Rule: Q[2, 4, 6, 10, 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.

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)
0.99828520505557600622 - 2.8701496169094008212e-876j 1.62e-239, 1.62e-239j
-0.99828520505557600622 + 6.3608724660090515217e-889j 1.57e-239, 1.57e-239j
-0.91248695683407599658 - 1.5493740910708843019e-888j 3.2e-239, 3.2e-239j
-0.95699433532754426818 + 8.9626753827084228795e-887j 2.27e-238, 2.27e-238j
0.93649524179130306529 - 9.5312311736194902449e-886j 7.93e-239, 7.93e-239j
0.91248695683407599658 - 2.6634094522022283957e-901j 2.91e-239, 2.91e-239j
0.039871185471799902249 - 5.628314430119515106e-920j 6.25e-255, 6.25e-255j
-0.93649524179130306529 + 8.0115439328327813371e-911j 7.96e-239, 7.96e-239j
-0.21435862552093206691 + 3.3166398717446995734e-924j 9.97e-251, 9.97e-251j
-0.99105250481616767714 - 6.5143585910997877968e-911j 5.71e-239, 5.71e-239j
0.84710180829252134773 - 4.1782010195536564256e-911j 2.5e-240, 2.5e-240j
0.97870344932433635 + 3.6007316450623644065e-926j 1.66e-238, 1.66e-238j
-0.96717105834762112122 - 4.7907058468276773894e-949j 3.13e-238, 3.13e-238j
-0.84710180829252134773 + 4.4830337886742800653e-957j 2.52e-240, 2.52e-240j
0.96717105834762112122 - 7.9770746674173023365e-954j 3.18e-238, 3.18e-238j
0.88348739118780414065 - 6.610710878680244033e-967j 9.65e-240, 9.65e-240j
0.80346492993495086006 - 1.5817971905390080625e-971j 5.97e-241, 5.97e-241j
-0.88348739118780414065 - 2.7907310303538006296e-971j 1.01e-239, 1.01e-239j
-0.80346492993495086006 - 5.4731531600188759126e-974j 6.06e-241, 6.06e-241j
-0.97870344932433635 + 1.6371369680949624138e-972j 1.75e-238, 1.75e-238j
0.28171656715435301931 + 2.0608694504363977056e-978j 1.59e-249, 1.59e-249j
0.74470078874836989945 + 1.2785544644571107915e-971j 2.14e-240, 2.14e-240j
0.95699433532754426818 - 5.1338466582928711254e-975j 2.62e-238, 2.62e-238j
-0.74470078874836989945 - 1.2085894222340385762e-987j 2.14e-240, 2.14e-240j
-0.74677180221832073614 + 6.0556717471413131572e-990j 2.38e-240, 2.38e-240j
0.99105250481616767714 + 1.7129316536654891396e-989j 5.98e-239, 5.98e-239j
0.74677180221832073614 - 3.0000016053477968704e-1001j 2.21e-240, 2.21e-240j
0.57735026918962576451 + 1.8169302526031773957e-1007j 3.81e-245, 3.81e-245j
-0.15655801081562154215 + 1.1003224541127134043e-1015j 4.74e-252, 4.74e-252j
-0.64195465766433247869 + 1.2176580221940649157e-1006j 7.74e-244, 7.74e-244j
-0.70322542709878689322 + 3.5103211699898774189e-1007j 2.3e-242, 2.3e-242j
0.70322542709878689322 - 1.3352157259380686615e-1007j 2.52e-242, 2.52e-242j
0.64195465766433247869 - 5.3652932997127771318e-1014j 7.12e-244, 7.12e-244j
0.15655801081562154215 + 2.0019307280726654168e-1023j 5.09e-252, 5.09e-252j
-0.57735026918962576451 - 3.1656792053617886236e-1016j 3.95e-245, 3.95e-245j
-0.43693939954921891801 - 2.2499761092793931381e-1018j 1.37e-247, 1.37e-247j
0.11512729103972178883 - 1.64853452472513845e-1023j 5.19e-253, 5.19e-253j
0.50889524570635335182 + 2.9823801939865525126e-1016j 2.17e-246, 2.17e-246j
0.2535630372636024051 - 4.5513233811643954577e-1020j 7.99e-250, 7.99e-250j
-0.2535630372636024051 + 1.3346865088984675325e-1020j 7.32e-250, 7.32e-250j
-0.50889524570635335182 - 6.3861620587764407075e-1017j 2.19e-246, 2.19e-246j
-0.039871185471799902249 + 4.1154883493819120679e-1025j 6.25e-255, 6.25e-255j
0.43693939954921891801 + 1.273267093935470735e-1017j 1.4e-247, 1.4e-247j
0.36184033632587490432 - 9.6209821033789798633e-1019j 9.68e-249, 9.68e-249j
-0.11512729103972178883 + 2.5085575803696945614e-1023j 5.28e-253, 5.28e-253j
-0.36184033632587490432 + 3.335931561024698672e-1019j 9.56e-249, 9.56e-249j
-0.28171656715435301931 + 4.3544106087022263704e-1021j 1.64e-249, 1.64e-249j
0.21435862552093206691 + 5.5956674349863684026e-1021j 1.02e-250, 1.02e-250j

