Rule: Q[14, 16, 32]

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)
0.98628380869681233884 - 5.5032814231168534876e-841j 1.67e-232, 1.67e-232j
0.99339809686067717402 + 4.7907404889392039497e-857j 2.08e-232, 2.08e-232j
-0.94721812617112572138 - 2.7347779161327850496e-870j 7.63e-233, 7.63e-233j
-0.99339809686067717402 + 2.2861282171005822888e-868j 1.94e-232, 1.94e-232j
0.92262017404469488517 + 1.6545627161760569096e-867j 1.19e-232, 1.19e-232j
0.90696964672074471834 - 3.2983062794037857053e-870j 2.01e-233, 2.01e-233j
0.99964437177015565725 + 1.3531932917750310037e-866j 7.43e-233, 7.43e-233j
-0.90696964672074471834 - 4.1002700544555687519e-880j 2.08e-233, 2.08e-233j
-0.92262017404469488517 - 4.434563518955405589e-879j 1.21e-232, 1.21e-232j
-0.99964437177015565725 - 1.9912879578241555433e-877j 7.88e-233, 7.88e-233j
0.85628388392046324444 - 2.9080049357332675502e-882j 5.37e-235, 5.37e-235j
0.96317629668969619272 + 2.5466396735853695374e-880j 9.12e-233, 9.12e-233j
-0.85628388392046324444 - 3.7943315214210510738e-889j 5.44e-235, 5.44e-235j
-0.8828887241549355409 + 3.5490773714523611762e-888j 2.82e-234, 2.82e-234j
-0.98628380869681233884 + 7.2757748568423641832e-885j 1.65e-232, 1.65e-232j
0.8828887241549355409 + 8.3544382429512832168e-887j 2.74e-234, 2.74e-234j
0.92843488366357351734 + 1.6482873914068122155e-884j 1.5e-232, 1.5e-232j
-0.92843488366357351734 - 1.0270819699558683342e-898j 1.45e-232, 1.45e-232j
-0.79568343830571553761 - 1.3002853765964128541e-902j 1.76e-236, 1.76e-236j
-0.82720131506976499319 + 2.4301143763716882256e-901j 1.05e-235, 1.05e-235j
0.97621648767639167531 + 4.1585535995633937934e-896j 1.28e-232, 1.28e-232j
0.76179216723427461219 + 2.3780868216407509922e-919j 3.08e-237, 3.08e-237j
0.9977135406837945019 + 1.33267871519959295e-913j 1.82e-232, 1.82e-232j
-0.72562095795621593446 + 1.2528004167570392595e-936j 4.08e-238, 4.08e-238j
-0.76179216723427461219 - 8.3285996408299564745e-936j 2.94e-237, 2.94e-237j
0.94721812617112572138 - 2.3034483509424826159e-931j 7.78e-233, 7.78e-233j
0.72562095795621593446 + 3.5393355223068314252e-946j 4.32e-238, 4.32e-238j
0.82720131506976499319 + 1.0831782351210281606e-941j 1.02e-235, 1.02e-235j
-0.36998962200058417398 - 1.0606069685868290123e-958j 1.84e-246, 1.84e-246j
-0.68729290481168547015 - 1.8726679685077094083e-952j 5.34e-239, 5.34e-239j
-0.97621648767639167531 + 1.5508002632835148811e-942j 1.26e-232, 1.26e-232j
