Rule: Q[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.

$P_{1}$ :
$16 \cdot t^{4} - 12 \cdot t^{2} + 1$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Node (ball center)	Error (ball radius)
0.8090169943749474241 + 4.0761538771797797299e-64j	2.76e-63, 2.76e-63j
-0.3090169943749474241 + 2.1125910064389710154e-76j	6.55e-64, 6.55e-64j
-0.8090169943749474241 + 1.3520862912410077395e-92j	7.6e-64, 7.6e-64j
0.3090169943749474241 - 2.8424948577935271301e-114j	6.55e-64, 6.55e-64j

Weights

Weight (ball center)	Error (ball radius)
0.06909830056250525759 - 9.8930332749760163204e-65j	2.38e-30, 1.09e-61j
0.18090169943749474241 - 6.5953555166495895028e-65j	1.09e-30, 5.15e-62j
0.06909830056250525759 + 1.7407255206206820426e-65j	4.63e-31, 2.32e-62j
0.18090169943749474241 + 1.4747663271004923781e-64j	8.31e-31, 3.42e-62j

Download

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