Rule: Q[1, 6]

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.

$P_{1}$ :
$t$
$P_{2}$ :
$t^{7} - \frac{21}{13} \cdot t^{5} + \frac{105}{143} \cdot t^{3} - \frac{35}{429} \cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Node (ball center)	Error (ball radius)
0.94910791234275852453 - 1.015251749321228105e-190j	1.29e-62, 1.29e-62j
-0.74153118559939443986 - 2.0199714960461442414e-189j	1.78e-62, 1.78e-62j
-0.94910791234275852453 + 1.4631905978258916167e-198j	1.51e-62, 1.51e-62j
-0.40584515137739716691 - 7.6043662651806392941e-211j	3.42e-63, 3.42e-63j
0.40584515137739716691 + 2.2131618651272261323e-220j	3.42e-63, 3.42e-63j
0.74153118559939443986 - 2.8180025866987458223e-232j	1.92e-62, 1.92e-62j
5.8581906792798084173e-244 - 4.6865525434238467338e-243j	3.31e-242, 3.31e-242j

Weights

Weight (ball center)	Error (ball radius)
0.12948496616886969327 + 2.3252331780058042477e-190j	6.18e-27, 1.47e-57j
0.2797053914892766679 - 9.5510152234100061989e-190j	2.69e-27, 6.41e-58j
0.12948496616886969327 - 8.624353422053862782e-190j	1.32e-27, 3.12e-58j
0.38183005050511894495 + 2.7271841055772997469e-189j	1.03e-27, 2.48e-58j
0.38183005050511894495 + 9.0432545079726647276e-190j	4.94e-28, 1.14e-58j
0.2797053914892766679 - 5.7924771342221715511e-190j	3.03e-28, 6.65e-59j
0.41795918367346938776 - 1.4672482962065425913e-189j	3.35e-28, 8.37e-59j

Download

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