0.79568343830571553761 + 1.477715793153534911e-944j 1.82e-236, 1.82e-236j
0.68729290481168547015 + 2.9379683341584954913e-954j 5.65e-239, 5.65e-239j
-0.9977135406837945019 - 1.7911506573405577087e-948j 1.83e-232, 1.83e-232j
-0.64695021453526921265 - 1.849927302716956925e-961j 7.01e-240, 7.01e-240j
-0.60473988684455551574 - 2.5387005915165163572e-963j 7.93e-241, 7.93e-241j
0.26727698009575076967 + 2.9865350635525159014e-970j 4.74e-249, 4.74e-249j
0.60473988684455551574 + 4.6186302236204683224e-963j 7.73e-241, 7.73e-241j
0.46819170164139456626 + 2.0766994948149107478e-965j 4.24e-244, 4.24e-244j
-0.96317629668969619272 - 1.5885136754428057722e-967j 9.15e-233, 9.15e-233j
-0.51524863635815409197 - 4.6711034009241299343e-980j 6.17e-243, 6.17e-243j
-0.054556945384316264904 - 5.8645697233611400222e-990j 2.51e-254, 2.51e-254j
0.64695021453526921265 - 2.2603014540851748299e-978j 6.92e-240, 6.92e-240j
0.56079949596631185046 + 7.4218279966540483427e-982j 7.28e-242, 7.28e-242j
-0.16153480264261248455 + 1.3845167481885598475e-992j 1.14e-251, 1.14e-251j
-0.56079949596631185046 + 1.451349558299052771e-984j 7.14e-242, 7.14e-242j
-0.31911236892788976044 + 2.967316816533095303e-989j 9.74e-248, 9.74e-248j
0.10805494870734366207 + 1.2751607790479698187e-994j 4.42e-253, 4.42e-253j
0.51524863635815409197 - 1.0582591102816292913e-983j 5.69e-243, 5.69e-243j
0.16153480264261248455 - 1.1730390609945633233e-992j 1.32e-251, 1.32e-251j
-0.10805494870734366207 + 5.358209483854719458e-995j 4.54e-253, 4.54e-253j
-0.41973204098279916916 + 4.4394764498566489469e-987j 3.04e-245, 3.04e-245j
0.0057957638609813197295 - 2.1116485738397161513e-997j 7.63e-256, 7.63e-256j
0.41973204098279916916 - 3.827242719520946231e-986j 2.91e-245, 2.91e-245j
0.31911236892788976044 - 1.6452712371358443119e-988j 9.37e-248, 9.37e-248j
-0.0057957638609813197295 + 2.0364607083557004403e-997j 7.63e-256, 7.63e-256j
-0.46819170164139456626 + 2.0523053196007097052e-986j 4.22e-244, 4.22e-244j
-0.21468148737211924164 + 2.7279327602508462959e-992j 2.34e-250, 2.34e-250j
0.21468148737211924164 + 1.6881492569279710419e-992j 2.28e-250, 2.28e-250j
0.36998962200058417398 + 1.7425849806340320309e-987j 1.8e-246, 1.8e-246j
0.054556945384316264904 + 1.4454047060195191067e-995j 1.95e-254, 1.95e-254j
-0.26727698009575076967 - 1.1444743881009076397e-990j 5.54e-249, 5.54e-249j

