Rule: Q[46]

Type

This rule is of Chebyshev U (second kind) 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)
0.97996170503658681679 + 1.8714595978570017775e-864j 5.08e-240, 5.08e-240j
-0.97996170503658681679 + 1.3815301905752220913e-869j 5.78e-240, 5.78e-240j
-0.89251883585988122582 + 3.3304356843574574621e-885j 1.59e-240, 1.59e-240j
0.99107748815478009891 - 2.7527531375927454733e-891j 3.33e-240, 3.33e-240j
0.92064988667642876747 - 1.0366680600388960389e-890j 3.27e-240, 3.27e-240j
0.94466909160791880067 + 2.4522709965837772904e-890j 4.57e-240, 4.57e-240j
-0.99107748815478009891 + 4.749964419183588005e-889j 3.54e-240, 3.54e-240j
-0.92064988667642876747 + 3.1193172521445366474e-899j 3.75e-240, 3.75e-240j
-0.94466909160791880067 + 1.3923022408397314748e-913j 4.87e-240, 4.87e-240j
0.99776687862315315956 + 3.7088165896919493395e-925j 1.18e-240, 1.18e-240j
0.89251883585988122582 + 1.0046463821631460202e-925j 1.61e-240, 1.61e-240j
-0.99776687862315315956 + 7.5932587612100523781e-924j 1.19e-240, 1.19e-240j
-0.86040157926013936987 + 1.095165643827816067e-939j 7.41e-241, 7.41e-241j
-0.78479938527866096605 - 1.5805070439912789192e-945j 6.26e-242, 6.26e-242j
0.96446917505437657452 - 5.6521990829300022284e-953j 7.17e-240, 7.17e-240j
0.78479938527866096605 + 1.5635954702222821852e-961j 7.04e-242, 7.04e-242j
0.64562785155880239765 + 8.6985104939095331541e-965j 5.33e-244, 5.33e-244j
-0.96446917505437657452 + 1.424679820514350414e-961j 6.26e-240, 6.26e-240j
-0.82444156034176031724 - 6.6416707849719308191e-979j 2.4e-241, 2.4e-241j
-0.48058175518668378052 - 5.9255852796061012892e-987j 9.81e-247, 9.81e-247j
0.86040157926013936987 - 1.4586948907657980728e-981j 6.94e-241, 6.94e-241j
0.74165210564795754011 + 6.2728427866466615907e-985j 1.67e-242, 1.67e-242j
0.82444156034176031724 - 2.7964114023636560481e-986j 2.91e-241, 2.91e-241j
-0.74165210564795754011 - 2.3502884212264120809e-986j 1.71e-242, 1.71e-242j
-0.69519242767464226355 + 8.453646735182724819e-991j 3.15e-243, 3.15e-243j
0.033414977007674570875 + 2.4464948841747448647e-1006j 2.71e-255, 2.71e-255j
0.69519242767464226355 - 1.724961586066456163e-994j 3.3e-243, 3.3e-243j
0.3594077728375128366 + 5.4351681197174128185e-1000j 5.03e-249, 5.03e-249j
-0.16632935458313003286 - 5.2312328980228028769e-1001j 1.08e-252, 1.08e-252j
-0.64562785155880239765 + 1.6505582848163322256e-994j 4.88e-244, 4.88e-244j
-0.29627558088563397732 - 7.8010819249016116428e-1001j 4.06e-250, 4.06e-250j
0.48058175518668378052 + 4.4016715825594312409e-998j 1e-246, 1e-246j
0.53808235316337267444 + 4.508887383689501586e-996j 1.16e-245, 1.16e-245j
0.10009569162409834512 - 2.7760816280984872804e-1007j 5.56e-254, 5.56e-254j
-0.3594077728375128366 + 6.5414885595592250121e-1001j 6.5e-249, 6.5e-249j
-0.42093476242833496963 + 2.738541224487812467e-999j 8.9e-248, 8.9e-248j
0.16632935458313003286 - 4.1207653467081424151e-1005j 1.46e-252, 1.46e-252j
0.5931797447293552111 - 7.5044316572805657321e-998j 8.03e-245, 8.03e-245j
0.23182015026752826926 + 2.2010524894128253745e-1004j 1.91e-251, 1.91e-251j
-0.23182015026752826926 + 1.1820311635114077828e-1003j 1.98e-251, 1.98e-251j
-0.53808235316337267444 + 5.0322683806719890785e-998j 1.08e-245, 1.08e-245j
-0.10009569162409834512 + 1.5632423318382433713e-1008j 4.89e-254, 4.89e-254j
0.29627558088563397732 - 8.4061722967573437311e-1004j 3.68e-250, 3.68e-250j
0.42093476242833496963 + 1.6979950486093025471e-1002j 8.85e-248, 8.85e-248j
-0.033414977007674570875 + 1.8918107819639743837e-1009j 2.71e-255, 2.71e-255j
-0.5931797447293552111 - 9.1897462761648100618e-1002j 7.68e-245, 7.68e-245j

