Rule: Q[4]

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.

$P_{1}$ :
$\frac{1}{24} \cdot t^{4} - \frac{2}{3} \cdot t^{3} + 3 \cdot t^{2} - 4 \cdot t + 1$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Node (ball center)	Error (ball radius)
9.3950709123011331292 + 0j	1.49e-125, 1.49e-125j
4.5366202969211279833 - 2.6015592699123717045e-259j	1.17e-125, 1.17e-125j
1.7457611011583465757 + 5.884263958341352191e-285j	2.11e-126, 2.11e-126j
0.3225476896193923118 + 1.2648080533535911531e-321j	1.68e-127, 1.68e-127j

Weights

Weight (ball center)	Error (ball radius)
0.0005392947055613274501 + 3.5289062346159404627e-262j	1.3e-31, 2.11e-126j
0.038887908515005384272 + 3.9434316603680187084e-261j	9.44e-31, 1.52e-125j
0.35741869243779968664 - 6.8173864495711308278e-261j	3.59e-30, 5.46e-125j
0.60315410434163360164 + 2.5210641657415180732e-261j	5.5e-30, 6.41e-125j

Download

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