Rule: Q[8]

Type

This rule is of Hermite (probabilists') 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.

$P_{1}$ :
$t^{8} - 28 \cdot t^{6} + 210 \cdot t^{4} - 420 \cdot t^{2} + 105$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Node (ball center)	Error (ball radius)
-4.1445471861258943321 + 4.4501477170144027662e-308j	4.36e-126, 4.36e-126j
0.53907981135137510807 + 1.0118464426828729225e-320j	4.12e-127, 4.12e-127j
4.1445471861258943321 - 4.044150784985703374e-335j	4.36e-126, 4.36e-126j
-2.8024858612875416991 - 3.1179925809354366044e-353j	5.75e-126, 5.75e-126j
-0.53907981135137510807 - 1.0817709856140433221e-370j	4.12e-127, 4.12e-127j
1.6365190424351079992 - 2.0149554789327891955e-379j	2.5e-126, 2.5e-126j
2.8024858612875416991 - 2.8634239568714139004e-393j	3.97e-126, 3.97e-126j
-1.6365190424351079992 + 0j	1.8e-126, 1.8e-126j

Weights

Weight (ball center)	Error (ball radius)
0.00011261453837536777039 + 1.0385226690552273047e-311j	1.25e-30, 2.35e-125j
0.37301225767907734993 + 6.1581591511216825579e-311j	1.05e-28, 1.91e-123j
0.00011261453837536777039 - 6.0459117529953964762e-313j	4.69e-31, 8.87e-126j
0.0096352201207882671869 - 3.4540619038962450041e-311j	7.81e-30, 1.47e-124j
0.37301225767907734993 - 7.9996620288301178807e-311j	4.98e-29, 8.99e-124j
0.11723990766175901512 - 2.7970578368588333559e-311j	2.75e-29, 5.25e-124j
0.0096352201207882671869 + 6.6727232523431961285e-312j	3.22e-30, 6.08e-125j
0.11723990766175901512 + 6.4472867417039207299e-311j	1.54e-29, 2.64e-124j

Download

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