Rule: Q[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.

$P_{1}$ :
$\frac{5}{2} \cdot t^{3} - \frac{3}{2} \cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Node (ball center)	Error (ball radius)
0.77459666924148337704 - 2.1683782415508138716e-151j	6.35e-128, 6.35e-128j
3.1931748581308990911e-200 + 3.2668034258561339517e-200j	1.37e-199, 1.37e-199j
-0.77459666924148337704 + 1.4996968138956309548e-241j	6.35e-128, 6.35e-128j

Weights

Weight (ball center)	Error (ball radius)
0.55555555555555555556 + 2.332803560501340444e-151j	2.55e-30, 2.62e-126j
0.88888888888888888889 - 3.1104047473351205919e-151j	1.75e-30, 1.86e-126j
0.55555555555555555556 + 7.7760118683378014798e-152j	7.69e-31, 7.65e-127j

Download

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