Rule: Q[3, 4]

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.

$P_{1}$ :
$8 \cdot t^{3} - 4 \cdot t$
$P_{2}$ :
$8 \cdot t^{7} - 12 \cdot t^{5} + 5 \cdot t^{3} - \frac{1}{2} \cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Node (ball center)	Error (ball radius)
0.92387953251128675613 - 1.2634920662350609083e-175j	7.16e-63, 7.16e-63j
-0.7071067811865475244 - 9.4137494730581410849e-184j	1.24e-62, 1.24e-62j
-0.92387953251128675613 + 4.1096425293907556995e-194j	7.02e-63, 7.02e-63j
-0.38268343236508977173 - 1.7542263113931718862e-203j	2.01e-63, 2.01e-63j
0.38268343236508977173 - 2.5991486257941638212e-213j	2.01e-63, 2.01e-63j
0.7071067811865475244 + 2.1612908839133067699e-223j	9.8e-63, 9.8e-63j
3.0192884857486562382e-233 - 6.4411487695971333082e-232j	4.51e-231, 4.51e-231j

Weights

Weight (ball center)	Error (ball radius)
0.018305826175840779725 + 2.188714612590892908e-176j	1.87e-27, 2.29e-58j
0.0625 - 4.8417485488448564611e-177j	8.14e-28, 1e-58j
0.018305826175840779725 + 1.2517467838735264539e-177j	3.82e-28, 4.67e-59j
0.10669417382415922028 + 1.031769993557970213e-176j	3.21e-28, 4.01e-59j
0.10669417382415922028 + 2.490913046171253849e-176j	1.53e-28, 1.83e-59j
0.0625 - 3.6429050121514803049e-176j	8.81e-29, 1.01e-59j
0.125 - 1.7094924636715036644e-176j	1.07e-28, 1.38e-59j

Download

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