Rule: Q[2, 3, 26, 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.

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)
0.9968412640397844141 - 1.9611948102341598579e-839j 4.46e-233, 4.46e-233j
0.95957025773729571464 + 3.9774290834597340641e-841j 4.31e-233, 4.31e-233j
-0.94390988813757961372 - 4.1333965289291362142e-840j 2.75e-233, 2.75e-233j
-0.99150243615497119297 - 2.2160419617776995614e-857j 6.04e-233, 6.04e-233j
0.8831199664004363681 + 2.4601325804795757214e-880j 3.81e-234, 3.81e-234j
0.94390988813757961372 + 9.0219350669812002045e-879j 2.6e-233, 2.6e-233j
0.99947322570045504751 - 3.5471597142284082596e-881j 1.73e-233, 1.73e-233j
-0.8831199664004363681 - 3.2525657250463045626e-878j 3.99e-234, 3.99e-234j
0.98342385701438370767 + 5.7694021920265523404e-881j 6.38e-233, 6.38e-233j
-0.9968412640397844141 + 2.2137423245388461294e-878j 4.5e-233, 4.5e-233j
0.85891759321631091998 + 2.7051321886712339128e-898j 1.67e-234, 1.67e-234j
0.99150243615497119297 - 2.7401776451049782125e-896j 6.52e-233, 6.52e-233j
-0.92582009977255146157 - 5.7393259782867039459e-895j 1.56e-233, 1.56e-233j
-0.85891759321631091998 + 5.6256958210251219046e-902j 1.7e-234, 1.7e-234j
-0.98342385701438370767 + 1.8442200318545723433e-898j 6.58e-233, 6.58e-233j
0.83305097489322702656 + 2.7666164316336022754e-918j 6.13e-235, 6.13e-235j
0.90547911644115554379 - 9.1105335214013462004e-917j 7.96e-234, 7.96e-234j
-0.99947322570045504751 - 1.6117555183041241271e-914j 1.66e-233, 1.66e-233j
-0.77781352330032879272 - 5.3647923041144289812e-936j 6.22e-236, 6.22e-236j
-0.90547911644115554379 + 1.1245081774663187104e-932j 7.78e-234, 7.78e-234j
0.92582009977255146157 - 4.0407513519937631087e-932j 1.56e-233, 1.56e-233j
0.74880552612818644868 + 1.4159290339051289219e-936j 1.8e-236, 1.8e-236j
0.97274734493422141433 + 2.8021718844001811291e-933j 5.47e-233, 5.47e-233j
-0.83305097489322702656 + 2.9106183270778381974e-933j 6.06e-235, 6.06e-235j
-0.80588143371411938138 - 8.4513698956317709115e-934j 2.07e-235, 2.07e-235j
0.65246301571950031282 - 1.9780405291801755787e-939j 1.18e-238, 1.18e-238j
0.71844447619592929261 - 1.2712130632774405546e-937j 4.31e-237, 4.31e-237j
0.80588143371411938138 + 4.6300359423601263249e-936j 2.07e-235, 2.07e-235j
-0.35534292342678142084 + 5.3087788670002481246e-947j 2.52e-246, 2.52e-246j
-0.68644652263397611155 - 7.2277678945384704761e-937j 7.39e-238, 7.39e-238j
-0.97274734493422141433 + 2.4338996699200606676e-933j 5.22e-233, 5.22e-233j
