Rule: Q[1, 4]

Type

This rule is of Hermite (physicists') 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.

$P_{1}$ :
$2 \cdot t$
$P_{2}$ :
$2 \cdot t^{5} - 10 \cdot t^{3} + \frac{15}{2} \cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Node (ball center)	Error (ball radius)
2.0201828704560856329 - 3.4395525670743494409e-136j	4.08e-63, 4.08e-63j
-0.95857246461381850711 - 7.6373409087490117051e-152j	2.02e-63, 2.02e-63j
-2.0201828704560856329 - 5.299469827377980908e-169j	4.08e-63, 4.08e-63j
-3.0123998313786051472e-182 - 1.5061999156893025736e-182j	1.68e-181, 1.68e-181j
0.95857246461381850711 + 6.4955023677599683308e-200j	1.1e-63, 1.1e-63j

Weights

Weight (ball center)	Error (ball radius)
0.011257411327720688933 + 7.8222406050184546634e-138j	1.69e-29, 1.3e-61j
0.2220759220056126444 - 5.7734727766650247506e-138j	1.26e-28, 9.72e-61j
0.011257411327720688933 + 9.5834042049202468584e-139j	9.02e-30, 6.97e-62j
0.53333333333333333333 + 1.3192584916113010174e-137j	6.95e-29, 5.48e-61j
0.2220759220056126444 - 1.6199693164958464773e-137j	2.99e-29, 2.15e-61j

Download

All rules of Hermite (physicists') type can be downloaded here packed into a single file.