Rule: Q[3]

Type

This rule is of Laguerre 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.

$P_{1}$ :
$\frac{- 1}{6} \cdot t^{3} + \frac{3}{2} \cdot t^{2} - 3 \cdot t + 1$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Node (ball center)	Error (ball radius)
6.2899450829374791969 - 1.8212580929833350566e-44j	7.12e-44, 7.12e-44j
2.2942803602790417198 - 1.3350217179225242266e-59j	2.02e-58, 2.02e-58j
0.41577455678347908331 - 1.1409127286316273104e-78j	7.58e-78, 7.58e-78j

Weights

Weight (ball center)	Error (ball radius)
0.010389256501586135749 + 7.9566504201739597789e-47j	6.13e-32, 3.1e-45j
0.2785177335692408488 - 1.4808154358501332164e-46j	4.11e-31, 2.07e-44j
0.71109300992917301545 + 6.8515039383273723852e-47j	8.65e-31, 2.76e-44j

Download

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