Rule: Q[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.

$P_{1}$ :
$\frac{231}{16} \cdot t^{6} - \frac{315}{16} \cdot t^{4} + \frac{105}{16} \cdot t^{2} - \frac{5}{16}$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Node (ball center)	Error (ball radius)
0.23861918608319690863 - 2.2227587494850774834e-162j	1.18e-63, 1.18e-63j
-0.66120938646626451366 - 2.7133285516175262249e-166j	4.65e-63, 4.65e-63j
-0.93246951420315202781 + 1.51619047948207309e-174j	3.98e-63, 3.98e-63j
-0.23861918608319690863 + 0j	7.56e-64, 7.56e-64j
0.66120938646626451366 + 0j	5.25e-63, 5.25e-63j
0.93246951420315202781 + 2.9008355198595578362e-216j	3.98e-63, 3.98e-63j

Weights

Weight (ball center)	Error (ball radius)
0.46791393457269104739 + 2.6300208712692714967e-163j	4.6e-28, 2.09e-59j
0.36076157304813860757 + 7.839168043825688295e-163j	1.8e-28, 8.18e-60j
0.17132449237917034504 - 2.000284267512244458e-163j	3.98e-29, 1.8e-60j
0.46791393457269104739 - 2.1789882882695476907e-162j	2.01e-28, 9.14e-60j
0.36076157304813860757 + 1.6695264138057666507e-162j	2.88e-29, 1.35e-60j
0.17132449237917034504 - 3.3742859029449049337e-163j	1.04e-29, 4.41e-61j

Download

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