Rule: Q[2, 4]

Type

This rule is of Chebyshev T (first 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.

$P_{1}$ :
$2 \cdot t^{2} - 1$
$P_{2}$ :
$2 \cdot t^{6} - 3 \cdot t^{4} + \frac{9}{8} \cdot t^{2} - \frac{1}{16}$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Node (ball center)	Error (ball radius)
0.25881904510252076235 + 5.6604444567330728693e-173j	8.74e-64, 8.74e-64j
-0.7071067811865475244 - 4.9355158837307066731e-178j	6.74e-63, 6.74e-63j
-0.96592582628906828675 - 6.8948360398375056774e-187j	3.79e-63, 3.79e-63j
-0.25881904510252076235 - 4.6822099130428531733e-197j	8.74e-64, 8.74e-64j
0.7071067811865475244 - 1.1331388749451397798e-217j	5.56e-63, 5.56e-63j
0.96592582628906828675 + 9.0176082774359866315e-231j	3.79e-63, 3.79e-63j

Weights

Weight (ball center)	Error (ball radius)
0.16666666666666666667 - 1.3086290897472299281e-174j	4.25e-28, 2.28e-59j
0.16666666666666666667 - 7.1499048428828689292e-174j	1.69e-28, 9.04e-60j
0.16666666666666666667 + 2.0638666206678195564e-174j	4.26e-29, 2.27e-60j
0.16666666666666666667 + 1.8225482289063433024e-173j	1.79e-28, 9.59e-60j
0.16666666666666666667 - 1.5405720319233865822e-173j	2.46e-29, 1.38e-60j
0.16666666666666666667 + 3.5749053421327120985e-174j	1.03e-29, 5.13e-61j

Download

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