Rule: Q[1, 2, 10, 14, 26]

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)
0.99957695133774918858 - 6.823232141616750192e-865j 8.81e-237, 8.81e-237j
0.99696345573553342034 - 5.0461194138193027947e-892j 2.07e-236, 2.07e-236j
-0.90591989788431806766 + 1.4570560496608656591e-902j 9.41e-238, 9.41e-238j
-0.98189373966174310941 + 4.6781718070944921788e-901j 1.52e-236, 1.52e-236j
0.93052494588857412015 - 1.343852564310742504e-901j 2.31e-237, 2.31e-237j
0.90591989788431806766 + 5.9607545247329814434e-905j 9.93e-238, 9.93e-238j
-0.99120386282427505819 - 1.7855841445160943848e-902j 2.26e-236, 2.26e-236j
-0.93052494588857412015 + 2.54928321530854261e-904j 2.24e-237, 2.24e-237j
-0.99696345573553342034 + 4.2021592482266629816e-902j 2.07e-236, 2.07e-236j
0.98189373966174310941 - 5.7319231157126410759e-904j 1.55e-236, 1.55e-236j
0.84648809715906767396 - 1.348782719313601024e-919j 1.01e-238, 1.01e-238j
-0.99957695133774918858 + 8.510060524667824361e-919j 9.03e-237, 9.03e-237j
-0.87785622038195063136 + 7.0393702227405682163e-920j 3.63e-238, 3.63e-238j
-0.84648809715906767396 - 9.0998233132283354107e-921j 9.67e-239, 9.67e-239j
0.96868735150406815612 - 7.9525105109507244389e-917j 9.57e-237, 9.57e-237j
0.81201211093350440783 + 1.5605116040216089989e-929j 3.21e-239, 3.21e-239j
0.33370517706399914938 - 4.2569906980198887272e-940j 3.43e-248, 3.43e-248j
-0.96868735150406815612 - 1.1707364177867077422e-928j 9.7e-237, 9.7e-237j
-0.73429410164122101584 + 4.2035512647262974422e-933j 1.24e-240, 1.24e-240j
-0.95151371618655174505 - 6.1094912604822963443e-929j 4.99e-237, 4.99e-237j
0.87785622038195063136 + 2.8565144026324658542e-928j 3.35e-238, 3.35e-238j
0.73429410164122101584 + 2.7641301974795742162e-939j 1.24e-240, 1.24e-240j
0.99120386282427505819 - 2.3538865937581911854e-936j 2.24e-236, 2.24e-236j
-0.81201211093350440783 + 4.6831853527249000694e-961j 2.8e-239, 2.8e-239j
-0.77459666924148337704 - 2.9864003101497895106e-961j 6.44e-240, 6.44e-240j
4.1044306207985875872e-977 - 2.6371407733140364192e-977j 2.59e-975, 2.59e-975j
0.77459666924148337704 - 2.4574523009079028278e-961j 6.47e-240, 6.47e-240j
0.95151371618655174505 - 1.2975433088282924093e-968j 5.11e-237, 5.11e-237j
-0.060379947809744553847 - 5.1355991992404779604e-1002j 1.73e-254, 1.73e-254j
-0.59706738604131558719 - 2.8042732806167804241e-990j 4.26e-243, 4.26e-243j
-0.22465173325748337758 + 5.3931695079111500313e-998j 1.63e-250, 1.63e-250j
0.6452892704418761578 - 2.759999690648807425e-989j 3.28e-242, 3.28e-242j
0.59706738604131558719 - 6.2047413528914699602e-992j 4.16e-243, 4.16e-243j
-0.38736385932378655649 + 8.9090178490857031692e-996j 3.86e-247, 3.86e-247j
-0.6452892704418761578 + 2.0463353985426654651e-989j 3.23e-242, 3.23e-242j
-0.69113262396834268581 + 1.1236573800521830069e-991j 2.15e-241, 2.15e-241j
0.17101852249474448773 - 4.6313678139377713852e-1001j 1.12e-251, 1.12e-251j
0.54673301418585891089 - 7.0095589192649837466e-994j 4.85e-244, 4.85e-244j
0.69113262396834268581 - 6.5767755594970668448e-1001j 2.16e-241, 2.16e-241j
-0.27944386352261028131 - 7.6348498749319318486e-1011j 2.36e-249, 2.36e-249j
-0.54673301418585891089 - 5.748419228525773367e-1006j 4.96e-244, 4.96e-244j
-0.1175150461453765527 + 7.8725419926731146972e-1015j 5.6e-253, 5.6e-253j
0.38736385932378655649 - 1.2147886868269249971e-1008j 4.16e-247, 4.16e-247j
0.44112086378199475299 + 1.0346724113335560037e-1006j 4.56e-246, 4.56e-246j
0.060379947809744553847 + 5.8406454269579164539e-1013j 1.73e-254, 1.73e-254j
-0.49455577980099296881 - 8.7472128924262614416e-1008j 4.39e-245, 4.39e-245j
-0.33370517706399914938 - 5.0408489876388502957e-1012j 3.1e-248, 3.1e-248j
0.27944386352261028131 - 3.3808799179917285125e-1010j 2.52e-249, 2.52e-249j
0.49455577980099296881 - 3.2008872260122728687e-1007j 5.55e-245, 5.55e-245j
0.22465173325748337758 + 1.8680220232281080289e-1013j 1.63e-250, 1.63e-250j
-0.17101852249474448773 - 3.5160997248822572283e-1014j 1.03e-251, 1.03e-251j
-0.44112086378199475299 + 1.0325684001417098779e-1008j 4.49e-246, 4.49e-246j
0.1175150461453765527 - 4.3618059844271610224e-1015j 5e-253, 5e-253j

