Rule: Q[2, 3]

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.

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

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Node (ball center)	Error (ball radius)
0.5 - 5.6023190959597236491e-82j	1.61e-63, 1.61e-63j
-0.5 - 3.3353547389900518457e-88j	1.61e-63, 1.61e-63j
-0.86602540378443864676 + 5.7147150155771642862e-103j	1.51e-63, 1.51e-63j
1.5490367659397273091e-120 + 7.7451838296986365456e-121j	8.66e-120, 8.66e-120j
0.86602540378443864676 + 6.8791051341486988818e-136j	1.51e-63, 1.51e-63j

Weights

Weight (ball center)	Error (ball radius)
0.125 + 7.0028947007562308238e-83j	7.27e-30, 3.16e-61j
0.125 + 7.0028947007562308238e-83j	3.26e-30, 1.44e-61j
0.041666666666666666667 - 1.7088297211726943533e-83j	1.49e-30, 6.63e-62j
0.16666666666666666667 - 1.8674385868683282197e-82j	2.09e-30, 9.13e-62j
0.041666666666666666667 + 6.3774261883435149025e-83j	4.22e-31, 1.52e-62j

Download

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