Rule: Q[5]

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.

$P_{1}$ :
$\frac{- 1}{120} \cdot t^{5} + \frac{5}{24} \cdot t^{4} - \frac{5}{3} \cdot t^{3} + 5 \cdot t^{2} - 5 \cdot t + 1$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Node (ball center)	Error (ball radius)
12.640800844275782659 - 3.2811114673930008062e-102j	3.36e-61, 3.36e-61j
7.0858100058588375569 - 3.0980735318794546183e-120j	5.2e-61, 5.2e-61j
3.5964257710407220812 + 3.6066322725725530394e-130j	1.41e-61, 1.41e-61j
0.2635603197181409102 - 4.4026272858551672844e-134j	1.04e-63, 1.04e-63j
1.4134030591065167922 + 3.2033329522929614791e-145j	2.14e-62, 2.14e-62j

Weights

Weight (ball center)	Error (ball radius)
2.3369972385776227891e-05 + 3.5306726907351767644e-107j	5.63e-31, 1.37e-61j
0.0036117586799220484545 - 1.2847941691772308869e-106j	4.48e-30, 1.09e-60j
0.075942449681707595388 + 2.5778763187229796628e-106j	1.73e-29, 4.24e-60j
0.52175561058280865248 + 1.3366340980635435088e-106j	4.05e-29, 9.58e-60j
0.39866681108317592745 - 2.9827835166828099611e-106j	4.9e-29, 1.1e-59j

Download

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