Rule: Q[13]

Type

This rule is of Chebyshev U (second kind) type.

Polynomials

One starts from the polynomial $P_{1}$ and extends one by one with $P_{i}$ 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.

$P_{1}$ :
$8192 \cdot t^{13} - 24576 \cdot t^{11} + 28160 \cdot t^{9} - 15360 \cdot t^{7} + 4032 \cdot t^{5} - 448 \cdot t^{3} + 14 \cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Node (ball center)	Error (ball radius)
0.97492791218182360702 - 1.2873467964455788583e-170j	6.97e-61, 6.97e-61j
-0.97492791218182360702 - 2.4480158783304305099e-174j	7.38e-61, 7.38e-61j
-0.90096886790241912624 + 2.1321428617716652828e-175j	1.36e-60, 1.36e-60j
-0.22252093395631440429 + 3.5535714362861088047e-176j	3.31e-63, 3.31e-63j
0.62348980185873353053 + 5.1775622101819775967e-182j	2.3e-61, 2.3e-61j
0.78183148246802980871 - 5.3304803367884361927e-190j	8.36e-61, 8.36e-61j
2.5107762769612816525e-200 + 1.69426366656736892e-200j	3.94e-199, 3.94e-199j
-0.78183148246802980871 - 1.0146604460217323751e-202j	9.38e-61, 9.38e-61j
-0.62348980185873353053 - 2.8499948063294607172e-205j	2.86e-61, 2.86e-61j
0.43388373911755812048 + 5.5696041981303510455e-214j	3.19e-62, 3.19e-62j
0.90096886790241912624 + 1.0235873626213420862e-219j	1.49e-60, 1.49e-60j
0.22252093395631440429 + 7.8324369038301141028e-228j	3.31e-63, 3.31e-63j
-0.43388373911755812048 - 1.4791761624517342573e-234j	3.76e-62, 3.76e-62j

Weights

Weight (ball center)	Error (ball radius)
0.003536826146342174063 + 1.344713257445316384e-171j	3.08e-20, 7.9e-50j
0.003536826146342174063 + 2.3105721029181429975e-173j	1.33e-20, 3.43e-50j
0.013446792790759516767 - 9.1814559521051696707e-173j	1.07e-20, 2.76e-50j
0.067891745282229254508 - 7.296438101461596899e-172j	2.37e-21, 6.07e-51j
0.043661461927011228725 - 1.5992805677798229296e-171j	1.44e-21, 3.71e-51j
0.027767109501560199847 + 1.8511510266068186254e-171j	9.64e-22, 2.47e-51j
0.071428571428571428571 + 9.4297327591440312959e-172j	1.03e-21, 2.65e-51j
0.027767109501560199847 + 2.030764010159490284e-172j	4.32e-22, 1.11e-51j
0.043661461927011228725 - 3.5131045778636764568e-172j	2.78e-22, 7.16e-52j
0.057981778637811911804 + 1.3794905974248982189e-171j	6.74e-23, 1.75e-52j
0.013446792790759516767 - 2.340557682277199348e-171j	2.23e-23, 5.77e-53j
0.067891745282229254508 - 1.1614512221269581898e-171j	5.08e-23, 1.32e-52j
0.057981778637811911804 + 5.2954802020099268353e-172j	3.56e-23, 8.58e-53j

Download

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