Rule: Q[1, 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.

$P_{1}$ :
$- t + 1$
$P_{2}$ :
$- t^{5} + \frac{319}{15} \cdot t^{4} - \frac{2104}{15} \cdot t^{3} + \frac{1656}{5} \cdot t^{2} - \frac{1208}{5} \cdot t + \frac{152}{5}$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Node (ball center)	Error (ball radius)
11.242378555161742866 + 5.4453680196577596895e-79j	1.96e-61, 1.96e-61j
6.0165843328122930598 - 2.0233064317867021126e-96j	3.04e-61, 3.04e-61j
2.8500082985710811872 + 1.3325451130151976654e-107j	1.19e-61, 1.19e-61j
0.15769548012154955374 + 1.9827670604028509557e-118j	9.45e-64, 9.45e-64j
1 - 2.2159148682685765874e-126j	1.97e-62, 1.97e-62j

Weights

Weight (ball center)	Error (ball radius)
9.0051191494212348933e-05 - 2.4437795696228550953e-83j	2.26e-31, 5.36e-62j
0.0097398365257067927443 + 9.6063816797102434362e-83j	2.19e-30, 5.17e-61j
0.14124368477493936961 - 2.1979578318408315366e-82j	1.07e-29, 2.53e-60j
0.369326094452072781 - 1.4956200324103430513e-82j	3.26e-29, 7.14e-60j
0.4796003330557868443 + 2.9773176532424357538e-82j	3.64e-29, 7.68e-60j

Download

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