Rule: Q[2, 3]

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.

$P_{1}$ :
$\frac{3}{2} \cdot t^{2} - \frac{1}{2}$
$P_{2}$ :
$\frac{3}{2} \cdot t^{5} - \frac{25}{14} \cdot t^{3} + \frac{3}{7} \cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Node (ball center)	Error (ball radius)
-0.57735026918962576451 + 4.2491977233165047252e-46j	3.29e-45, 3.29e-45j
-0.92582009977255146157 - 7.8102562207981019423e-48j	5.83e-47, 5.83e-47j
8.5640419806916836211e-55 - 2.244993814816318712e-54j	1.2e-53, 1.2e-53j
0.57735026918962576451 + 3.8802583362145473181e-74j	2.16e-63, 2.16e-63j
0.92582009977255146157 - 1.1725888531383528573e-87j	3.38e-63, 3.38e-63j

Weights

Weight (ball center)	Error (ball radius)
0.49090909090909090909 + 9.3524020395050691423e-47j	4.37e-29, 1.75e-42j
0.1979797979797979798 + 2.248209235192606628e-46j	7.57e-30, 3.04e-43j
0.62222222222222222222 - 4.468386730023124834e-46j	2.63e-29, 1.05e-42j
0.49090909090909090909 + 1.8329544793646682766e-46j	7.05e-30, 2.89e-43j
0.1979797979797979798 - 5.4801718848465698489e-47j	2.74e-30, 1.03e-43j

Download

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