Weights

Weight (ball center) Error (ball radius)
0.0043921734320268083696 + 4.2691286373220046422e-876j 4.95e-65, 1.43e-179j
0.0043921734320268083696 - 6.313924531914090948e-879j 2.38e-65, 6.87e-180j
0.025866802053879067549 - 2.6921026217282818001e-877j 1.17e-65, 3.36e-180j
0.016992418977147831732 - 4.0949553395171407272e-877j 5.42e-66, 1.56e-180j
0.02256470652443578032 - 9.3478009083642212242e-876j 5.29e-67, 1.52e-181j
0.025866802053879067549 + 5.9954542815763867862e-876j 4.33e-67, 1.25e-181j
0.079324441626995873773 - 3.5996508033346713465e-876j 6.57e-68, 1.89e-182j
0.02256470652443578032 + 2.9853530695178072376e-877j 4.85e-66, 1.4e-180j
0.081471858640576446609 - 1.1104738953786169173e-875j 3.04e-68, 8.77e-183j
0.010000565094787576133 + 3.1638369710452147446e-878j 1.48e-66, 4.26e-181j
0.04009344901075679706 + 2.7889349220262785413e-876j 1.82e-68, 5.24e-183j
0.014119114384877022405 + 1.3785812219245311253e-875j 1.35e-68, 3.88e-183j
0.0069285154634232206795 + 3.6470065065904035598e-877j 1.06e-66, 3.05e-181j
0.04009344901075679706 - 2.2848359276938405168e-877j 8.07e-69, 2.33e-183j
0.0069285154634232206795 - 2.3037854280126907787e-875j 1.33e-68, 3.83e-183j
0.032585295870418524837 - 3.8877080306560594376e-876j 6.16e-69, 1.78e-183j
0.047221459872190562569 - 2.8462382443482065727e-876j 4.13e-70, 1.19e-184j
0.032585295870418524837 + 2.3717019992969458477e-877j 6.34e-69, 1.83e-183j
0.047221459872190562569 + 3.0775905440509918975e-877j 1.17e-70, 3.36e-185j
0.014119114384877022405 - 1.3654626032425572961e-877j 5.49e-68, 1.58e-182j
0.092063333732778591917 + 1.1501762651479661366e-875j 7.73e-74, 2.23e-188j
-0.25508225066804025924 - 7.2317590041211529537e-875j 1.03e-72, 2.98e-187j
0.016992418977147831732 + 1.9391169153000620769e-875j 1.03e-70, 2.97e-185j
-0.25508225066804025924 + 1.0521377638395518466e-875j 1.51e-72, 4.36e-187j
0.29980837559033129112 - 1.026653561639694179e-875j 1.64e-72, 4.72e-187j
0.010000565094787576133 - 8.7020614514935424143e-876j 4.38e-72, 1.26e-186j
0.29980837559033129112 + 7.1231551542844181611e-875j 7.47e-73, 2.16e-187j
0.066572074674262787305 + 7.4237604506701860586e-877j 1.53e-76, 4.42e-191j
0.031848914819706196639 + 9.4551695387649127173e-876j 1.92e-77, 5.53e-192j
0.062641699179867766946 + 2.4095147713851843396e-877j 1.18e-76, 3.41e-191j
0.061555089061859553864 - 5.8594426792320040462e-877j 2.53e-75, 7.29e-190j
0.061555089061859553864 + 3.3789437809168263089e-876j 5.38e-76, 1.55e-190j
0.062641699179867766946 - 1.1091336981315303623e-876j 4.63e-77, 1.34e-191j
0.031848914819706196639 - 1.2972419652688368384e-875j 5.47e-80, 1.58e-194j
0.066572074674262787305 - 1.9832760687714939722e-877j 3e-79, 8.65e-194j
0.073569730384607933234 - 3.5091744397440570713e-877j 1.28e-80, 3.68e-195j
0.065486386448591229266 + 8.6810144650190439765e-876j 2.59e-80, 7.47e-195j
0.070274456331786446641 - 6.9877598541300072257e-877j 1.19e-80, 3.43e-195j
-0.0269603603729055096 - 2.1033993108115228266e-875j 1.3e-80, 3.75e-195j
-0.0269603603729055096 + 1.2513082988208295386e-875j 1.26e-81, 3.64e-196j
0.070274456331786446641 + 2.2689648802292309442e-877j 1.37e-81, 3.95e-196j
0.079324441626995873773 + 3.3231561516169345306e-876j 6.35e-82, 1.83e-196j
0.073569730384607933234 + 8.9721049812370926783e-877j 2.13e-82, 6.13e-197j
0.076661749865638459874 - 1.7425019046727266702e-876j 2.09e-82, 6.02e-197j
0.065486386448591229266 - 6.8857738289731130421e-876j 2.27e-82, 6.56e-197j
0.076661749865638459874 + 8.1537061266618469658e-877j 9.06e-84, 2.61e-198j
0.092063333732778591917 - 6.4388992074564509195e-876j 5.46e-83, 1.58e-197j
0.081471858640576446609 + 1.7177747934603121828e-875j 7.01e-83, 2e-197j

Download

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