Weights

Weight (ball center) Error (ball radius)
0.0012416694331595054052 + 5.9849915586100468853e-865j 1.64e-56, 4.85e-169j
0.0041180967733741188587 - 8.1970153178459295871e-865j 1.42e-56, 4.22e-169j
0.026357635571118182961 - 1.6152329761667128666e-867j 6.82e-58, 2.02e-170j
0.011219826124796217513 - 1.4527222914002772075e-867j 3.91e-58, 1.16e-170j
0.022827155905846598559 + 4.2409873878346638112e-866j 5.37e-58, 1.59e-170j
0.026357635571118182961 - 3.2862675403039791108e-866j 2.84e-58, 8.43e-171j
0.0074641729612672928396 + 1.373967676418292297e-867j 1.44e-58, 4.27e-171j
0.022827155905846598559 + 1.5172705888506909995e-867j 3.29e-59, 9.76e-172j
0.0041180967733741188587 - 1.072999244522643051e-867j 4.09e-59, 1.21e-171j
0.011219826124796217513 - 1.6278302241199069276e-865j 1.7e-60, 5.04e-173j
0.032956801977760672913 - 2.3331453128080409746e-866j 1.58e-61, 4.69e-174j
0.0012416694331595054052 + 4.2378922274360741036e-868j 1.84e-59, 5.47e-172j
0.029745223743913219929 + 1.7539586464852166183e-867j 1.61e-61, 4.77e-174j
0.032956801977760672913 - 1.9348101675018540376e-867j 2.23e-62, 6.63e-175j
0.015202876555733164772 + 9.2506977164879748019e-866j 5.23e-62, 1.55e-174j
0.03596491608813496268 + 2.0849031789053472337e-866j 1.18e-63, 3.5e-176j
0.053808771424412480245 + 2.7459556418662305521e-866j 6.06e-66, 1.8e-178j
0.015202876555733164772 + 1.4517885135247775176e-867j 5.32e-61, 1.58e-173j
0.041745231555284987212 + 2.7246262120410685468e-867j 2.31e-65, 6.84e-178j
0.01911565828621516734 - 1.4631158429195149085e-867j 2.15e-61, 6.39e-174j
0.029745223743913219929 + 2.7053239977105660015e-866j 8.44e-64, 2.5e-176j
0.041745231555284987212 + 1.7807975617911106462e-866j 2.58e-66, 7.66e-179j
0.0074641729612672928396 + 3.2667378173426298937e-865j 5.7e-63, 1.69e-175j
0.03596491608813496268 + 2.1586271420705371863e-867j 1.99e-64, 5.9e-177j
0.03885906516491572751 - 2.4213110833892171891e-867j 3.47e-65, 1.03e-177j
0.060972262822216224675 + 2.2426955785182833875e-866j 3.86e-70, 1.15e-182j
0.03885906516491572751 - 1.909423444285286115e-866j 2.02e-66, 6e-179j
0.01911565828621516734 - 5.939408068655768619e-866j 2.3e-64, 6.82e-177j
0.059208492341856826876 - 2.2453247980875197947e-866j 2.07e-70, 6.15e-183j
0.049315099930713928494 - 4.2188989641855013918e-867j 8.08e-70, 2.4e-182j
0.054474365574885662191 + 2.0532094845414250542e-866j 3.97e-71, 1.18e-183j
0.047084648914412203515 + 1.6587414960826011479e-866j 9.14e-70, 2.71e-182j
0.049315099930713928494 - 1.6735207612222344933e-866j 2.32e-70, 6.88e-183j
0.053668878313676638248 - 1.0736822763626382193e-866j 2.8e-72, 8.29e-185j
0.047084648914412203515 + 3.5727627576730082304e-867j 1.58e-70, 4.69e-183j
0.044547669932057428453 - 3.0930174739555156468e-867j 5.62e-70, 1.67e-182j
0.052924315911426386941 - 3.3228167904070825925e-866j 4e-74, 1.18e-186j
0.051315434910366105862 + 1.7433176614243168289e-866j 5.81e-73, 1.72e-185j
0.044547669932057428453 - 1.6954094453300475858e-866j 2.86e-71, 8.47e-184j
0.054732607496544087279 - 1.6932452909227375309e-866j 2.96e-74, 8.79e-187j
0.051315434910366105862 + 5.1053854085360663697e-867j 1.76e-73, 5.23e-186j
0.054917302055172140802 + 2.3859901095119999656e-866j 1.88e-74, 5.57e-187j
0.053668878313676638248 - 2.4323781804021892898e-866j 2.22e-75, 6.57e-188j
0.053753713015489835706 + 2.1184381291282809965e-866j 2.36e-75, 6.99e-188j
0.059208492341856826876 - 2.5340237475415407457e-866j 4.91e-76, 1.46e-188j
0.05294423862635834456 - 6.3683793157419666084e-867j 7.47e-76, 2.22e-188j
0.053808771424412480245 + 1.3713934330750483446e-866j 6.67e-76, 1.98e-188j
0.054732607496544087279 - 3.0073551797558969455e-866j 7.01e-77, 2.08e-189j
0.05294423862635834456 - 1.8841198183835917311e-866j 1.4e-76, 4.14e-189j
0.054474365574885662191 + 3.2436651793131461514e-866j 3.7e-77, 1.1e-189j
0.052924315911426386941 - 2.3519208135831299279e-866j 1.51e-77, 4.55e-190j
0.053753713015489835706 + 8.2116780972808100141e-867j 6.15e-78, 1.9e-190j
0.054917302055172140802 + 3.0217498814081988812e-866j 1.3e-77, 3.8e-190j

Download

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