Rule: Q[2, 4]

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.

$P_{1}$ :
$\frac{3}{2} \cdot t^{2} - \frac{1}{2}$
$P_{2}$ :
$\frac{3}{2} \cdot t^{6} - \frac{25}{14} \cdot t^{4} + \frac{45}{98} \cdot t^{2} - \frac{1}{98}$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Node (ball center)	Error (ball radius)
0.15655801081562154215 + 0j	7.53e-64, 7.53e-64j
-0.57735026918962576451 + 5.9784679246222015251e-196j	3.75e-63, 3.75e-63j
-0.91248695683407599658 + 1.7123510539128148748e-195j	4.8e-63, 4.8e-63j
-0.15655801081562154215 - 3.9256215858480658591e-225j	7.53e-64, 7.53e-64j
0.57735026918962576451 - 2.1612908839133067699e-224j	3.75e-63, 3.75e-63j
0.91248695683407599658 - 2.3995149022330095277e-240j	4.8e-63, 4.8e-63j

Weights

Weight (ball center)	Error (ball radius)
0.35617300446694280136 - 2.5390310967369762008e-195j	4.16e-28, 1.65e-59j
0.42352941176470588235 - 4.0747132904989561756e-195j	1.45e-28, 5.75e-60j
0.22029758376835131628 + 2.6200634077816070542e-195j	2.01e-29, 7.89e-61j
0.35617300446694280136 + 3.3313989872161308755e-195j	2.17e-28, 8.64e-60j
0.42352941176470588235 + 8.2789041861092480661e-196j	2.68e-29, 1.11e-60j
0.22029758376835131628 - 1.6560842637273035992e-196j	7.23e-30, 2.61e-61j

Download

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