0.77781352330032879272 - 6.4636481264162435827e-945j 6.56e-236, 6.56e-236j
0.68644652263397611155 + 7.558856772375559641e-947j 7.92e-238, 7.92e-238j
-0.95957025773729571464 - 3.8346080377057650833e-946j 4.15e-233, 4.15e-233j
-0.65246301571950031282 - 1.7347238677582049274e-962j 1.1e-238, 1.1e-238j
-0.74880552612818644868 + 1.0555578122071807672e-960j 1.81e-236, 1.81e-236j
0.25707491444441020811 + 2.7716375869703139648e-976j 6.48e-249, 6.48e-249j
0.57735026918962576451 + 6.6344920073868134913e-969j 1.51e-240, 1.51e-240j
0.49358657563127178514 - 6.491807736072956797e-971j 9.79e-243, 9.79e-243j
-0.71844447619592929261 - 7.4243849280356623505e-967j 4.02e-237, 4.02e-237j
-0.53643635303440163935 + 2.522054842748904511e-971j 1.27e-241, 1.27e-241j
-0.30670145626967542233 + 3.2455630099311449866e-978j 1.22e-247, 1.22e-247j
0.53643635303440163935 - 1.38476730040785034e-970j 1.18e-241, 1.18e-241j
0.61610455241662967452 + 2.872871152995415732e-970j 1.43e-239, 1.43e-239j
-1.7067026399177804639e-999 + 4.367654460191566561e-1000j 1.11e-997, 1.11e-997j
-0.57735026918962576451 - 1.678480451123342069e-969j 1.4e-240, 1.4e-240j
-0.61610455241662967452 - 2.4508267563172955347e-979j 1.44e-239, 1.44e-239j
0.052062370812045531375 + 8.6271447000741335399e-993j 2.61e-254, 2.61e-254j
0.44898530687602732674 + 7.1214111809259511414e-983j 6.72e-244, 6.72e-244j
0.15553454150150909675 - 2.4650642819381660682e-990j 1.37e-251, 1.37e-251j
-0.15553454150150909675 + 2.7450990833069169253e-990j 1.33e-251, 1.33e-251j
-0.49358657563127178514 - 1.1343728962238137389e-982j 9.07e-243, 9.07e-243j
-0.052062370812045531375 - 7.8310523947405186445e-993j 2.61e-254, 2.61e-254j
0.35534292342678142084 - 6.812624744335288307e-985j 2.32e-246, 2.32e-246j
0.20662862991166444777 + 5.5301650423735454303e-989j 2.73e-250, 2.73e-250j
-0.10395987413267970804 + 6.7751680103569753814e-992j 5.64e-253, 5.64e-253j
-0.44898530687602732674 - 1.0245778424374306926e-983j 6.78e-244, 6.78e-244j
-0.20662862991166444777 - 5.5505227768643972296e-989j 2.7e-250, 2.7e-250j
0.10395987413267970804 + 3.1146729022015353726e-992j 5.37e-253, 5.37e-253j
0.40283366757363332694 - 1.3861416466299735615e-983j 4.28e-245, 4.28e-245j
0.30670145626967542233 + 4.4449355131336407864e-986j 1.21e-247, 1.21e-247j
-0.25707491444441020811 + 1.4868231850424594294e-987j 5.7e-249, 5.7e-249j
-0.40283366757363332694 - 2.7486025418269591516e-984j 4.23e-245, 4.23e-245j

