523340851146891547 - 3.4856952186702368531e-909j 9.7e-252, 9.7e-252j
-0.76990267419430468704 - 2.2702044848860847888e-892j 2.47e-232, 2.47e-232j
-0.48137014190150823522 + 9.8273110562513548876e-901j 1.48e-240, 1.48e-240j
0.55295131338298778661 - 5.4192501001633729198e-897j 1.99e-238, 1.99e-238j
0.51761471334093533372 - 2.0572996284565571645e-898j 1.97e-239, 1.97e-239j
0.62065432472342213376 - 1.5476798931703258995e-898j 2.01e-236, 2.01e-236j
-0.041842286875995166032 + 3.6510792953161031726e-917j 2.42e-254, 2.42e-254j
-0.44428116303155462665 + 4.7298785994474358399e-905j 1.14e-241, 1.14e-241j
0.99981909887392141229 - 1.8520865022587763694e-908j 7.64e-226, 7.64e-226j
0.083611179536946957493 - 8.0351173697413127458e-946j 4.38e-253, 4.38e-253j
0.40641281441652795092 + 3.5584864887424913994e-934j 8.24e-243, 8.24e-243j
0.48137014190150823522 + 3.5525142362995871793e-931j 1.52e-240, 1.52e-240j
-0.51761471334093533372 + 2.0179858886138374917e-930j 1.81e-239, 1.81e-239j
-0.40641281441652795092 - 1.2982760246816273765e-933j 8.22e-243, 8.22e-243j
-0.1666359542725288216 - 3.8821181554231750294e-941j 2.17e-250, 2.17e-250j
0.36783149899818019375 - 6.3608785769086427494e-935j 5.48e-244, 5.48e-244j
0.2888017454095650778 + 9.760195155810906821e-938j 1.91e-246, 1.91e-246j
-0.20774617492467426914 - 1.5898702502189190467e-940j 5.11e-249, 5.11e-249j
-0.36783149899818019375 - 3.5955416009157581708e-935j 5.17e-244, 5.17e-244j
-0.24849193680288850225 + 1.5203934297284006046e-938j 9.15e-248, 9.15e-248j
0.1666359542725288216 - 9.0816186824593343101e-943j 2.31e-250, 2.31e-250j
0.32860487521866815658 + 6.3667419852194396043e-936j 3.4e-245, 3.4e-245j
0.041842286875995166032 - 1.2837386914772036494e-945j 2.42e-254, 2.42e-254j
-0.2888017454095650778 - 3.449031994361429526e-937j 1.65e-246, 1.65e-246j
-0.32860487521866815658 + 1.2499872416007895786e-935j 3.51e-245, 3.51e-245j
-0.083611179536946957493 - 6.9544493394173099579e-944j 4.31e-253, 4.31e-253j
0.24849193680288850225 + 1.0303199986643018848e-938j 9.42e-248, 9.42e-248j
0.20774617492467426914 - 2.4772457701422295743e-940j 4.75e-249, 4.75e-249j

