Rule: Q[8]

Type

This rule is of Hermite (physicists') 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.

$P_{1}$ :
$256 \cdot t^{8} - 3584 \cdot t^{6} + 13440 \cdot t^{4} - 13440 \cdot t^{2} + 1680$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Node (ball center)	Error (ball radius)
-1.9816567566958429259 + 0j	3.18e-62, 3.18e-62j
-2.9306374202572440192 - 1.0250665447337476733e-143j	1.63e-62, 1.63e-62j
-1.1571937124467801947 + 1.4916681462400413487e-154j	9.57e-63, 9.57e-63j
1.9816567566958429259 - 4.3413256825880419598e-165j	2.66e-62, 2.66e-62j
0.38118699020732211685 + 0j	1.76e-63, 1.76e-63j
1.1571937124467801947 + 5.7456966998645880645e-188j	1.34e-62, 1.34e-62j
2.9306374202572440192 + 1.2274132354447057023e-191j	1.63e-62, 1.63e-62j
-0.38118699020732211685 + 1.3698808431302518998e-194j	1.76e-63, 1.76e-63j

Weights

Weight (ball center)	Error (ball radius)
0.0096352201207882671869 + 1.1251819258858012162e-146j	2.45e-28, 4.63e-59j
0.00011261453837536777039 - 3.38305151680977352e-147j	1.32e-29, 2.49e-60j
0.11723990766175901512 - 2.100243337777473621e-146j	4.87e-28, 8.93e-59j
0.0096352201207882671869 - 2.1736806690087630747e-147j	1.47e-29, 2.76e-60j
0.37301225767907734993 - 2.0060582455351269349e-146j	3.09e-28, 4.85e-59j
0.11723990766175901512 + 9.1115880569376347633e-147j	1.12e-28, 1.83e-59j
0.00011261453837536777039 + 1.9694929653115567296e-148j	8.22e-31, 1.67e-61j
0.37301225767907734993 + 2.6059391406617739555e-146j	2.35e-28, 3.39e-59j

Download

All rules of Hermite (physicists') type can be downloaded here packed into a single file.