Rule: Q[7]

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.

$P_{1}$ :
$128 \cdot t^{7} - 1344 \cdot t^{5} + 3360 \cdot t^{3} - 1680 \cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Node (ball center)	Error (ball radius)
-2.6519613568352334924 - 1.3120851772591970218e-141j	1.08e-62, 1.08e-62j
-1.673551628767471445 + 0j	1.02e-62, 1.02e-62j
0.81628788285896466304 - 2.276104959472719343e-159j	4.84e-63, 4.84e-63j
6.4690793791235118506e-173 - 6.4690793791235118506e-173j	6.4e-172, 6.4e-172j
2.6519613568352334924 - 5.8835934206613381781e-185j	1.08e-62, 1.08e-62j
1.673551628767471445 + 0j	1.52e-62, 1.52e-62j
-0.81628788285896466304 + 0j	4.84e-63, 4.84e-63j

Weights

Weight (ball center)	Error (ball radius)
0.00054826885597221779162 - 1.9077558654806389246e-144j	5.8e-29, 1.61e-60j
0.03075712396758649704 + 5.5069472575335120217e-144j	7.47e-28, 2.08e-59j
0.24012317860501271374 - 4.3407578541940789901e-144j	1.9e-27, 5.2e-59j
0.45714285714285714286 + 7.8328100604353257246e-144j	1.27e-27, 3.56e-59j
0.00054826885597221779162 - 1.3563082984219733006e-145j	5.02e-30, 1.4e-61j
0.03075712396758649704 + 1.2456443401420320875e-144j	6.27e-29, 1.77e-60j
0.24012317860501271374 - 8.2012571085939545891e-144j	2.4e-28, 5.13e-60j

Download

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