Weights

Weight (ball center) Error (ball radius)
0.000844150141740119495 - 5.853060398510661297e-866j 9.74e-67, 3.4e-183j
0.000844150141740119495 + 8.0648035422308387032e-868j 2.37e-67, 8.27e-184j
0.0043278750560706892436 + 4.3261991155724597735e-867j 2.24e-67, 7.81e-184j
0.00037798749942152580299 - 6.3638188752961219611e-866j 3.07e-67, 1.07e-183j
0.0032426337481421035793 + 1.0231450689039511567e-865j 7.19e-68, 2.51e-184j
0.0022893682417163727016 - 1.2139822848845964857e-865j 1.14e-67, 3.98e-184j
0.00037798749942152580299 - 3.5842127057932213501e-868j 6.29e-69, 2.2e-185j
0.0032426337481421035793 - 3.1936528223939660847e-867j 5.72e-69, 2e-185j
0.0022893682417163727016 + 2.2270167244774352935e-867j 4.28e-69, 1.5e-185j
9.4920338778935118003e-05 + 9.9768511871066330837e-867j 2.24e-69, 7.83e-186j
0.0043278750560706892436 - 9.2625575766664591851e-866j 4.25e-70, 1.49e-186j
9.4920338778935118003e-05 + 8.9746348696389627849e-869j 8.03e-70, 2.8e-186j
0.0055257260086523002072 - 5.6197317893085801819e-867j 1.17e-70, 4.1e-187j
0.0081721260609837418163 - 8.6667961690620136034e-867j 3.46e-72, 1.21e-188j
0.0014850895823389428737 + 1.7939518717787644571e-865j 1.03e-69, 3.61e-186j
0.0081721260609837418163 + 7.836459546178005522e-866j 5.61e-73, 1.96e-189j
0.012407759091309893967 - 6.945349641678625475e-866j 3.87e-74, 1.35e-190j
0.0014850895823389428737 - 1.4306809341397254953e-867j 2.3e-70, 8.03e-187j
0.0068148109272605017383 + 7.0686724583403013327e-867j 5.33e-72, 1.86e-188j
0.016362578225142262494 - 2.0966555287297987995e-866j 7.54e-76, 2.63e-192j
0.0055257260086523002072 + 8.6493535083720083513e-866j 9.05e-73, 3.16e-189j
0.0095734500891053367541 - 7.5180955393996782324e-866j 1.35e-74, 4.73e-191j
0.0068148109272605017383 - 8.2006427251150667916e-866j 2.2e-73, 7.67e-190j
0.0095734500891053367541 + 1.0407258832307062389e-866j 2.45e-75, 8.57e-192j
0.010993776351145474158 - 1.2282631976674361118e-866j 2.84e-76, 9.93e-193j
0.0212528391342888634 - 4.2020222407371113452e-866j 3.89e-80, 1.36e-196j
0.010993776351145474158 + 7.224948659845780826e-866j 1.77e-76, 6.18e-193j
0.018528213889871888725 + 5.5877371027682692193e-866j 5.47e-80, 1.91e-196j
0.020687969059658710645 + 3.3775977399394438418e-866j 1.05e-80, 3.66e-197j
0.012407759091309893967 + 1.4284942471602791506e-866j 2.13e-78, 7.44e-195j
0.019408952769593194864 + 2.8461456097379929701e-866j 1.11e-80, 3.88e-197j
0.016362578225142262494 + 6.1320005669626855312e-866j 1.32e-80, 4.6e-197j
0.015116327259875903932 - 6.4021222996857607599e-866j 3.01e-80, 1.05e-196j
0.021063422394006242732 + 4.4801799890530526557e-866j 3.81e-82, 1.33e-198j
0.018528213889871888725 - 2.5889313416450194477e-866j 6.95e-82, 2.43e-198j
0.017506679271902153166 + 2.3387630564709792625e-866j 8.2e-82, 2.86e-198j
0.020687969059658710645 - 4.7585252850813647058e-866j 4.13e-83, 1.44e-199j
0.01379016575410248912 + 6.6724375866148106556e-866j 6.96e-82, 2.43e-198j
0.020133179104892353466 + 5.0362932997726924479e-866j 1.65e-83, 5.76e-200j
0.020133179104892353466 - 3.1093782784090852566e-866j 2.19e-83, 7.64e-200j
0.015116327259875903932 + 1.8636029056543767129e-866j 1.04e-83, 3.64e-200j
0.021063422394006242732 - 3.6497783665542154955e-866j 4.7e-84, 1.64e-200j
0.019408952769593194864 - 5.3128494649830988602e-866j 2.92e-84, 1.01e-200j
0.017506679271902153166 - 5.8607442623896490279e-866j 2.93e-84, 1.02e-200j
0.0212528391342888634 + 3.9249121110691011317e-866j 1.73e-84, 6.11e-201j
0.01379016575410248912 - 1.6405716685554925945e-866j 7.14e-85, 2.32e-201j

Download

All rules of Chebyshev U (second kind) type can be downloaded here packed into a single file.