Rule: Q[1, 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.

$P_{1}$ :
$- t + 1$
$P_{2}$ :
$- t^{4} + \frac{49}{4} \cdot t^{3} - \frac{153}{4} \cdot t^{2} + \frac{57}{2} \cdot t - \frac{3}{2}$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Node (ball center)	Error (ball radius)
7.8232631436879996743 + 5.1542346341469476734e-52j	2.26e-51, 2.26e-51j
1 - 2.4036439412511271442e-63j	2.45e-62, 2.45e-62j
3.369839231310923141 - 2.2193744376829232312e-80j	3.76e-79, 3.76e-79j
0.056897625001077184683 - 1.5173879336958873637e-96j	6.27e-96, 6.27e-96j

Weights

Weight (ball center)	Error (ball radius)
0.0024291259712280832595 - 6.258441494115490332e-55j	4.01e-32, 5.49e-53j
0.5901639344262295082 - 2.8395939459486371056e-54j	2.07e-30, 2.04e-51j
0.11097445421890710086 + 1.8975685188059878246e-54j	4.29e-31, 6.07e-52j
0.29643248538363530768 + 1.5678695765541983142e-54j	1.55e-30, 1.46e-51j

Download

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