Weights

Weight (ball center) Error (ball radius)
0.0044105095164088760152 - 4.4549240980180149017e-783j 5.32e-19, 1.37e-123j
0.0095676909519500318422 - 1.0690631294955268987e-785j 2.57e-19, 6.62e-124j
0.014595457059896544649 + 7.313921731210526322e-786j 1.58e-19, 4.06e-124j
0.00033250269030628347036 - 2.2435940420184062199e-785j 4.43e-20, 1.14e-124j
0.0095676909519500318422 - 1.002892314685301618e-783j 8.56e-21, 2.21e-125j
0.012941206873783919939 - 3.6414266434217574147e-784j 5.38e-21, 1.39e-125j
0.026679309304902570145 + 3.5073476004412595694e-785j 1.86e-21, 4.8e-126j
0.019393579803402120439 - 5.7097447964605766142e-786j 3.43e-21, 8.84e-126j
0.012941206873783919939 - 8.1462476509471112926e-786j 2.34e-20, 6.03e-125j
0.0010579297082446588464 + 3.9043941074506339305e-785j 2.34e-20, 6.04e-125j
0.019393579803402120439 - 9.9071287757893563696e-785j 5.04e-25, 1.3e-129j
0.0027270395581509685978 - 2.8234089263496072442e-785j 6.43e-21, 1.66e-125j
0.016224236768362384071 - 6.6598126148967628118e-786j 2.39e-22, 6.15e-127j
0.017824510827350975967 + 6.1358937014132161052e-786j 8.51e-23, 2.19e-127j
0.03168413833834878535 + 1.9439054683230041923e-785j 6.67e-27, 1.72e-131j
0.023887471434191995017 + 5.0513296331346868984e-785j 2.3e-26, 5.92e-131j
0.016224236768362384071 - 1.7549150434577401031e-784j 1.5e-26, 3.87e-131j
0.028006425196871204808 - 4.3115125791561207409e-786j 1.84e-27, 4.75e-132j
0.023887471434191995017 + 4.8254015312943845379e-786j 1.99e-26, 5.12e-131j
0.0044105095164088760152 + 2.0396672565438509502e-785j 3.27e-23, 8.42e-128j
0.020928870700162553145 + 7.7551545879862818368e-785j 3.91e-27, 1.01e-131j
0.02530550214592359816 - 4.179942067093941062e-785j 2.75e-27, 7.1e-132j
0.0078532844391408336911 + 2.0534460232742676669e-783j 1.47e-28, 3.79e-133j
0.020928870700162553145 + 5.3590888700141605995e-786j 3.44e-26, 8.86e-131j
0.02530550214592359816 - 4.6224148968463841352e-786j 8.71e-28, 2.24e-132j
0.0010579297082446588464 - 1.443091307361058614e-782j 6.03e-30, 1.55e-134j
0.029284444778723552982 + 2.5593042116661388068e-785j 5.29e-30, 1.36e-134j
0.022427728703333884217 - 6.201932807961050048e-785j 3.63e-28, 9.34e-133j
0.0061282229876923416036 - 1.574042859600474107e-785j 3.92e-25, 1.01e-129j
0.03168413833834878535 + 4.0243920262790825693e-786j 1.03e-32, 2.65e-137j
0.0078532844391408336911 + 1.2735169713427636503e-785j 1.44e-25, 3.72e-130j
0.017824510827350975967 + 1.298292874536484578e-784j 8.23e-29, 2.12e-133j
0.028006425196871204808 - 2.9795419046929213488e-785j 2.82e-30, 7.28e-135j
0.011264502834811377827 + 5.7536153465186813571e-784j 2.3e-29, 5.93e-134j
0.029284444778723552982 + 4.1949044708278931581e-786j 4.94e-32, 1.27e-136j
0.034861815482237064164 - 3.8975905055916613082e-786j 2.68e-35, 6.9e-140j
0.041854523406172184536 - 5.0598255446676929424e-786j 1.94e-38, 4.99e-143j
0.033861412612963675658 + 1.5264713309308100551e-785j 1.92e-35, 4.95e-140j
0.041524530135688704904 + 5.8350616769430102688e-786j 1.07e-38, 2.75e-143j
0.0027270395581509685978 + 1.5812961600726989744e-782j 4.69e-31, 1.21e-135j
0.033861412612963675658 + 3.9244421685958431016e-786j 1.61e-36, 4.15e-141j
0.0061282229876923416036 - 5.9279144121000572369e-783j 7.56e-31, 1.95e-135j
0.014595457059896544649 + 2.4656445300608402303e-784j 4.95e-31, 1.28e-135j
0.030511073521150023871 - 2.2203870209215712402e-785j 6.55e-35, 1.69e-139j
0.022427728703333884217 - 5.068127021944697218e-786j 7.32e-34, 1.89e-138j
0.032801572003700334069 - 3.9663518984412107255e-786j 1.34e-37, 3.44e-142j
0.011264502834811377827 + 9.2323745716042076217e-786j 1.57e-32, 4.05e-137j
0.030511073521150023871 - 4.0999709399137244171e-786j 7.38e-37, 1.9e-141j
0.037489620796754429521 + 1.0208004616952216673e-785j 6.12e-43, 1.58e-147j
0.041524530135688704904 + 4.5290511730478913158e-786j 1.08e-44, 2.78e-149j
0.026679309304902570145 + 4.4527529153928962559e-786j 8.27e-36, 2.13e-140j
0.036677495501597910903 - 3.8861650665657389033e-786j 3.18e-42, 8.18e-147j
0.034861815482237064164 - 1.3674654071460190303e-785j 2.62e-41, 6.74e-146j
0.035801051681978099458 + 1.2330771763598425162e-785j 3.27e-42, 8.42e-147j
0.032801572003700334069 - 1.7160298641373412787e-785j 3.57e-40, 9.19e-145j
0.04181781589742061128 + 4.8596337900773218421e-786j 3.63e-46, 9.36e-151j
0.037489620796754429521 + 3.9007446176991747971e-786j 2.17e-44, 5.59e-149j
0.00033250269030628347036 + 7.5939305074965298922e-783j 4.64e-37, 1.2e-141j
0.041707755766146206716 - 5.5439317674699756335e-786j 1.85e-46, 4.76e-151j
0.038236007449230962694 - 9.3649579393954058359e-786j 2.74e-45, 7.07e-150j
0.036677495501597910903 - 1.1187175718128205437e-785j 7.08e-44, 1.82e-148j
0.035801051681978099458 + 3.8850101571965710402e-786j 9.94e-44, 2.56e-148j
0.038236007449230962694 - 3.9286452673249647269e-786j 3.88e-46, 1e-150j
0.041268452218411300309 - 4.3943880828400086954e-786j 4.16e-48, 1.07e-152j
0.038915345139824559479 + 8.6354981617452675108e-786j 7.19e-47, 1.85e-151j
0.040068186238755102224 + 7.4483941567104093358e-786j 2.6e-48, 6.71e-153j
0.040939964621735261216 + 4.2778701745305633932e-786j 6.29e-49, 1.62e-153j
0.038915345139824559479 + 3.9699589656238960343e-786j 1.43e-48, 3.69e-153j
0.040539641226572523764 - 4.1781539417858640847e-786j 2.04e-49, 5.26e-154j
0.041268452218411300309 - 6.1648942791016659754e-786j 1.8e-50, 4.63e-155j
0.03952643338078767672 - 8.001526330812146887e-786j 1.45e-49, 3.75e-154j
0.04181781589742061128 + 5.2868269893915087348e-786j 3.86e-50, 9.95e-155j
0.040068186238755102224 + 4.0941439155101674725e-786j 2.11e-50, 5.43e-155j
0.03952643338078767672 - 4.0249678338782882964e-786j 2.49e-50, 6.42e-155j
0.041707755766146206716 - 4.6834838432429057348e-786j 5.51e-51, 1.42e-155j
0.040539641226572523764 - 6.9641597224825879971e-786j 3.57e-52, 9.23e-157j
0.040939964621735261216 + 6.5390229626246456779e-786j 3.58e-52, 9.21e-157j

Download

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