Rule: Q[2, 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.

$P_{1}$ :
$\frac{3}{2} \cdot t^{2} - \frac{1}{2}$
$P_{2}$ :
$\frac{3}{2} \cdot t^{8} - \frac{161}{52} \cdot t^{6} + \frac{105}{52} \cdot t^{4} - \frac{245}{572} \cdot t^{2} + \frac{25}{1716}$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Node (ball center)	Error (ball radius)
0.98219129046748981137 - 3.2802129431479925546e-140j	4.75e-62, 4.75e-62j
-0.98219129046748981137 + 3.0751996342012430199e-143j	4.88e-62, 4.88e-62j
-0.85110112875893547946 + 1.4014581666281706471e-145j	7.05e-62, 7.05e-62j
-0.2041968861768067152 + 4.3701215221876211386e-157j	1.46e-63, 1.46e-63j
0.57735026918962576451 + 1.061333335637451163e-173j	1.63e-62, 1.63e-62j
0.85110112875893547946 + 6.0329815348578174678e-187j	6.44e-62, 6.44e-62j
0.2041968861768067152 - 8.561755269564074374e-196j	1.46e-63, 1.46e-63j
-0.57735026918962576451 + 6.2708168478252497857e-199j	1.63e-62, 1.63e-62j

Weights

Weight (ball center)	Error (ball radius)
0.057803247064693176633 + 2.6397017025755927815e-140j	9.17e-25, 3.65e-55j
0.057803247064693176633 - 9.4038839065751156808e-142j	3.97e-25, 1.58e-55j
0.20679180755892348773 + 2.5713202801425305823e-141j	3.23e-25, 1.29e-55j
0.40241419511944602834 + 5.8503730533448332445e-141j	1.21e-25, 4.83e-56j
0.3329907502569373073 + 1.5493984052362221367e-140j	2.62e-26, 1.05e-56j
0.20679180755892348773 - 3.643500571224654255e-140j	2.08e-26, 8.3e-57j
0.40241419511944602834 - 8.9286385965045666961e-141j	1.79e-26, 7.21e-57j
0.3329907502569373073 - 4.0086617121968921939e-141j	1.11e-26, 4.01e-57j

Download

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