Rule: Q[7]

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.

$P_{1}$ :
$64 \cdot t^{7} - 112 \cdot t^{5} + 56 \cdot t^{3} - 7 \cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Node (ball center)	Error (ball radius)
0.97492791218182360702 + 3.6772458879133363613e-185j	6.91e-63, 6.91e-63j
-0.78183148246802980871 + 5.7512620986259116333e-204j	1.26e-62, 1.26e-62j
-0.97492791218182360702 + 5.9803169706585405213e-204j	6.65e-63, 6.65e-63j
-0.43388373911755812048 - 8.9113667170085616727e-213j	2.27e-63, 2.27e-63j
0.43388373911755812048 - 4.2492707810442741741e-219j	2.27e-63, 2.27e-63j
0.78183148246802980871 + 4.9468022550505983807e-229j	1.14e-62, 1.14e-62j
0 + 0j	0, 0j

Weights

Weight (ball center)	Error (ball radius)
0.14285714285714285714 - 5.171605534755325598e-185j	2.42e-27, 3.23e-58j
0.14285714285714285714 + 8.3785878285375226656e-186j	1.06e-27, 1.41e-58j
0.14285714285714285714 - 2.6941522268802604862e-186j	5.54e-28, 7.31e-59j
0.14285714285714285714 - 1.5097693580996879959e-185j	3.79e-28, 5.21e-59j
0.14285714285714285714 - 3.9312513993436636513e-185j	1.89e-28, 2.39e-59j
0.14285714285714285714 + 7.6227006907889753721e-185j	1.29e-28, 1.52e-59j
0.14285714285714285714 + 2.4214820412439756551e-185j	1.16e-28, 1.71e-59j

Download

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