Rule: Q[1, 7]

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.

$P_{1}$ :
$- t + 1$
$P_{2}$ :
$- t^{8} + \frac{19265}{204} \cdot t^{7} - \frac{624113}{204} \cdot t^{6} + \frac{1552467}{34} \cdot t^{5} - \frac{11604425}{34} \cdot t^{4} + \frac{21609490}{17} \cdot t^{3} - \frac{36977850}{17} \cdot t^{2} + \frac{23737980}{17} \cdot t - \frac{3293220}{17}$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Node (ball center)	Error (ball radius)
18.75251539166561618 + 1.5905613560981500367e-51j	1.29e-50, 1.29e-50j
46.925435925679186168 - 1.9234284409937586193e-58j	1.55e-57, 1.55e-57j
12.35199612685986194 - 3.2359896078147878237e-61j	1.55e-59, 1.55e-59j
7.9509208918881512072 + 1.7068768103323251639e-67j	8.35e-60, 8.35e-60j
1 + 1.0952425019310141659e-73j	7.1e-62, 7.1e-62j
2.5000206754193299535 - 9.3149978868365853744e-83j	6.15e-61, 6.15e-61j
4.7673099177671066141 - 2.0510679483514782909e-93j	2.75e-60, 2.75e-60j
0.18807558052466950658 + 5.9407391807983284519e-101j	2.21e-63, 2.21e-63j

Weights

Weight (ball center)	Error (ball radius)
5.7687476475340704087e-08 - 4.1891032588518249168e-59j	1.19e-28, 1.02e-49j
1.1414772815362815237e-15 - 3.1137248876834343648e-63j	1.01e-31, 8.7e-53j
2.2429609219043039391e-05 + 2.0814165601207445905e-58j	8.87e-28, 7.62e-49j
0.0013112218161578048114 - 7.1438248750026441519e-58j	3.29e-27, 2.83e-48j
0.4218508636893898486 + 2.554851673768660415e-57j	6.42e-26, 5.15e-47j
0.15317411483171853001 - 2.7017972036970573423e-57j	2.45e-26, 2.11e-47j
0.022892592003574634765 + 1.7190550963372385688e-57j	7.33e-27, 6.3e-48j
0.40074872036246252196 - 1.0239745886072457527e-57j	3.51e-26, 2.64e-47j

Download

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