Weights

Weight (ball center) Error (ball radius)
0.0085791380934980433651 - 2.1978087809665489645e-842j 4.63e-38, 1.19e-147j
0.0056730530944136578175 + 5.78985741150673263e-841j 3.11e-38, 7.98e-148j
0.0173868947035020822 + 6.267573902098964506e-843j 9.48e-40, 2.43e-149j
0.0056730530944136578175 + 2.0806733615897705007e-843j 1.23e-40, 3.15e-150j
-4.5432070641429925932e-05 - 9.4220299247143685004e-841j 4.4e-39, 1.13e-148j
0.022799334659690625926 + 2.5769927816038245649e-841j 2.95e-39, 7.57e-149j
0.00097716880261654413087 + 9.2408527776372969886e-842j 6.11e-39, 1.57e-148j
0.022799334659690625926 - 1.0795808786531654935e-842j 2.46e-40, 6.31e-150j
-4.5432070641429925932e-05 + 3.1423302388780245117e-842j 2.63e-40, 6.76e-150j
0.00097716880261654413087 + 6.2168913056096521636e-844j 1.2e-41, 3.09e-151j
0.027850249943817143496 + 4.1051822179238101047e-842j 1.22e-41, 3.12e-151j
0.014512810719938397054 + 3.1501325788557564676e-841j 4.52e-41, 1.16e-150j
0.027850249943817143496 - 2.896356978696640503e-843j 5.43e-42, 1.39e-151j
0.025352045820391034777 + 4.5240005840768343845e-843j 1.9e-41, 4.87e-151j
0.0085791380934980433651 - 2.3935002724360610203e-843j 7.42e-42, 1.9e-151j
0.025352045820391034777 - 8.1784716051339957576e-842j 4.29e-42, 1.1e-151j
0.020180959098806070627 + 9.1185828841292207152e-841j 4.93e-41, 1.26e-150j
0.020180959098806070627 - 2.754975024676264709e-842j 4.89e-41, 1.26e-150j
0.032717381215650796938 - 1.7436509677443951219e-843j 8.79e-45, 2.26e-154j
0.030308255536005611525 + 2.1575468797828725364e-843j 7.21e-44, 1.85e-153j
0.011557938103653143359 - 5.5112398140524309549e-841j 3.07e-43, 7.87e-153j
0.035049536475637127394 - 1.1592726000276496381e-842j 3.97e-48, 1.02e-157j
0.0030235183961356037568 - 2.7475096692225730666e-841j 6.01e-43, 1.54e-152j
0.037272179853303751022 - 1.327068297641628644e-843j 2.89e-48, 7.42e-158j
0.035049536475637127394 + 1.488762573629754768e-843j 2.73e-47, 7e-157j
0.0173868947035020822 - 3.1020490320802729256e-841j 2.55e-44, 6.53e-154j
0.037272179853303751022 + 8.7155286530172388148e-843j 3.94e-50, 1.01e-159j
0.030308255536005611525 - 2.4595284377978836118e-842j 9.05e-48, 2.32e-157j
0.050337030025705078848 - 1.494103925449236676e-843j 2.18e-54, 5.59e-164j
0.039359979063828716049 + 1.2270236304329464489e-843j 4.13e-51, 1.06e-160j
0.011557938103653143359 + 2.8271802318259705634e-843j 5.91e-49, 1.52e-158j
0.032717381215650796938 + 1.6301798933282196071e-842j 5.91e-50, 1.52e-159j
0.039359979063828716049 - 6.8681627037262761212e-843j 1.01e-52, 2.6e-162j
0.0030235183961356037568 - 1.5828296928249405701e-843j 1.15e-48, 2.95e-158j
0.041300650723705492061 - 1.1713936168790407368e-843j 5.08e-53, 1.3e-162j
0.043096916549187145568 + 1.1500396700155274426e-843j 4.65e-54, 1.19e-163j
0.052249689689017004058 + 3.5724142979669906212e-843j 7.94e-59, 2.04e-168j
0.043096916549187145568 - 4.7956218432849261654e-843j 3.5e-56, 8.99e-166j
0.047776365791941281108 + 3.5154976819228187226e-843j 3.87e-58, 9.92e-168j
0.014512810719938397054 - 3.7339428587837213515e-843j 9.75e-51, 2.5e-160j
0.046320600462614811223 + 1.1906422112103363146e-843j 1.89e-57, 4.86e-167j
0.053260113038706545595 - 1.1282406203968512173e-842j 7.43e-61, 1.91e-170j
0.041300650723705492061 + 5.637991470932749692e-843j 3.73e-56, 9.56e-166j
0.04476397754068500324 + 4.2075602978490791889e-843j 1.09e-57, 2.78e-167j
0.053351272920280200854 - 3.539685871442485664e-843j 1.33e-61, 3.4e-171j
0.04476397754068500324 - 1.1571780887340650988e-843j 4.87e-58, 1.25e-167j
0.05138789006628002241 + 1.7126989092638161967e-843j 7.2e-61, 1.85e-170j
0.05356425364683012163 - 6.8408263113869970587e-843j 7.28e-63, 1.87e-172j
0.046320600462614811223 - 3.7954446197893464868e-843j 2.68e-60, 6.89e-170j
0.053351272920280200854 + 4.9262470057101152086e-843j 6.78e-63, 1.74e-172j
0.05356425364683012163 + 5.4899006840315975279e-843j 7.6e-63, 1.95e-172j
0.049123159902599996419 + 1.3488063700966251239e-843j 3.74e-62, 9.6e-172j
0.028006704495949936205 - 5.5866704626083652606e-842j 1.88e-63, 4.83e-173j
0.049123159902599996419 - 3.3473430718549535107e-843j 1.1e-63, 2.83e-173j
0.05138789006628002241 - 3.3510886052756440914e-843j 2.25e-64, 5.76e-174j
0.028006704495949936205 + 5.5213954107555843434e-842j 1.32e-63, 3.39e-173j
0.047776365791941281108 - 1.2522394419362303249e-843j 4.4e-64, 1.13e-173j
0.052906363636250441267 + 2.5908430486357897486e-843j 4.2e-65, 1.08e-174j
0.052906363636250441267 - 4.0325339919029074378e-843j 2.37e-65, 6.09e-175j
0.050337030025705078848 + 3.2880619362166789225e-843j 2.13e-65, 5.47e-175j
0.053260113038706545595 + 1.260368101810282251e-842j 4.71e-65, 1.21e-174j
0.052249689689017004058 - 2.0490352743917704238e-843j 9.4e-66, 2.38e-175j

Download

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