Rule: Q[7]

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.

$P_{1}$ :
$t^{7} - 21 \cdot t^{5} + 105 \cdot t^{3} - 105 \cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Node (ball center)	Error (ball radius)
-3.7504397177257422563 - 4.3836186980168060795e-193j	9.25e-63, 9.25e-63j
3.7504397177257422563 - 1.306420176630260372e-200j	9.25e-63, 9.25e-63j
-1.1544053947399681272 + 7.7868710555449746371e-208j	3.63e-63, 3.63e-63j
2.3667594107345412886 - 1.4504177599297789181e-216j	1.7e-62, 1.7e-62j
-3.3770170061145418279e-226 + 8.4425425152863545698e-227j	2.44e-225, 2.44e-225j
1.1544053947399681272 + 3.0713790748582521955e-238j	3.63e-63, 3.63e-63j
-2.3667594107345412886 + 1.8010659137179383904e-256j	1.7e-62, 1.7e-62j

Weights

Weight (ball center)	Error (ball radius)
0.00054826885597221779162 - 4.5069064156832613669e-196j	1.81e-30, 5.77e-62j
0.00054826885597221779162 - 3.2041584213852762554e-197j	8.95e-31, 2.9e-62j
0.24012317860501271374 - 1.9374752526501058367e-195j	1.79e-28, 5.71e-60j
0.03075712396758649704 + 2.9427254514314096949e-196j	6.84e-30, 2.23e-61j
0.45714285714285714286 + 1.850432834498382747e-195j	9.83e-29, 3.32e-60j
0.24012317860501271374 - 1.025466031365207918e-195j	4.28e-29, 1.41e-60j
0.03075712396758649704 + 1.3009681301559689375e-195j	4.65e-30, 1.32e-61j

Download

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