Rule: Q[7]

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.

$P_{1}$ :
$\frac{429}{16} \cdot t^{7} - \frac{693}{16} \cdot t^{5} + \frac{315}{16} \cdot t^{3} - \frac{35}{16} \cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Node (ball center)	Error (ball radius)
0.94910791234275852453 - 9.1931147197833409032e-187j	1.22e-62, 1.22e-62j
-0.74153118559939443986 - 6.7332383201538141381e-190j	8.87e-63, 8.87e-63j
-0.94910791234275852453 - 8.3610891304336663809e-199j	1.15e-62, 1.15e-62j
-0.40584515137739716691 - 3.6500958072867068611e-209j	2.48e-63, 2.48e-63j
0.40584515137739716691 - 6.639485595381678397e-221j	2.48e-63, 2.48e-63j
0.74153118559939443986 + 0j	8.87e-63, 8.87e-63j
-4.6865525434238467338e-243 + 2.8119315260543080403e-242j	2e-241, 2e-241j

Weights

Weight (ball center)	Error (ball radius)
0.12948496616886969327 + 1.139003443020110068e-186j	6.18e-27, 1.22e-57j
0.2797053914892766679 - 2.2075435825792859283e-187j	2.69e-27, 5.33e-58j
0.12948496616886969327 + 6.2420160642985473279e-188j	1.32e-27, 2.59e-58j
0.38183005050511894495 + 4.3867569629938314119e-187j	1.03e-27, 2.06e-58j
0.38183005050511894495 + 1.0921363434799892846e-186j	4.94e-28, 9.43e-59j
0.2797053914892766679 - 1.7955663451285942093e-186j	3.02e-28, 5.52e-59j
0.41795918367346938776 - 7.1591494005594516494e-187j	3.35e-28, 6.96e-59j

Download

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