Rule: Q[8]

Type

This rule is of Legendre 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.

$P_{1}$ :
$\frac{6435}{128} \cdot t^{8} - \frac{3003}{32} \cdot t^{6} + \frac{3465}{64} \cdot t^{4} - \frac{315}{32} \cdot t^{2} + \frac{35}{128}$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Node (ball center)	Error (ball radius)
0.96028985649753623168 - 4.9529556965870631949e-134j	1.89e-62, 1.89e-62j
-0.79666647741362673959 - 9.1845962408143791528e-141j	2.26e-62, 2.26e-62j
-0.96028985649753623168 - 3.341336647577692621e-152j	1.89e-62, 1.89e-62j
0.18343464249564980494 + 1.5194639889058146859e-164j	1.35e-63, 1.35e-63j
0.79666647741362673959 + 8.6865079553660437447e-176j	2.58e-62, 2.58e-62j
0.52553240991632898582 + 2.3534373682645352712e-184j	9.98e-63, 9.98e-63j
-0.18343464249564980494 + 8.9776510935384188508e-189j	8.45e-64, 8.45e-64j
-0.52553240991632898582 - 2.1918093490084030398e-193j	8.39e-63, 8.39e-63j

Weights

Weight (ball center)	Error (ball radius)
0.10122853629037625915 + 6.1851180105998157557e-134j	1.68e-24, 2.23e-55j
0.22238103445337447054 + 9.1628582046023694776e-135j	7.03e-25, 9.3e-56j
0.10122853629037625915 - 2.6105722076478128237e-135j	4.73e-25, 6.26e-56j
0.36268378337836198297 - 4.3042412190382389396e-134j	2.62e-25, 3.46e-56j
0.22238103445337447054 - 9.8389053357252791563e-134j	9.18e-26, 1.21e-56j
0.31370664587788728734 + 6.1906158430203434462e-134j	1.04e-25, 1.38e-56j
0.36268378337836198297 + 2.9235814930160041358e-134j	2.98e-26, 3.98e-57j
0.31370664587788728734 - 1.8113973915681009073e-134j	1.93e-26, 2.49e-57j

Download

All rules of Legendre type can be downloaded here packed into a single file.