Weights

Weight (ball center) Error (ball radius)
0.0039468190689844390836 + 6.3898743199381907172e-840j 1.7e-38, 1.93e-148j
0.014419542956499860318 + 9.6463523280068365477e-840j 7.55e-39, 8.56e-149j
0.016894068796742055525 - 1.0958853808280523297e-840j 3.41e-40, 3.86e-150j
0.0067283546699018718049 + 3.3524620846373121861e-841j 2.32e-40, 2.64e-150j
0.02330396781839369038 + 9.8432228176398979646e-840j 1.53e-39, 1.73e-149j
0.016894068796742055525 - 8.6041582491343905889e-840j 4.17e-39, 4.73e-149j
0.0014160160113585758102 + 9.8225198277988573707e-840j 1.68e-39, 1.91e-149j
0.02330396781839369038 + 3.3174927905564543656e-840j 9.89e-43, 1.12e-152j
0.0094017858647266371844 + 1.4446867288462988624e-839j 5.19e-40, 5.89e-150j
0.0039468190689844390836 - 1.7491510830927720781e-841j 2.29e-43, 2.59e-153j
0.025075326479237366528 - 1.0921180446849685408e-839j 4.4e-42, 5e-152j
0.0067283546699018718049 - 2.453414658937965837e-839j 1.01e-39, 1.14e-149j
0.019254317584496763758 + 5.4353691217778731207e-840j 1.16e-43, 1.32e-153j
0.025075326479237366528 - 3.4174911564244670588e-840j 2.21e-44, 2.5e-154j
0.0094017858647266371844 - 6.1251013502178902976e-841j 5.91e-44, 6.7e-154j
0.026595983691757152774 + 1.2324795920406039029e-839j 6.58e-44, 7.46e-154j
0.02138622621927467366 - 9.0860451239901841447e-840j 8.55e-43, 9.7e-153j
0.0014160160113585758102 + 5.5133843380001370358e-842j 5.83e-44, 6.61e-154j
0.028479308562852180189 + 4.8080508750102262457e-840j 6.76e-47, 7.67e-157j
0.02138622621927467366 - 3.6486842766581972115e-840j 1.03e-44, 1.16e-154j
0.019254317584496763758 + 8.683784686904571762e-840j 7.91e-43, 8.97e-153j
0.029619785116582400514 - 1.5681815053077738748e-839j 3.27e-47, 3.71e-157j
0.011934294293173626318 - 1.1456049862865930054e-839j 4.73e-43, 5.37e-153j
0.026595983691757152774 + 3.7657623735691572849e-840j 3e-46, 3.41e-156j
0.027664246633103173457 - 4.2850629606629351698e-840j 7.28e-47, 8.26e-157j
0.035129845351373985339 + 1.0208302682121539027e-839j 2.7e-49, 3.06e-159j
0.031141262620650868183 + 1.4723276346761650504e-839j 3.92e-48, 4.45e-158j
0.027664246633103173457 - 1.3957906747177401147e-839j 1.01e-46, 1.15e-156j
0.048094922580554704534 - 1.055561745823130366e-840j 3.52e-54, 4e-164j
0.032912925495373117463 - 4.4973023117626602337e-840j 8.25e-52, 9.36e-162j
0.011934294293173626318 + 1.219404365637247773e-840j 4.4e-48, 4.99e-158j
0.028479308562852180189 + 1.5323243373744952898e-839j 9.66e-48, 1.1e-157j
0.032912925495373117463 - 1.271635533091372515e-839j 1.35e-49, 1.53e-159j
0.014419542956499860318 - 3.1821581806028326304e-840j 1.89e-48, 2.14e-158j
0.035129845351373985339 + 3.8028763918090389621e-840j 1.82e-53, 2.06e-163j
0.029619785116582400514 - 5.0837818831303318607e-840j 1.84e-51, 2.09e-161j
0.050064743421478261388 - 1.2950171276381626452e-840j 1.62e-57, 1.84e-167j
0.039877283469782869192 + 5.8729148562184153803e-840j 2.17e-54, 2.47e-164j
0.043756611564463508881 + 3.4206719502741734165e-840j 6.14e-56, 6.97e-166j
0.031141262620650868183 + 4.9699974394152531634e-840j 2.92e-53, 3.31e-163j
0.041913530696029529692 - 1.9897951869547039838e-840j 1.88e-57, 2.13e-167j
0.049160899746185901608 + 9.581396187214925605e-841j 2.19e-59, 2.49e-169j
0.041913530696029529692 - 4.4464954753672057816e-840j 5.4e-56, 6.13e-166j
0.037586447119797018434 - 7.805328301993255971e-840j 1.29e-54, 1.46e-164j
0.052090237303545023476 + 8.4051559063631325822e-841j 2.77e-61, 3.14e-171j
0.039877283469782869192 + 2.462952565013487912e-840j 1.11e-57, 1.26e-167j
0.037586447119797018434 - 3.0783358922572852772e-840j 5.47e-57, 6.21e-167j
0.052006865219034176409 - 8.8123935729272743887e-841j 3.09e-62, 3.5e-172j
0.045412110977275016796 - 2.6867128164801207129e-840j 5.75e-60, 6.52e-170j
0.051361307451890516621 - 1.0263432455816504752e-840j 1.76e-62, 2e-172j
0.051361307451890516621 - 8.1889740755980948888e-841j 1.68e-63, 1.91e-173j
0.043756611564463508881 + 1.6378191053433912101e-840j 1.46e-61, 1.66e-171j
0.052006865219034176409 - 8.1726690206975602188e-841j 2.33e-63, 2.64e-173j
0.048094922580554704534 - 1.7805099124823060921e-840j 2.1e-63, 2.38e-173j
0.050798896624992950802 + 1.1409603248846098097e-840j 2.27e-63, 2.57e-173j
0.051761959026824604199 + 8.101390695275212437e-841j 6.2e-64, 7.04e-174j
0.045412110977275016796 - 1.3793094580421523667e-840j 6.9e-64, 7.82e-174j
0.050798896624992950802 + 8.4463670705630268858e-841j 1.18e-64, 1.34e-174j
0.051761959026824604199 + 9.4186222537450077516e-841j 2.42e-64, 2.74e-174j
0.046855226215435991416 + 2.1607644657763942297e-840j 1.75e-64, 1.99e-174j
0.049160899746185901608 + 1.5017511879971642539e-840j 9.78e-65, 1.11e-174j
0.050064743421478261388 - 8.8978453267095059561e-841j 1.1e-65, 1.26e-175j
0.046855226215435991416 + 1.1913454907741988742e-840j 1.33e-65, 1.48e-175j

Download

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